From 2c4ca97c72dd238a1e3d5edba3b1e05f625cf885 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Tue, 7 Jun 2022 20:27:17 -0500 Subject: [PATCH 01/20] HexN class compling with MATAR/Kokkos types --- CMakeLists.txt | 6 ++ build_scripts/build_matar_kokkos_openmp.sh | 46 +++++++++++ elements/CMakeLists.txt | 55 +++++++++++--- elements/elements.cpp | 88 +++++++++++----------- elements/elements.h | 43 ++++++----- 5 files changed, 162 insertions(+), 76 deletions(-) create mode 100755 build_scripts/build_matar_kokkos_openmp.sh diff --git a/CMakeLists.txt b/CMakeLists.txt index c0104d50..6cd2999e 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -52,6 +52,12 @@ if (ENABLE_VTK) find_package(VTK REQUIRED NO_MODULE) endif() +# Optional Kokkos dependency for MATAR +option(MATAR_WITH_KOKKOS "MATAR is to be compiled against Kokkos" OFF) +if (MATAR_WITH_KOKKOS) + find_package(Kokkos REQUIRED) +endif() + ################################################################################ # Build organization ################################################################################ diff --git a/build_scripts/build_matar_kokkos_openmp.sh b/build_scripts/build_matar_kokkos_openmp.sh new file mode 100755 index 00000000..1e672209 --- /dev/null +++ b/build_scripts/build_matar_kokkos_openmp.sh @@ -0,0 +1,46 @@ +#!/bin/sh + +# Build configuration (modify this!) +ELEMENTS_DIR=/path/to/elements +MATAR_DIR=/path/to/matar/within/elements +PROJECT_BUILD_DIR=/path/to/project/build/directory +OMP_NUM_THREADS=sensible_number_of_openmp_threads_for_your_machine + + +# Build and install Kokkos with OpenMP +KOKKOS_SOURCE_DIR=${MATAR_DIR}/src/Kokkos/kokkos +KOKKOS_BUILD_DIR=${PROJECT_BUILD_DIR}/kokkos +KOKKOS_INSTALL_DIR=${KOKKOS_BUILD_DIR} + +OPTIONS=( + -DCMAKE_BUILD_TYPE=Release + -DCMAKE_INSTALL_PREFIX=${KOKKOS_INSTALL_DIR} + -DCMAKE_CXX_STANDARD=17 + -DKokkos_ENABLE_SERIAL=ON + -DKokkos_ENABLE_OPENMP=ON + -DKokkos_ENABLE_TESTS=OFF + -DBUILD_TESTING=OFF +) + +cmake "${OPTIONS[@]}" -S ${KOKKOS_SOURCE_DIR} -B ${KOKKOS_BUILD_DIR} +cmake --build ${KOKKOS_BUILD_DIR} +cmake --install ${KOKKOS_BUILD_DIR} + + +# Build and install ELEMENTS with MATAR/Kokkos +ELEMENTS_SOURCE_DIR=${ELEMENTS_DIR} +ELEMENTS_BUILD_DIR=${PROJECT_BUILD_DIR}/elements +ELEMENTS_INSTALL_DIR=${ELEMENTS_BUILD_DIR} + +OPTIONS=( + -DCMAKE_BUILD_TYPE=Release + -DCMAKE_INSTALL_PREFIX=${ELEMENTS_INSTALL_DIR} + -DMATAR_WITH_KOKKOS=ON + -DKokkos_DIR=${KOKKOS_INSTALL_DIR}/lib/cmake/Kokkos + -DKOKKOS=ON + -DOPENMP=ON +) + +cmake "${OPTIONS[@]}" -S ${ELEMENTS_SOURCE_DIR} -B ${ELEMENTS_BUILD_DIR} +cmake --build ${ELEMENTS_BUILD_DIR} --verbose +cmake --install ${ELEMENTS_BUILD_DIR} diff --git a/elements/CMakeLists.txt b/elements/CMakeLists.txt index 2e9026f5..c7a21251 100644 --- a/elements/CMakeLists.txt +++ b/elements/CMakeLists.txt @@ -1,15 +1,46 @@ add_library( elements - elements.cpp - lagrange_polynomials.cpp - lagrange_element.cpp - legendre_polynomials.cpp - legendre_element.cpp - jacobi_polynomials.cpp - gauss_jacobi_quadrature.cpp - point_distributions.cpp -) -target_link_libraries( - elements - common + elements.cpp + lagrange_polynomials.cpp + lagrange_element.cpp + legendre_polynomials.cpp + legendre_element.cpp + jacobi_polynomials.cpp + gauss_jacobi_quadrature.cpp + point_distributions.cpp ) + +if (MATAR_WITH_KOKKOS) + target_compile_definitions( + elements + PUBLIC + MATAR_WITH_KOKKOS + HAVE_KOKKOS=1 + HAVE_OPENMP=1 + ) + + if (CUDA) + target_compile_definitions(elements PUBLIC -DHAVE_CUDA=1) + elseif (HIP) + target_compile_definitions(elements PUBLIC -DHAVE_HIP=1) + elseif (OPENMP) + target_compile_definitions(elements PUBLIC -DHAVE_OPENMP=1) + elseif (THREADS) + target_compile_definitions(elements PUBLIC -DHAVE_THREADS=1) + else() + message(FATAL_ERROR "Please specify whether you are using CUDA, HIP, OPENMP, etc.") + endif() + + target_link_libraries( + elements + common + matar + Kokkos::kokkos + ) +else() + target_link_libraries( + elements + common + matar + ) +endif() diff --git a/elements/elements.cpp b/elements/elements.cpp index ec546b01..3c695ca6 100644 --- a/elements/elements.cpp +++ b/elements/elements.cpp @@ -123,9 +123,7 @@ patch 6; [1,3,7,5] * in place. The integer num is the numer of points being defined in 1D. *****************************************************************************************/ -void lobatto_nodes_1D( - CArray &lob_nodes_1D, - const int &num){ +void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num){ if (num == 1){ lob_nodes_1D(0) = 0.0; } @@ -2637,14 +2635,14 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // --- evaluate the basis at the nodal positions for(int node_rlid = 0; node_rlid < num_ref_nodes_in_elem_; node_rlid++){ - auto point = CArray (3); + auto point = MatarRealCArray(3); // Get the nodal coordinates for(int dim = 0; dim < 3; dim++){ point(dim) = ref_node_positions_(node_rlid, dim); } - auto node_basis = CArray (num_ref_verts_in_elem_); + auto node_basis = MatarRealCArray(num_ref_verts_in_elem_); elem.basis(node_basis, point); @@ -2658,15 +2656,15 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // --- evaluate grad_basis functions at the ref nodes --- - auto partial_xi = CArray (num_ref_nodes_in_elem_); - auto partial_eta = CArray (num_ref_nodes_in_elem_); - auto partial_mu = CArray (num_ref_nodes_in_elem_); + auto partial_xi = MatarRealCArray(num_ref_nodes_in_elem_); + auto partial_eta = MatarRealCArray(num_ref_nodes_in_elem_); + auto partial_mu = MatarRealCArray(num_ref_nodes_in_elem_); for(int node_lid = 0; node_lid < num_ref_nodes_in_elem_; node_lid++){ - auto point = CArray (3); + auto point = MatarRealCArray(3); // Get the nodal coordinates for(int dim = 0; dim < 3; dim++){ @@ -2906,7 +2904,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ - auto point = CArray (3); + auto point = MatarRealCArray(3); // Get the patch coordinates for(int dim = 0; dim < 3; dim++){ @@ -2914,7 +2912,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // the basis function values at the patch for each vertex - auto patch_basis = CArray (num_ref_verts_in_elem_); + auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); // calculate the patch basis function values at the point, for each vertex elem.basis(patch_basis, point); @@ -2934,7 +2932,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // loop over the patches for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ - auto point = CArray (3); + auto point = MatarRealCArray(3); // Get the patch coordinates for(int dim = 0; dim < 3; dim++){ @@ -2967,7 +2965,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ - auto point = CArray (3); + auto point = MatarRealCArray(3); // Get the patch coordinates for(int dim = 0; dim < 3; dim++){ @@ -2975,7 +2973,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // the basis function values at the patch for each vertex - auto cell_basis = CArray (num_ref_verts_in_elem_); + auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); // calculate the cell basis function values at the point, for each vertex elem.basis(cell_basis, point); @@ -2994,7 +2992,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // loop over the patches for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ - auto point = CArray (3); + auto point = MatarRealCArray(3); // Get the cell coordinates for(int dim = 0; dim < 3; dim++){ @@ -5380,8 +5378,8 @@ representative linear element for visualization num_nodes_1d_ = 2; num_nodes_ = pow(num_nodes_1d_, 3); - HexN_Nodes_1d_ = CArray (num_nodes_); - HexN_Nodes_ = CArray (num_nodes_, 3); + HexN_Nodes_1d_ = MatarRealCArray (num_nodes_); + HexN_Nodes_ = MatarRealCArray (num_nodes_, 3); // Vertices @@ -5389,11 +5387,11 @@ representative linear element for visualization num_verts_ = pow(num_verts_1d_, 3); num_basis_ = pow(num_verts_1d_, 3); - HexN_Verts_1d_ = CArray (num_verts_); - HexN_Verts_ = CArray (num_verts_, 3); + HexN_Verts_1d_ = MatarRealCArray (num_verts_); + HexN_Verts_ = MatarRealCArray (num_verts_, 3); - Vert_Node_map_ = CArray (num_verts_); + Vert_Node_map_ = MatarUIntCArray (num_verts_); order_ = elem_order+1; @@ -5407,8 +5405,8 @@ representative linear element for visualization num_nodes_1d_ = 2 * elem_order + 1; num_nodes_ = pow(num_nodes_1d_, 3); - HexN_Nodes_1d_ = CArray (num_nodes_); - HexN_Nodes_ = CArray (num_nodes_, 3); + HexN_Nodes_1d_ = MatarRealCArray (num_nodes_); + HexN_Nodes_ = MatarRealCArray (num_nodes_, 3); // Vertices @@ -5416,11 +5414,11 @@ representative linear element for visualization num_verts_ = pow(num_verts_1d_, 3); num_basis_ = pow(num_verts_1d_, 3); - HexN_Verts_1d_ = CArray (num_verts_); - HexN_Verts_ = CArray (num_verts_, 3); + HexN_Verts_1d_ = MatarRealCArray (num_verts_); + HexN_Verts_ = MatarRealCArray (num_verts_, 3); - Vert_Node_map_ = CArray (num_verts_); + Vert_Node_map_ = MatarUIntCArray (num_verts_); order_ = elem_order; @@ -5502,11 +5500,11 @@ representative linear element for visualization return i + j*num_verts_1d_ + k*num_verts_1d_*num_verts_1d_; }; - void HexN::basis(CArray &basis, CArray &point) + void HexN::basis(MatarRealCArray &basis, MatarRealCArray &point) { - auto val_1d = CArray (num_verts_1d_); - auto val_3d = CArray (num_verts_1d_, 3); + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); // Calculate 1D basis for the X coordinate of the point lagrange_basis_1D(val_1d, point(0)); @@ -5549,15 +5547,15 @@ representative linear element for visualization }; - void HexN::partial_xi_basis(CArray &partial_xi, CArray &point) + void HexN::partial_xi_basis(MatarRealCArray &partial_xi, MatarRealCArray &point) { - auto val_1d = CArray (num_verts_1d_); - auto val_3d = CArray (num_verts_1d_, 3); + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); - auto Dval_1d = CArray (num_verts_1d_); - auto Dval_3d = CArray (num_verts_1d_, 3); + auto Dval_1d = MatarRealCArray (num_verts_1d_); + auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); // Calculate 1D partial w.r.t. xi for the X coordinate of the point lagrange_derivative_1D(Dval_1d, point(0)); @@ -5609,14 +5607,14 @@ representative linear element for visualization }; - void HexN::partial_eta_basis(CArray &partial_eta, CArray &point) + void HexN::partial_eta_basis(MatarRealCArray &partial_eta, MatarRealCArray &point) { - auto val_1d = CArray (num_verts_1d_); - auto val_3d = CArray (num_verts_1d_, 3); + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); - auto Dval_1d = CArray (num_verts_1d_); - auto Dval_3d = CArray (num_verts_1d_, 3); + auto Dval_1d = MatarRealCArray (num_verts_1d_); + auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); // Calculate 1D basis for the Y coordinate of the point lagrange_basis_1D(val_1d, point(0)); @@ -5667,14 +5665,14 @@ representative linear element for visualization }; - void HexN::partial_mu_basis(CArray &partial_mu, CArray &point){ + void HexN::partial_mu_basis(MatarRealCArray &partial_mu, MatarRealCArray &point){ - auto val_1d = CArray (num_verts_1d_); - auto val_3d = CArray (num_verts_1d_, 3); + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); - auto Dval_1d = CArray (num_verts_1d_); - auto Dval_3d = CArray (num_verts_1d_, 3); + auto Dval_1d = MatarRealCArray (num_verts_1d_); + auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); // Calculate 1D basis for the X coordinate of the point lagrange_basis_1D(val_1d, point(0)); @@ -5727,7 +5725,7 @@ representative linear element for visualization void HexN::lagrange_basis_1D( - CArray &interp, // interpolant from each basis + MatarRealCArray &interp, // interpolant from each basis const real_t &x_point){ // point of interest in element @@ -5761,7 +5759,7 @@ representative linear element for visualization } // end of Legrange_1D function void HexN::lagrange_derivative_1D( - CArray &derivative, // derivative + MatarRealCArray &derivative, // derivative const real_t &x_point){ // point of interest in element for(int vert_i = 0; vert_i < num_verts_1d_; vert_i++){ // looping over the nodes diff --git a/elements/elements.h b/elements/elements.h index a1e10ec2..4869f257 100644 --- a/elements/elements.h +++ b/elements/elements.h @@ -54,8 +54,13 @@ ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. using namespace utils; - - +#ifdef MATAR_WITH_KOKKOS +typedef CArrayKokkos MatarRealCArray; +typedef CArrayKokkos MatarUIntCArray; +#else +typedef CArray MatarRealCArray; +typedef CArray MatarUIntCArray; +#endif // MATAR_WITH_KOKKOS namespace elements { @@ -961,7 +966,7 @@ class Hex8: public Element3D { 0--------1 */ - class HexN{ + class HexN { protected: @@ -971,18 +976,18 @@ class Hex8: public Element3D { int num_nodes_1d_; int num_nodes_; - CArray HexN_Nodes_1d_; - CArray HexN_Nodes_; + MatarRealCArray HexN_Nodes_1d_; + MatarRealCArray HexN_Nodes_; // Vertices int num_verts_1d_; int num_verts_; int num_basis_; - CArray HexN_Verts_1d_; - CArray HexN_Verts_; + MatarRealCArray HexN_Verts_1d_; + MatarRealCArray HexN_Verts_; - CArray Vert_Node_map_; + MatarUIntCArray Vert_Node_map_; int order_; @@ -1005,33 +1010,33 @@ class Hex8: public Element3D { // Evaluate the basis at a given point void basis( - CArray &basis, - CArray &point); + MatarRealCArray &basis, + MatarRealCArray &point); void build_nodal_gradient( - CArray &gradient); + MatarRealCArray &gradient); // calculate the partial of the basis w.r.t xi at a given point void partial_xi_basis( - CArray &partial_xi, - CArray &point); + MatarRealCArray &partial_xi, + MatarRealCArray &point); // calculate the partial of the basis w.r.t eta at a given point void partial_eta_basis( - CArray &partial_eta, - CArray &point); + MatarRealCArray &partial_eta, + MatarRealCArray &point); // calculate the partial of the basis w.r.t mu at a given point void partial_mu_basis( - CArray &partial_mu, - CArray &point); + MatarRealCArray &partial_mu, + MatarRealCArray &point); void lagrange_basis_1D( - CArray &interp, // interpolant + MatarRealCArray &interp, // interpolant const real_t &x_point); // point of interest in element void lagrange_derivative_1D( - CArray &partials, //derivative + MatarRealCArray &partials, //derivative const real_t &x_point); // point of interest in element void create_lobatto_nodes(int element_order); From 7f8785b0e21c9ef6f39f01b6b4757a88cb747bd7 Mon Sep 17 00:00:00 2001 From: Eric Collins Date: Wed, 8 Jun 2022 14:03:22 -0500 Subject: [PATCH 02/20] Update lobotto quadrature functions to use the new MatarRealCArray typedef. --- elements/elements.cpp | 54 ++++++++++++++++++++++--------------------- elements/elements.h | 16 ++++++------- 2 files changed, 36 insertions(+), 34 deletions(-) diff --git a/elements/elements.cpp b/elements/elements.cpp index 3c695ca6..6e596d65 100644 --- a/elements/elements.cpp +++ b/elements/elements.cpp @@ -395,9 +395,10 @@ void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num){ * defined in 1D. *****************************************************************************************/ -void lobatto_weights_1D( - CArray &lob_weights_1D, // Lobbatto weights - const int &num){ // Interpolation order +/// @param lob_weights_1D Lobatto weights +/// @param num Interpolation order +void lobatto_weights_1D( MatarRealCArray &lob_weights_1D, + const int &num) { if (num == 1){ lob_weights_1D(0) = 2.0; } @@ -662,8 +663,7 @@ void lobatto_weights_1D( } // end if } // end of lobatto_weights_1D function -void legendre_nodes_1D( - CArray &leg_nodes_1D, +void legendre_nodes_1D(CArray &leg_nodes_1D, const int &num){ if (num == 1){ @@ -1163,11 +1163,12 @@ void legendre_weights_1D( * polynomial order of the desired element. Note: This function currently only supports up * to third order elements. *****************************************************************************************/ -void length_weights( - CArray &len_weights_1D, // partitioned Lobbatto weights - CArray &lob_weights_1D, // Lobbatto weights - CArray &lob_nodes_1D, - const int &p_order){ +/// @param len_weights_1D Partitioned Lobotto weights +/// @param lob_weights_1D Lobotto weights +void length_weights( MatarRealCArray &len_weights_1D, + MatarRealCArray &lob_weights_1D, + MatarRealCArray &lob_nodes_1D, + const int &p_order) { real_t alpha1 = (lob_nodes_1D(1) - lob_nodes_1D(0) - lob_weights_1D(0)) /lob_weights_1D(1); @@ -1201,15 +1202,15 @@ void length_weights( } -/**************************************************************************************//** -* sub_weights partitions quadrature weights to the corners corresponding the 1D nodal -* positions defined on [-1,1] using a distance weighted partition. -*****************************************************************************************/ -void sub_weights( - CArray &sub_weights_1D, // Labbatto weights - CArray &lob_weights_1D, // Labbatto weights - CArray &lob_nodes_1D, - const int &p_order){ +/******************************************************************** +* sub_weights partitions quadrature weights to the corners +* corresponding the 1D nodal positions defined on [-1,1] using a +* distance weighted partition. +*********************************************************************/ +void sub_weights( MatarRealCArray &sub_weights_1D, // Labbatto weights + MatarRealCArray &lob_weights_1D, // Labbatto weights + MatarRealCArray &lob_nodes_1D, + const int &p_order ) { real_t alpha1 = (lob_nodes_1D(1) - lob_nodes_1D(0) - lob_weights_1D(0)) /lob_weights_1D(1); @@ -1326,10 +1327,10 @@ void mat_inverse( * partitioned weights and initializes everyting based of the desired polynomial order *****************************************************************************************/ void set_nodes_wgts( - CArray &lob_nodes_1D, - CArray &lob_weights_1D, - CArray &len_weights_1D, - CArray &sub_weights_1D, + MatarRealCArray &lob_nodes_1D, + MatarRealCArray &lob_weights_1D, + MatarRealCArray &len_weights_1D, + MatarRealCArray &sub_weights_1D, const int p_order){ int num_g_pts_1d = 2 * p_order + 1; @@ -1348,7 +1349,8 @@ void set_nodes_wgts( } -/**************************************************************************************//** +/**************************************************************************************/ +/** * set_unit_normals takes in the CArray defined to hold the unit normals of the corners * in a cell in reference space and initializes them. *****************************************************************************************/ @@ -2392,10 +2394,10 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ ref_inside_nodes_in_elem_ = CArray (num_ref_inside_nodes_in_elem_); // --- build gauss nodal positions and weights --- - auto lob_nodes_1D = CArray (num_ref_nodes_1D_); + auto lob_nodes_1D = MatarRealCArray(num_ref_nodes_1D_); lobatto_nodes_1D(lob_nodes_1D, num_ref_nodes_1D_); - auto lob_weights_1D = CArray (num_ref_nodes_1D_); + auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); lobatto_weights_1D(lob_weights_1D, num_ref_nodes_1D_); for(int k = 0; k < num_ref_nodes_1D_; k++){ diff --git a/elements/elements.h b/elements/elements.h index 4869f257..620ed2e8 100644 --- a/elements/elements.h +++ b/elements/elements.h @@ -72,11 +72,11 @@ namespace elements { // Used by Lobatto 1D/2D to set Lobatto quadrature points void lobatto_nodes_1D( - CArray &lob_nodes_1D, + MatarRealCArray &lob_nodes_1D, const int &num); void lobatto_weights_1D( - CArray &lob_weights_1D, // Labbatto weights + MatarRealCArray &lob_weights_1D, // Labbatto weights const int &num); @@ -90,15 +90,15 @@ namespace elements { void length_weights( - CArray &len_weights_1D, // Labbatto weights - CArray &lab_weights_1D, // Labbatto weights - CArray &lab_nodes_1D, + MatarRealCArray &len_weights_1D, // Labbatto weights + MatarRealCArray &lab_weights_1D, // Labbatto weights + MatarRealCArray &lab_nodes_1D, const int &order); void sub_weights( - CArray &sub_weights_1D, // Labbatto weights - CArray &lab_weights_1D, // Labbatto weights - CArray &lab_nodes_1D, + MatarRealCArray &sub_weights_1D, // Labbatto weights + MatarRealCArray &lab_weights_1D, // Labbatto weights + MatarRealCArray &lab_nodes_1D, const int &order); void mat_inverse( From 65435b6dbe90f1a6c935254ec25bb34bafb33f24 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Thu, 9 Jun 2022 14:06:04 -0500 Subject: [PATCH 03/20] Split up elements header file --- elements/elements.h | 1389 ++---------------------- elements/elements_2d.h | 387 +++++++ elements/elements_3d.h | 464 ++++++++ elements/elements_4d.h | 184 ++++ elements/elements_jacobians.h | 90 ++ elements/elements_points_and_weights.h | 137 +++ elements/elements_ref_element.h | 232 ++++ 7 files changed, 1573 insertions(+), 1310 deletions(-) create mode 100644 elements/elements_2d.h create mode 100644 elements/elements_3d.h create mode 100644 elements/elements_4d.h create mode 100644 elements/elements_jacobians.h create mode 100644 elements/elements_points_and_weights.h create mode 100644 elements/elements_ref_element.h diff --git a/elements/elements.h b/elements/elements.h index 620ed2e8..0d7feac3 100644 --- a/elements/elements.h +++ b/elements/elements.h @@ -1,5 +1,3 @@ -#ifndef ELEMENTS_H -#define ELEMENTS_H /***************************************************************************** © 2020. Triad National Security, LLC. All rights reserved. This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos @@ -40,20 +38,23 @@ OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. **********************************************************************************************/ +#ifndef ELEMENTS_H +#define ELEMENTS_H - - +// C/C++ standard library includes #include #include #include #include -#include "utilities.h" + +// MATAR includes #include "matar.h" -using namespace utils; +// Switch between MATAR Kokkos/non-Kokkos data structures, depending on +// availability of Kokkos #ifdef MATAR_WITH_KOKKOS typedef CArrayKokkos MatarRealCArray; typedef CArrayKokkos MatarUIntCArray; @@ -62,44 +63,20 @@ typedef CArray MatarRealCArray; typedef CArray MatarUIntCArray; #endif // MATAR_WITH_KOKKOS -namespace elements { - - //============================================================================== - // Function Declaration - //============================================================================== - - // Used by Lobatto 1D/2D to set Lobatto quadrature points - - void lobatto_nodes_1D( - MatarRealCArray &lob_nodes_1D, - const int &num); - - void lobatto_weights_1D( - MatarRealCArray &lob_weights_1D, // Labbatto weights - const int &num); +// ELEMENTS includes +#include "utilities.h" +using namespace utils; - - void legendre_nodes_1D( - CArray &leg_nodes_1D, - const int &num); - - void legendre_weights_1D( - CArray &leg_weights_1D, // Legendre weights - const int &num); - +#include "elements_jacobians.h" +#include "elements_points_and_weights.h" +#include "elements_2d.h" +#include "elements_3d.h" +#include "elements_4d.h" +#include "elements_ref_element.h" - void length_weights( - MatarRealCArray &len_weights_1D, // Labbatto weights - MatarRealCArray &lab_weights_1D, // Labbatto weights - MatarRealCArray &lab_nodes_1D, - const int &order); - void sub_weights( - MatarRealCArray &sub_weights_1D, // Labbatto weights - MatarRealCArray &lab_weights_1D, // Labbatto weights - MatarRealCArray &lab_nodes_1D, - const int &order); +namespace elements { void mat_inverse( ViewCArray &mat_inv, @@ -114,13 +91,6 @@ namespace elements { // CArray &trans, // CArray &mat); - void set_nodes_wgts( - CArray &lab_nodes_1D, - CArray &lab_weights_1D, - CArray &len_weights_1D, - CArray &sub_weights_1D, - int p_order); - // void sub_cells( // CArray &lab_nodes_1D, // int &p_order, @@ -130,1275 +100,74 @@ namespace elements { void set_unit_normals(CArray &unit_normals); - // Used by Gauss2/3D to set quadrature points - void line_gauss_info( - real_t &x, - real_t &w, - int &m, - int &p); - - // Used by Lovatto 1D/2D to set Lobatto quadrature points - void line_lobatto_info( - real_t &x, - real_t &w, - int &m, - int &p); - - // setting gauss quadrature points for 2D elements - void gauss_2d( - ViewCArray &these_g_pts, // gauss points - ViewCArray &these_weights, // gauss weights - ViewCArray &tot_g_weight, // 2D product of gauss weights - int &quad_order); // quadrature order (n) - - // setting gauss quadrature points for 2D elements - void gauss_3d( - ViewCArray &these_g_pts, // gauss points - ViewCArray &these_weights, // gauss weights - ViewCArray &tot_g_weight, // 3D product of gauss weights - int &quad_order); // quadrature order (n) - - // setting gauss quadrature points for 4D elements - void gauss_4d( - ViewCArray &these_g_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order, // quadrature order (n) - const int &dim); - - // setting Gauss-Lobatto quadrature points for 2D elements - void lobatto_2d( - ViewCArray &these_L_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order); // quadrature order (n) - - // setting Gauss-Lobatto quadrature points for 3D elements - void lobatto_3d( - ViewCArray &these_L_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order); - - // setting gauss quadrature points for 4D elements - void lobatto_4d( - ViewCArray &these_L_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order, // quadrature order (n) - const int &dim); - - //defining the jacobian for 2D elements - void jacobian_2d( - ViewCArray &J_matrix, - real_t &det_J, - const ViewCArray &vertices, - const ViewCArray &this_partial, - const int &num_nodes); - - //defining the jacobian for 3D elements - void jacobian_3d( - ViewCArray &J_matrix, - real_t &det_J, - const ViewCArray &vertices, - const ViewCArray &this_partial, - const int &num_nodes); - - //defining the jacobian for 4D elements - void jacobian_4d( - ViewCArray &J_matrix, - real_t &det_J, - const ViewCArray &vertices, - const ViewCArray &this_partial, - const int &num_nodes, - const int &dim); - - //defining the inverse jacobian for 2D element - void jacobian_inverse_2d( - ViewCArray &J_inverse, - const ViewCArray &jacobian); - - //defining the inverse jacobian for 2D element - void jacobian_inverse_3d( - ViewCArray &J_inverse_matrix, - const ViewCArray &jacobian); - - // defining the inverse of the Jacobian for 4D elements - void jacobian_inverse_4d( - ViewCArray &J_inverse_matrix, - const ViewCArray &jacobian, - const real_t &det_J); - - // creates nodal positions with Chebyshev spacing - void chebyshev_nodes_1D( - ViewCArray &cheb_nodes_1D, // Chebyshev nodes - const int &order); // Interpolation order - - - - - class Element2D { - - protected: - const static int num_dim_ = 2; - - public: - - virtual int num_verts() = 0; - virtual int num_nodes() = 0; - virtual int num_basis() = 0; - - //list of local ids to basis functions needed to interpolate throughout a given element surface - RaggedRightArray surface_to_dof_lid; - int nsurfaces; - - // calculate a physical position in an element for a given xi,eta - virtual void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices) = 0; - - // calculate the value for the basis at each node for a given xi,eta - virtual void basis( - ViewCArray &basis, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Xi - virtual void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point) = 0; - - - // Partial derivative of shape functions with respect to Xi - virtual void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point) = 0; - - // Map from vertex to node - virtual int vert_node_map( const int vert_lid) = 0; - - }; // end of 2D element class - - class Element3D { - - protected: - const static int num_dim_ = 3; - - public: - - virtual int num_verts() = 0; - virtual int num_nodes() = 0; - virtual int num_basis() = 0; - - //list of local ids to basis functions needed to interpolate throughout a given element surface - RaggedRightArray surface_to_dof_lid; - int nsurfaces; - - // calculate a physical position in an element for a given xi,eta,mu - virtual void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices) = 0; - - // calculate the value for the basis at each node for a given xi,eta, mu - virtual void basis( - ViewCArray &basis, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Xi at Xi_point - virtual void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Eta - virtual void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Mu - virtual void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point) = 0; - - // Map from vertex to node - virtual inline int vert_node_map(const int vert_lid) = 0; - - // Reference vertices location - virtual real_t& ref_locs(const int vert_lid, const int dim) = 0; - - }; // end of 3D parent class - - class Element4D { - - public: - - //list of local ids to basis functions needed to interpolate throughout a given element surface - CArray surface_to_dof_lid; - - // calculate a physical position in an element for a given xi,eta,mu,tau - virtual void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices) = 0; - - // calculate the value for the basis at each node for a given xi,eta,mu,tau - virtual void basis( - ViewCArray &basis, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Xi at Xi_point - virtual void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Eta - virtual void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Mu - virtual void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Tau - virtual void partial_tau_basis( - ViewCArray &partial_tau, - const ViewCArray &xi_point) = 0; - - - }; // end of 3D parent class - - - - - /* - .-------------------------------. - | .----------------------------. | - | | _____ ________ | | - | | / ___ `. |_ ___ `. | | - | | |_/___) | | | `. \ | | - | | .'____.' | | | | | | - | | / /____ _| |___.' / | | - | | |_______| |________.' | | - | | | | - | '----------------------------' | - '-------------------------------' - */ - /* - =========================== - 2D Quad 4 Elements - =========================== - - - The finite element local point numbering for a 4 node quadralateral is - as follows - - Eta - ^ - | - 3------+-----2 - | | | - | | | - | | | - | ------+------> Xi - | | - | | - 0------------1 - */ - - - - - class Quad4: public Element2D { - - protected: - - static const int num_verts_ = 4; - static const int num_nodes_ = 4; - static const int num_basis_ = 4; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Quad4(); - ~Quad4(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map( const int vert_lid); - - }; // end of quad_4_2D class - - - /* - =========================== - 2D Quad 8 Elements - =========================== - - - The finite element local point numbering for a 8 node Hexahedral is - as follows - - Eta - ^ - | - 3-------6------2 - | | | - | | | - | | | - | | | - 7 +------5-----> Xi - | | - | | - | | - 0------4-------1 - */ - - class Quad8: public Element2D { - - protected: - - static const int num_verts_ = 8; - static const int num_nodes_ = 8; - static const int num_basis_ = 8; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Quad8(); - ~Quad8(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map( const int vert_lid); - - }; // end of quad_8_2D class - - /* - =========================== - 2D Quad 12 Elements - =========================== - - - The finite element local point numbering for a 8 node Hexahedral is - as follows (NEED TO DEFINE) - - Eta - ^ - | - 3---7------6---2 - | | | - | | | - 11 | 10 - | | | - | +------|-----> Xi - | | - 8 9 - | | - 0----4-----5---1 - - */ - - class Quad12: public Element2D { - - protected: - - static const int num_verts_ = 12; - static const int num_nodes_ = 12; - static const int num_basis_ = 12; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Quad12(); - ~Quad12(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map( const int vert_lid); - - }; // end of quad_8_2D class - - /* - ========================== - Arbitrary Order Elements - ========================== - - __ _ _ _ - / __ \ | | \ | | - | | | |_ _ __ _ __| | \| | - | | | | | | |/ _` |/ _` | . ` | - | |__| | |_| | (_| | (_| | |\ | - \___\_\\__,_|\__,_|\__,_|_| \_| - - Representative linear element for visualization - - Eta (j) - ^ - | - 3--------------2 - | | | - | | | - | | | - | | | - | +------|-----> Xi (i) - | | - | | - | | - 0--------------1 - */ - - - class QuadN{ - public: - - const static int num_dim = 2; - - int num_basis; - int num_verts; - - // calculates the basis values and derivatives in 1D - // used in the basis_partials functiosn to build the 3D element - void lagrange_1D( - ViewCArray &interp, // interpolant - ViewCArray &Dinterp, // derivative of function - const real_t &x_point, // point of interest in element - const ViewCArray &xi_point, // nodal positions in 1D, normally chebyshev - const int &orderN); // order of element - - void corners ( - ViewCArray &lag_nodes, // Nodes of Lagrange elements - ViewCArray &lag_corner, // corner nodes of QuadN element - const int &orderN); // Element order - - void physical_position ( - ViewCArray &x_point, // location in real space - const ViewCArray &lag_nodes, // Nodes of Lagrange elements - const ViewCArray &lag_basis_2d, // 2D basis values - const int &orderN); // order of the element - - void basis_partials ( - ViewCArray &lag_nodes, // Nodes of Lagrange elements (to be filled in) - ViewCArray &nodes_1d, // Nodal spacing in 1D, any spacing is accepted - ViewCArray &val_1d, // Interpolant Value in 1D - ViewCArray &DVal_1d, // Derivateive of basis in 1D - ViewCArray &val_2d, // for holding the interpolant in each direction - ViewCArray &DVal_2d, // for holding the derivatives in each direction - ViewCArray &lag_basis_2d, // 2D basis values - ViewCArray &lag_partial, // Partial of basis - const ViewCArray &xi_point, // point of interest - const int &orderN); // Element order - }; - - - - /* - .-------------------------------. - | .----------------------------. | - | | ______ ________ | | - | | / ____ `. |_ ___ `. | | - | | `' __) | | | `. \ | | - | | _ |__ '. | | | | | | - | | | \____) | _| |___.' / | | - | | \______.' |________.' | | - | | | | - | '----------------------------' | - '------------------------------' - */ - - /* - ========================== - Hex 8 - ========================== - - The finite element local vertex numbering for a 8 node Hexahedral is - as follows - - Mu (k) - | Eta (j) - | / - | / - 6---+----7 - /| | /| - / | | / | - 4--------5 | - | | -|--+---> Xi (i) - | | | | - | 2-----|--3 - | / | / - |/ |/ - 0----*----1 - -*/ - -class Hex8: public Element3D { - - protected: - - static const int num_verts_ = 8; - static const int num_nodes_ = 8; - static const int num_basis_ = 8; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Hex8(); - ~Hex8(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // with repsect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Map from vertex to node - inline int vert_node_map(const int vert_lid); - - real_t& ref_locs(const int vert_lid, const int dim); - - }; // end of hex 8 class - - - /* - ========================== - Hex 20 - ========================== - - The finite element local point numbering for a 20 node Hexahedral is - as follows - - Mu (k) - | Eta (j) - | / - | / - 7----14----6 - /| /| - 15 | 13 | - / 19 / 18 - 4----12----5 | - | | | | --> Xi (i) - | | | | - | 3---10-|---2 - 16 / 17 / - | 11 | 9 - |/ |/ - 0-----8----1 - */ - - class Hex20: public Element3D { - protected: - - static const int num_verts_ = 20; - static const int num_nodes_ = 20; - static const int num_basis_ = 20; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Hex20(); - ~Hex20(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // with repsect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Map from vertex to node - inline int vert_node_map(const int vert_lid); - - real_t& ref_locs(const int vert_lid, const int dim); - - }; // end of hex20 class - - /* - ========================== - Hex 32 - ========================== - - The finite element local point numbering for a 32 node Hexahedral is - shown below - - - Mu (k) - ^ Eta (j) - | / - | / - / - 7----23------22----6 - /| /| - 15 | 14 | - / | / | - 12 31 13 30 - / | / | - 4-----20-----21----5 | - | | | | ----> Xi (i) - | 27 | 26 - | | | | - 28 | 29 | - | 3----19------|18---2 - | / | / - | 11 | 10 - 24 / 25 / - | 8 | 9 - |/ |/ - 0----16------17----1 - */ - - class Hex32: public Element3D { - - protected: - - static const int num_verts_ = 32; - static const int num_nodes_ = 32; - static const int num_basis_ = 32; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Hex32(); - ~Hex32(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // with repsect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map(const int vert_lid); - - real_t& ref_locs(const int vert_lid, const int dim); - - }; // end of hex32 class - - - /* - ========================== - Arbitrary Order Elements - ========================== - _ _ _ _ - | | | | _____ _| \ | | - | |_| |/ _ \ \/ / \| | - | _ | __/> <| |\ | - |_| |_|\___/_/\_\_| \_| - - Representative linear element for visualization - - k - | j - | / - | / - 6---+----7 - /| | /| - / | | / | - 4--------5 | - | | -|--+---> i - | | | | - | 2-----|--3 - | / | / - |/ |/ - 0--------1 - */ - - class HexN { - - protected: - - const static int num_dim_ = 3; - - // Nodes - int num_nodes_1d_; - int num_nodes_; - - MatarRealCArray HexN_Nodes_1d_; - MatarRealCArray HexN_Nodes_; - - // Vertices - int num_verts_1d_; - int num_verts_; - int num_basis_; - - MatarRealCArray HexN_Verts_1d_; - MatarRealCArray HexN_Verts_; - - MatarUIntCArray Vert_Node_map_; - - int order_; - - - public: - - void setup_HexN(int elem_order); - - int num_verts(); - int num_nodes(); - int num_basis(); - int node_rid(int i, int j, int k) const; - int vert_rid(int i, int j, int k) const; - - // Return the noda coordinates in reference space - real_t &node_coords(int node_rlid, int dim); - - - int vert_node_map(int vert_rid) const; - - // Evaluate the basis at a given point - void basis( - MatarRealCArray &basis, - MatarRealCArray &point); - - void build_nodal_gradient( - MatarRealCArray &gradient); - - // calculate the partial of the basis w.r.t xi at a given point - void partial_xi_basis( - MatarRealCArray &partial_xi, - MatarRealCArray &point); - - // calculate the partial of the basis w.r.t eta at a given point - void partial_eta_basis( - MatarRealCArray &partial_eta, - MatarRealCArray &point); - - // calculate the partial of the basis w.r.t mu at a given point - void partial_mu_basis( - MatarRealCArray &partial_mu, - MatarRealCArray &point); - - void lagrange_basis_1D( - MatarRealCArray &interp, // interpolant - const real_t &x_point); // point of interest in element - - void lagrange_derivative_1D( - MatarRealCArray &partials, //derivative - const real_t &x_point); // point of interest in element - - void create_lobatto_nodes(int element_order); - - }; - - - - /* - ========================== - 4D Tesseract element - ========================== - - The finite element local point numbering for a 16 node Tesseract is - based on the 3D Hex8 Ensight element - - - _.15--------------------------------------14 - _.+< |\ . >-"/ | - _ .+> | \ .>"" ./ | - .>"" | \ ."" / | - 12----------------------+------------------13 ./ | - | )<= | \ / | _/"" | - | )\+ | \ / /"| | - | (\= | _. 7---------+--6 | | - | \> .|+< | / . "| | | - | '4--+------+------5' | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | _ .3------+-----2_ | | - | | | " / | /' '| \= _ | - | 0--+---+---------1*" | '\ | - | ./' | " \ | ""\ | - | / |/ \ | '". | - | / 11----------------+-----+---------------10 - | ./ .+<"" ) | .( - 8------------------------------------------9' - - j - ^ k - | / - | / - | / - |/ - +---------->i - - i = Xi - j = Eta - k = Mu - t = Tau - - */ - - class Tess16: public Element4D { - public: - const static int num_verts = 16; - const static int num_dim = 4; - const static int num_basis = 16; - - protected: - static real_t ref_vert[num_verts*num_dim]; // listed as {Xi, Eta, Mu, Tau} - - - public: + /* Add enumerated list of element types to choose from */ + namespace elem_types + { - // calculate a physical position in an element for a given xi,eta,mu - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); + enum elem_type + { + // 2D element types + Quad4 = 0, // 4 node serendipity quadrilateral element + Quad8 = 1, // 8 node serendipity quadrilateral element + Quad12 = 2, // 12 node serendipity quadrilateral element + QuadN = 3, // N node lagrangian quadrilateral element - // calculate the value for the basis at each node for a given xi,eta,mu,tau - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi at Xi_point - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Tau - void partial_tau_basis( - ViewCArray &partial_tau, - const ViewCArray &xi_point); - }; // End of Tess16 Element Class - -/* Add enumerated list of element types to choose from */ - -namespace elem_types -{ - - enum elem_type - { - // 2D element types - Quad4 = 0, // 4 node serendipity quadrilateral element - Quad8 = 1, // 8 node serendipity quadrilateral element - Quad12 = 2, // 12 node serendipity quadrilateral element - QuadN = 3, // N node lagrangian quadrilateral element + // 3D element types + Hex8 = 4, // 8 node lagrangian hexahedral element + Hex20 = 5, // 20 node serendipity hexahedral element + Hex32 = 6, // 32 node serendipity hexahedral element + HexN = 7 // N node lagrangian hexahedral element - // 3D element types - Hex8 = 4, // 8 node lagrangian hexahedral element - Hex20 = 5, // 20 node serendipity hexahedral element - Hex32 = 6, // 32 node serendipity hexahedral element - HexN = 7 // N node lagrangian hexahedral element - - // add tesseract element - + // add tesseract element + + }; + + //Nodes per each element type + //CArray Nodes_Per_Element_Type(8); + //Quad4 + //Nodes_Per_Element_Type(0) = 4; + //Quad8 + //Nodes_Per_Element_Type(1) = 8; + //Quad12 + //Nodes_Per_Element_Type(2) = 12; + //QuadN has to be set on a casewise base + //Nodes_Per_Element_Type(3) = 0; + //Hex8 + //Nodes_Per_Element_Type(4) = 8; + //Hex20 + //Nodes_Per_Element_Type(5) = 20; + //Hex32 + //Nodes_Per_Element_Type(6) = 32; + //HexN set on a casewise basis + //Nodes_Per_Element_Type(7) = 0; + + } // end of elem_type namespace + + + // Choose the type of element to use for the calculation + struct elem_type_t { + // element type + elem_types::elem_type type; }; - //Nodes per each element type - //CArray Nodes_Per_Element_Type(8); - //Quad4 - //Nodes_Per_Element_Type(0) = 4; - //Quad8 - //Nodes_Per_Element_Type(1) = 8; - //Quad12 - //Nodes_Per_Element_Type(2) = 12; - //QuadN has to be set on a casewise base - //Nodes_Per_Element_Type(3) = 0; - //Hex8 - //Nodes_Per_Element_Type(4) = 8; - //Hex20 - //Nodes_Per_Element_Type(5) = 20; - //Hex32 - //Nodes_Per_Element_Type(6) = 32; - //HexN set on a casewise basis - //Nodes_Per_Element_Type(7) = 0; - -} // end of elem_type namespace - - -// Choose the type of element to use for the calculation -struct elem_type_t { - // element type - elem_types::elem_type type; -}; - -class element_selector{ - public: - //2D element objects - Quad4 Quad4_Object; - Quad8 Quad8_Object; - Quad12 Quad12_Object; - QuadN QuadN_Object; - - //3D element objects - Hex8 Hex8_Object; - Hex20 Hex20_Object; - Hex32 Hex32_Object; - HexN HexN_Object; - - void choose_3Delem_type(elem_types::elem_type element_type, Element3D *&elem); - void choose_2Delem_type(elem_types::elem_type element_type, Element2D *&elem2D); -}; - - - -// Reference Element Informations -class ref_element{ -private: - - // this assumes i,j,k structured indexing of nodes - const int node_rlid_in_patch_in_cell_[24] = { - // patches in xi-dir - 0,2,6,4, - 1,3,7,5, - // patches in eta-dir - 0,4,5,1, - 2,6,7,3, - // patches in mu-dir - 0,1,3,2, - 4,5,7,6 + class element_selector{ + public: + //2D element objects + Quad4 Quad4_Object; + Quad8 Quad8_Object; + Quad12 Quad12_Object; + QuadN QuadN_Object; + + //3D element objects + Hex8 Hex8_Object; + Hex20 Hex20_Object; + Hex32 Hex32_Object; + HexN HexN_Object; + + void choose_3Delem_type(elem_types::elem_type element_type, Element3D *&elem); + void choose_2Delem_type(elem_types::elem_type element_type, Element2D *&elem2D); }; - - // return the local ref id for the same patch in the cell-patch neighbor - const int patch_rlid_cell_neighbor_[6] = { - 1, // xi left side of my cell - 0, // xi right side of my cell - 3, // eta front side of my cell - 2, // eta bact side of my cell - 5, // mu bottom side of my cell - 4 // mu top side of my cell - }; - - // return the reference coordinate unit normal of the sides in a cell - const real_t cell_side_unit_normals_[18] = { - -1, 0, 0, // xi left side of my cell - 1, 0, 0, // xi right side of my cell - 0,-1, 0, // eta minus side of my cell - 0, 1, 0, // eta plus side of my cell - 0, 0,-1, // mu minus side of my cell - 0, 0, 1 // mu plus side of my cell - }; - - int num_dim_; - - int num_ref_nodes_1D_; - int num_ref_cells_1D_; - int num_ref_corners_1D_; - - int num_ref_surface_nodes_in_elem_; - int num_ref_inside_nodes_in_elem_; - - // Zones - int num_zones_1d_; - int num_zones_in_elem_; - - // cells - int num_ref_cells_in_elem_; - - CArray cells_in_zone_list_; - - // nodes - int num_ref_nodes_in_elem_; - int num_ref_nodes_in_cell_; - - CArray ref_nodes_in_cell_; - CArray ref_surface_nodes_in_elem_; - CArray ref_inside_nodes_in_elem_; - - CArray ref_node_positions_; - CArray ref_node_g_weights_; - - CArray cell_nodes_in_elem_list_; - - // Vertices - int num_ref_verts_1d_; - int num_ref_verts_in_elem_; - - // corners - int num_ref_corners_in_cell_; - int num_ref_corners_in_elem_; - - CArray ref_corners_in_cell_; - - CArray ref_corner_surf_normals_; - CArray ref_corner_g_weights_; - CArray ref_corner_surf_g_weights_; - - // patches and sides - int num_patches_in_elem_; - int num_sides_in_elem_; - - CArray ref_cell_positions_; - CArray ref_cell_g_weights_; - CArray ref_patch_positions_; - CArray ref_patch_g_weights_; - - CArray ref_patches_in_cell_list_; - - CArray ref_patch_basis_; - CArray ref_patch_gradient_; // grad basis at patch - - CArray ref_cell_basis_; - CArray ref_cell_gradient_; // grad basis at cell - - // Num basis functions - int num_basis_; - - // Basis evaluation at nodes - CArray ref_nodal_basis_; - - // Pointer to HexN object - HexN *elem_ptr; - -public: - - // Gradient of basis - CArray ref_nodal_gradient_; - //real_t * ref_nodal_gradient_; - - // Function Declarations - - // Default constructor - ref_element() : elem_ptr(nullptr) {}; - - // Initialize reference element information - void init(int poly_order, int num_dim, HexN &elem); - - int num_dim() const; - - int num_basis() const; - - int num_ref_nodes() const; - - int num_ref_cells_in_elem() const; - int num_ref_corners_in_cell() const; - - // local i,j,k indexing - int node_rid(int i, int j, int k) const; - int cell_rid(int i, int j, int k) const; - int corner_rid(int i, int j, int k) const; - - int ref_corners_in_cell(int cell_rid, int corner_rlid) const; - int ref_nodes_in_cell(int cell_rid, int node_rlid) const; - - int ref_surface_nodes_in_elem(int node_rlid) const; - int ref_inside_nodes_in_elem(int node_rlid) const; - int num_ref_surface_nodes_in_elem() const; - int num_ref_inside_nodes_in_elem() const; - - real_t ref_node_positions(int node_rid, int dim) const; - - real_t ref_corner_surface_normals(int corner_rid, int surf_rlid, int dim) const; - - real_t ref_corner_g_surface_weights(int corner_rid, int surf_rlid) const; - - real_t ref_node_g_weights(int node_rid) const; - - real_t ref_corner_g_weights(int corner_rid) const; - - real_t &ref_nodal_gradient(int node_rid, int basis_id, int dim) const; - - real_t &ref_nodal_basis(int node_rid, int basis_id) const; - - int& cell_lid_in_zone(int zone_lid, int cell_lid) const; - - real_t ref_cell_positions(int cell_rid, int dim) const; - real_t ref_cell_g_weights(int cell_rid) const; - real_t ref_cell_basis(int cell_rid, int basis_id) const; - real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; - - real_t cell_side_unit_normals(int side_rlid, int dim) const; - - int& cell_nodes_in_elem(int cell_lid, int node_lid) const; - - int node_in_patch_in_cell(int patch_lid, int node_lid) const; - - int patch_rlid_in_cell_neighbor(int patch_rlid) const; - - int ref_patches_in_cell(int cell_lid, int patch_rlid) const; - - real_t ref_patch_positions(int patch_rid, int dim) const; - real_t ref_patch_g_weights(int patch_rid) const; - real_t ref_patch_basis(int patch_rid, int basis_id) const; - real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; - - int vert_node_map(int vert_lid); - - // Deconstructor - ~ref_element(); - -}; - } // end namespace elements -#endif //ELEMENTS_H +#endif // ELEMENTS_H diff --git a/elements/elements_2d.h b/elements/elements_2d.h new file mode 100644 index 00000000..4fbee2f6 --- /dev/null +++ b/elements/elements_2d.h @@ -0,0 +1,387 @@ +/***************************************************************************** +© 2020. Triad National Security, LLC. All rights reserved. +This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos +National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. +Department of Energy/National Nuclear Security Administration. All rights in the program are +reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear +Security Administration. The Government is granted for itself and others acting on its behalf a +nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare +derivative works, distribute copies to the public, perform publicly and display publicly, and +to permit others to do so. + + +This program is open source under the BSD-3 License. +Redistribution and use in source and binary forms, with or without modification, are permitted +provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, this list of + conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, this list of + conditions and the following disclaimer in the documentation and/or other materials + provided with the distribution. + + 3. Neither the name of the copyright holder nor the names of its contributors may be used + to endorse or promote products derived from this software without specific prior + written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; +OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, +WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR +OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +**********************************************************************************************/ +#ifndef ELEMENTS_2D_H +#define ELEMENTS_2D_H + +namespace elements { + + /* + .-------------------------------. + | .----------------------------. | + | | _____ ________ | | + | | / ___ `. |_ ___ `. | | + | | |_/___) | | | `. \ | | + | | .'____.' | | | | | | + | | / /____ _| |___.' / | | + | | |_______| |________.' | | + | | | | + | '----------------------------' | + '-------------------------------' + */ + class Element2D { + + protected: + const static int num_dim_ = 2; + + public: + + virtual int num_verts() = 0; + virtual int num_nodes() = 0; + virtual int num_basis() = 0; + + //list of local ids to basis functions needed to interpolate throughout a given element surface + RaggedRightArray surface_to_dof_lid; + int nsurfaces; + + // calculate a physical position in an element for a given xi,eta + virtual void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices) = 0; + + // calculate the value for the basis at each node for a given xi,eta + virtual void basis( + ViewCArray &basis, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Xi + virtual void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point) = 0; + + + // Partial derivative of shape functions with respect to Xi + virtual void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point) = 0; + + // Map from vertex to node + virtual int vert_node_map( const int vert_lid) = 0; + + }; + + + /* + =========================== + 2D Quad 4 Elements + =========================== + + + The finite element local point numbering for a 4 node quadralateral is + as follows + + Eta + ^ + | + 3------+-----2 + | | | + | | | + | | | + | ------+------> Xi + | | + | | + 0------------1 + */ + class Quad4: public Element2D { + + protected: + + static const int num_verts_ = 4; + static const int num_nodes_ = 4; + static const int num_basis_ = 4; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Quad4(); + ~Quad4(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map( const int vert_lid); + + }; // end of quad_4_2D class + + + /* + =========================== + 2D Quad 8 Elements + =========================== + + + The finite element local point numbering for a 8 node Hexahedral is + as follows + + Eta + ^ + | + 3-------6------2 + | | | + | | | + | | | + | | | + 7 +------5-----> Xi + | | + | | + | | + 0------4-------1 + */ + class Quad8: public Element2D { + + protected: + + static const int num_verts_ = 8; + static const int num_nodes_ = 8; + static const int num_basis_ = 8; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Quad8(); + ~Quad8(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map( const int vert_lid); + + }; // end of quad_8_2D class + + + /* + =========================== + 2D Quad 12 Elements + =========================== + + + The finite element local point numbering for a 8 node Hexahedral is + as follows (NEED TO DEFINE) + + Eta + ^ + | + 3---7------6---2 + | | | + | | | + 11 | 10 + | | | + | +------|-----> Xi + | | + 8 9 + | | + 0----4-----5---1 + + */ + class Quad12: public Element2D { + + protected: + + static const int num_verts_ = 12; + static const int num_nodes_ = 12; + static const int num_basis_ = 12; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Quad12(); + ~Quad12(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map( const int vert_lid); + + }; // end of quad_8_2D class + + + /* + ========================== + Arbitrary Order Elements + ========================== + + __ _ _ _ + / __ \ | | \ | | + | | | |_ _ __ _ __| | \| | + | | | | | | |/ _` |/ _` | . ` | + | |__| | |_| | (_| | (_| | |\ | + \___\_\\__,_|\__,_|\__,_|_| \_| + + Representative linear element for visualization + + Eta (j) + ^ + | + 3--------------2 + | | | + | | | + | | | + | | | + | +------|-----> Xi (i) + | | + | | + | | + 0--------------1 + */ + class QuadN { + public: + + const static int num_dim = 2; + + int num_basis; + int num_verts; + + // calculates the basis values and derivatives in 1D + // used in the basis_partials functiosn to build the 3D element + void lagrange_1D( + ViewCArray &interp, // interpolant + ViewCArray &Dinterp, // derivative of function + const real_t &x_point, // point of interest in element + const ViewCArray &xi_point, // nodal positions in 1D, normally chebyshev + const int &orderN); // order of element + + void corners ( + ViewCArray &lag_nodes, // Nodes of Lagrange elements + ViewCArray &lag_corner, // corner nodes of QuadN element + const int &orderN); // Element order + + void physical_position ( + ViewCArray &x_point, // location in real space + const ViewCArray &lag_nodes, // Nodes of Lagrange elements + const ViewCArray &lag_basis_2d, // 2D basis values + const int &orderN); // order of the element + + void basis_partials ( + ViewCArray &lag_nodes, // Nodes of Lagrange elements (to be filled in) + ViewCArray &nodes_1d, // Nodal spacing in 1D, any spacing is accepted + ViewCArray &val_1d, // Interpolant Value in 1D + ViewCArray &DVal_1d, // Derivateive of basis in 1D + ViewCArray &val_2d, // for holding the interpolant in each direction + ViewCArray &DVal_2d, // for holding the derivatives in each direction + ViewCArray &lag_basis_2d, // 2D basis values + ViewCArray &lag_partial, // Partial of basis + const ViewCArray &xi_point, // point of interest + const int &orderN); // Element order + }; + +} +#endif // ELEMENTS_2D_H diff --git a/elements/elements_3d.h b/elements/elements_3d.h new file mode 100644 index 00000000..b20c5c00 --- /dev/null +++ b/elements/elements_3d.h @@ -0,0 +1,464 @@ +/***************************************************************************** +© 2020. Triad National Security, LLC. All rights reserved. +This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos +National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. +Department of Energy/National Nuclear Security Administration. All rights in the program are +reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear +Security Administration. The Government is granted for itself and others acting on its behalf a +nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare +derivative works, distribute copies to the public, perform publicly and display publicly, and +to permit others to do so. + + +This program is open source under the BSD-3 License. +Redistribution and use in source and binary forms, with or without modification, are permitted +provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, this list of + conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, this list of + conditions and the following disclaimer in the documentation and/or other materials + provided with the distribution. + + 3. Neither the name of the copyright holder nor the names of its contributors may be used + to endorse or promote products derived from this software without specific prior + written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; +OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, +WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR +OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +**********************************************************************************************/ +#ifndef ELEMENTS_3D_H +#define ELEMENTS_3D_H + +namespace elements { + + /* + .-------------------------------. + | .----------------------------. | + | | ______ ________ | | + | | / ____ `. |_ ___ `. | | + | | `' __) | | | `. \ | | + | | _ |__ '. | | | | | | + | | | \____) | _| |___.' / | | + | | \______.' |________.' | | + | | | | + | '----------------------------' | + '------------------------------' + */ + class Element3D { + + protected: + const static int num_dim_ = 3; + + public: + + virtual int num_verts() = 0; + virtual int num_nodes() = 0; + virtual int num_basis() = 0; + + //list of local ids to basis functions needed to interpolate throughout a given element surface + RaggedRightArray surface_to_dof_lid; + int nsurfaces; + + // calculate a physical position in an element for a given xi,eta,mu + virtual void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices) = 0; + + // calculate the value for the basis at each node for a given xi,eta, mu + virtual void basis( + ViewCArray &basis, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Xi at Xi_point + virtual void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Eta + virtual void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Mu + virtual void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point) = 0; + + // Map from vertex to node + virtual inline int vert_node_map(const int vert_lid) = 0; + + // Reference vertices location + virtual real_t& ref_locs(const int vert_lid, const int dim) = 0; + + }; // end of 3D parent class + + + /* + ========================== + Hex 8 + ========================== + + The finite element local vertex numbering for a 8 node Hexahedral is + as follows + + Mu (k) + | Eta (j) + | / + | / + 6---+----7 + /| | /| + / | | / | + 4--------5 | + | | -|--+---> Xi (i) + | | | | + | 2-----|--3 + | / | / + |/ |/ + 0----*----1 + + */ + class Hex8: public Element3D { + + protected: + + static const int num_verts_ = 8; + static const int num_nodes_ = 8; + static const int num_basis_ = 8; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Hex8(); + ~Hex8(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // with repsect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Map from vertex to node + inline int vert_node_map(const int vert_lid); + + real_t& ref_locs(const int vert_lid, const int dim); + + }; // end of hex 8 class + + + /* + ========================== + Hex 20 + ========================== + + The finite element local point numbering for a 20 node Hexahedral is + as follows + + Mu (k) + | Eta (j) + | / + | / + 7----14----6 + /| /| + 15 | 13 | + / 19 / 18 + 4----12----5 | + | | | | --> Xi (i) + | | | | + | 3---10-|---2 + 16 / 17 / + | 11 | 9 + |/ |/ + 0-----8----1 + */ + class Hex20: public Element3D { + protected: + + static const int num_verts_ = 20; + static const int num_nodes_ = 20; + static const int num_basis_ = 20; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Hex20(); + ~Hex20(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // with repsect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Map from vertex to node + inline int vert_node_map(const int vert_lid); + + real_t& ref_locs(const int vert_lid, const int dim); + + }; // end of hex20 class + + + /* + ========================== + Hex 32 + ========================== + + The finite element local point numbering for a 32 node Hexahedral is + shown below + + + Mu (k) + ^ Eta (j) + | / + | / + / + 7----23------22----6 + /| /| + 15 | 14 | + / | / | + 12 31 13 30 + / | / | + 4-----20-----21----5 | + | | | | ----> Xi (i) + | 27 | 26 + | | | | + 28 | 29 | + | 3----19------|18---2 + | / | / + | 11 | 10 + 24 / 25 / + | 8 | 9 + |/ |/ + 0----16------17----1 + */ + class Hex32: public Element3D { + + protected: + + static const int num_verts_ = 32; + static const int num_nodes_ = 32; + static const int num_basis_ = 32; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Hex32(); + ~Hex32(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // with repsect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map(const int vert_lid); + + real_t& ref_locs(const int vert_lid, const int dim); + + }; // end of hex32 class + + + /* + ========================== + Arbitrary Order Elements + ========================== + _ _ _ _ + | | | | _____ _| \ | | + | |_| |/ _ \ \/ / \| | + | _ | __/> <| |\ | + |_| |_|\___/_/\_\_| \_| + + Representative linear element for visualization + + k + | j + | / + | / + 6---+----7 + /| | /| + / | | / | + 4--------5 | + | | -|--+---> i + | | | | + | 2-----|--3 + | / | / + |/ |/ + 0--------1 + */ + class HexN { + + protected: + + const static int num_dim_ = 3; + + // Nodes + int num_nodes_1d_; + int num_nodes_; + + MatarRealCArray HexN_Nodes_1d_; + MatarRealCArray HexN_Nodes_; + + // Vertices + int num_verts_1d_; + int num_verts_; + int num_basis_; + + MatarRealCArray HexN_Verts_1d_; + MatarRealCArray HexN_Verts_; + + MatarUIntCArray Vert_Node_map_; + + int order_; + + + public: + + void setup_HexN(int elem_order); + + int num_verts(); + int num_nodes(); + int num_basis(); + int node_rid(int i, int j, int k) const; + int vert_rid(int i, int j, int k) const; + + // Return the noda coordinates in reference space + real_t &node_coords(int node_rlid, int dim); + + + int vert_node_map(int vert_rid) const; + + // Evaluate the basis at a given point + void basis( + MatarRealCArray &basis, + MatarRealCArray &point); + + void build_nodal_gradient( + MatarRealCArray &gradient); + + // calculate the partial of the basis w.r.t xi at a given point + void partial_xi_basis( + MatarRealCArray &partial_xi, + MatarRealCArray &point); + + // calculate the partial of the basis w.r.t eta at a given point + void partial_eta_basis( + MatarRealCArray &partial_eta, + MatarRealCArray &point); + + // calculate the partial of the basis w.r.t mu at a given point + void partial_mu_basis( + MatarRealCArray &partial_mu, + MatarRealCArray &point); + + void lagrange_basis_1D( + MatarRealCArray &interp, // interpolant + const real_t &x_point); // point of interest in element + + void lagrange_derivative_1D( + MatarRealCArray &partials, //derivative + const real_t &x_point); // point of interest in element + + void create_lobatto_nodes(int element_order); + + }; + +} + +#endif // ELEMENTS_3D_H diff --git a/elements/elements_4d.h b/elements/elements_4d.h new file mode 100644 index 00000000..d7d38326 --- /dev/null +++ b/elements/elements_4d.h @@ -0,0 +1,184 @@ +/***************************************************************************** +© 2020. Triad National Security, LLC. All rights reserved. +This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos +National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. +Department of Energy/National Nuclear Security Administration. All rights in the program are +reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear +Security Administration. The Government is granted for itself and others acting on its behalf a +nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare +derivative works, distribute copies to the public, perform publicly and display publicly, and +to permit others to do so. + + +This program is open source under the BSD-3 License. +Redistribution and use in source and binary forms, with or without modification, are permitted +provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, this list of + conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, this list of + conditions and the following disclaimer in the documentation and/or other materials + provided with the distribution. + + 3. Neither the name of the copyright holder nor the names of its contributors may be used + to endorse or promote products derived from this software without specific prior + written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; +OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, +WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR +OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +**********************************************************************************************/ +#ifndef ELEMENTS_4D_H +#define ELEMENTS_4D_H + +namespace elements { + + class Element4D { + + public: + + //list of local ids to basis functions needed to interpolate throughout a given element surface + CArray surface_to_dof_lid; + + // calculate a physical position in an element for a given xi,eta,mu,tau + virtual void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices) = 0; + + // calculate the value for the basis at each node for a given xi,eta,mu,tau + virtual void basis( + ViewCArray &basis, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Xi at Xi_point + virtual void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Eta + virtual void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Mu + virtual void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Tau + virtual void partial_tau_basis( + ViewCArray &partial_tau, + const ViewCArray &xi_point) = 0; + + + }; + + + /* + ========================== + 4D Tesseract element + ========================== + + The finite element local point numbering for a 16 node Tesseract is + based on the 3D Hex8 Ensight element + + + _.15--------------------------------------14 + _.+< |\ . >-"/ | + _ .+> | \ .>"" ./ | + .>"" | \ ."" / | + 12----------------------+------------------13 ./ | + | )<= | \ / | _/"" | + | )\+ | \ / /"| | + | (\= | _. 7---------+--6 | | + | \> .|+< | / . "| | | + | '4--+------+------5' | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | _ .3------+-----2_ | | + | | | " / | /' '| \= _ | + | 0--+---+---------1*" | '\ | + | ./' | " \ | ""\ | + | / |/ \ | '". | + | / 11----------------+-----+---------------10 + | ./ .+<"" ) | .( + 8------------------------------------------9' + + j + ^ k + | / + | / + | / + |/ + +---------->i + + i = Xi + j = Eta + k = Mu + t = Tau + + */ + class Tess16: public Element4D { + public: + const static int num_verts = 16; + const static int num_dim = 4; + const static int num_basis = 16; + + protected: + static real_t ref_vert[num_verts*num_dim]; // listed as {Xi, Eta, Mu, Tau} + + + public: + + // calculate a physical position in an element for a given xi,eta,mu + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + // calculate the value for the basis at each node for a given xi,eta,mu,tau + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi at Xi_point + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Tau + void partial_tau_basis( + ViewCArray &partial_tau, + const ViewCArray &xi_point); + }; // End of Tess16 Element Class + +} + +#endif // ELEMENTS_4D_H diff --git a/elements/elements_jacobians.h b/elements/elements_jacobians.h new file mode 100644 index 00000000..74b4d43f --- /dev/null +++ b/elements/elements_jacobians.h @@ -0,0 +1,90 @@ +/***************************************************************************** +© 2020. Triad National Security, LLC. All rights reserved. +This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos +National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. +Department of Energy/National Nuclear Security Administration. All rights in the program are +reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear +Security Administration. The Government is granted for itself and others acting on its behalf a +nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare +derivative works, distribute copies to the public, perform publicly and display publicly, and +to permit others to do so. + + +This program is open source under the BSD-3 License. +Redistribution and use in source and binary forms, with or without modification, are permitted +provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, this list of + conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, this list of + conditions and the following disclaimer in the documentation and/or other materials + provided with the distribution. + + 3. Neither the name of the copyright holder nor the names of its contributors may be used + to endorse or promote products derived from this software without specific prior + written permission. + + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; +OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, +WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR +OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +**********************************************************************************************/ +#ifndef ELEMENTS_JACOBIANS_H +#define ELEMENTS_JACOBIANS_H + +namespace elements { + + //defining the jacobian for 2D elements + void jacobian_2d( + ViewCArray &J_matrix, + real_t &det_J, + const ViewCArray &vertices, + const ViewCArray &this_partial, + const int &num_nodes); + + //defining the inverse jacobian for 2D element + void jacobian_inverse_2d( + ViewCArray &J_inverse, + const ViewCArray &jacobian); + + //defining the jacobian for 3D elements + void jacobian_3d( + ViewCArray &J_matrix, + real_t &det_J, + const ViewCArray &vertices, + const ViewCArray &this_partial, + const int &num_nodes); + + //defining the inverse jacobian for 2D element + void jacobian_inverse_3d( + ViewCArray &J_inverse_matrix, + const ViewCArray &jacobian); + + //defining the jacobian for 4D elements + void jacobian_4d( + ViewCArray &J_matrix, + real_t &det_J, + const ViewCArray &vertices, + const ViewCArray &this_partial, + const int &num_nodes, + const int &dim); + + // defining the inverse of the Jacobian for 4D elements + void jacobian_inverse_4d( + ViewCArray &J_inverse_matrix, + const ViewCArray &jacobian, + const real_t &det_J); + +} + +#endif // ELEMENTS_JACOBIANS_H diff --git a/elements/elements_points_and_weights.h b/elements/elements_points_and_weights.h new file mode 100644 index 00000000..72e18565 --- /dev/null +++ b/elements/elements_points_and_weights.h @@ -0,0 +1,137 @@ +/***************************************************************************** +© 2020. Triad National Security, LLC. All rights reserved. +This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos +National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. +Department of Energy/National Nuclear Security Administration. All rights in the program are +reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear +Security Administration. The Government is granted for itself and others acting on its behalf a +nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare +derivative works, distribute copies to the public, perform publicly and display publicly, and +to permit others to do so. + + +This program is open source under the BSD-3 License. +Redistribution and use in source and binary forms, with or without modification, are permitted +provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, this list of + conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, this list of + conditions and the following disclaimer in the documentation and/or other materials + provided with the distribution. + + 3. Neither the name of the copyright holder nor the names of its contributors may be used + to endorse or promote products derived from this software without specific prior + written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; +OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, +WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR +OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +**********************************************************************************************/ +#ifndef ELEMENTS_POINTS_AND_WEIGHTS_H +#define ELEMENTS_POINTS_AND_WEIGHTS_H + +namespace elements { + + // Used by Lobatto 1D/2D to set Lobatto quadrature points + void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num); + void lobatto_weights_1D(MatarRealCArray &lob_weights_1D, const int &num); + + + void legendre_nodes_1D(CArray &leg_nodes_1D, const int &num); + void legendre_weights_1D(CArray &leg_weights_1D, const int &num); + + + // creates nodal positions with Chebyshev spacing + void chebyshev_nodes_1D( + ViewCArray &cheb_nodes_1D, // Chebyshev nodes + const int &order); // Interpolation order + + + void length_weights( + MatarRealCArray &len_weights_1D, // Lobatto weights + MatarRealCArray &lab_weights_1D, // Lobatto weights + MatarRealCArray &lab_nodes_1D, + const int &order); + + void sub_weights( + MatarRealCArray &sub_weights_1D, // Lobatto weights + MatarRealCArray &lab_weights_1D, // Lobatto weights + MatarRealCArray &lab_nodes_1D, + const int &order); + + + void set_nodes_wgts( + CArray &lab_nodes_1D, + CArray &lab_weights_1D, + CArray &len_weights_1D, + CArray &sub_weights_1D, + int p_order); + + // Used by Gauss2/3D to set quadrature points + void line_gauss_info( + real_t &x, + real_t &w, + int &m, + int &p); + + // Used by Lovatto 1D/2D to set Lobatto quadrature points + void line_lobatto_info( + real_t &x, + real_t &w, + int &m, + int &p); + + // setting gauss quadrature points for 2D elements + void gauss_2d( + ViewCArray &these_g_pts, // gauss points + ViewCArray &these_weights, // gauss weights + ViewCArray &tot_g_weight, // 2D product of gauss weights + int &quad_order); // quadrature order (n) + + // setting gauss quadrature points for 2D elements + void gauss_3d( + ViewCArray &these_g_pts, // gauss points + ViewCArray &these_weights, // gauss weights + ViewCArray &tot_g_weight, // 3D product of gauss weights + int &quad_order); // quadrature order (n) + + // setting gauss quadrature points for 4D elements + void gauss_4d( + ViewCArray &these_g_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order, // quadrature order (n) + const int &dim); + + // setting Gauss-Lobatto quadrature points for 2D elements + void lobatto_2d( + ViewCArray &these_L_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order); // quadrature order (n) + + // setting Gauss-Lobatto quadrature points for 3D elements + void lobatto_3d( + ViewCArray &these_L_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order); + + // setting gauss quadrature points for 4D elements + void lobatto_4d( + ViewCArray &these_L_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order, // quadrature order (n) + const int &dim); + +} + +#endif // ELEMENTS_POINTS_AND_WEIGHTS_H diff --git a/elements/elements_ref_element.h b/elements/elements_ref_element.h new file mode 100644 index 00000000..e904020f --- /dev/null +++ b/elements/elements_ref_element.h @@ -0,0 +1,232 @@ +/***************************************************************************** +© 2020. Triad National Security, LLC. All rights reserved. +This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos +National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. +Department of Energy/National Nuclear Security Administration. All rights in the program are +reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear +Security Administration. The Government is granted for itself and others acting on its behalf a +nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare +derivative works, distribute copies to the public, perform publicly and display publicly, and +to permit others to do so. + + +This program is open source under the BSD-3 License. +Redistribution and use in source and binary forms, with or without modification, are permitted +provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, this list of + conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, this list of + conditions and the following disclaimer in the documentation and/or other materials + provided with the distribution. + + 3. Neither the name of the copyright holder nor the names of its contributors may be used + to endorse or promote products derived from this software without specific prior + written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR +CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; +OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, +WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR +OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF +ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +**********************************************************************************************/ +#ifndef ELEMENTS_REF_ELEMENT_H +#define ELEMENTS_REF_ELEMENT_H +namespace elements { + + // Reference Element Informations + class ref_element{ + private: + + // this assumes i,j,k structured indexing of nodes + const int node_rlid_in_patch_in_cell_[24] = { + // patches in xi-dir + 0,2,6,4, + 1,3,7,5, + // patches in eta-dir + 0,4,5,1, + 2,6,7,3, + // patches in mu-dir + 0,1,3,2, + 4,5,7,6 + }; + + // return the local ref id for the same patch in the cell-patch neighbor + const int patch_rlid_cell_neighbor_[6] = { + 1, // xi left side of my cell + 0, // xi right side of my cell + 3, // eta front side of my cell + 2, // eta bact side of my cell + 5, // mu bottom side of my cell + 4 // mu top side of my cell + }; + + // return the reference coordinate unit normal of the sides in a cell + const real_t cell_side_unit_normals_[18] = { + -1, 0, 0, // xi left side of my cell + 1, 0, 0, // xi right side of my cell + 0,-1, 0, // eta minus side of my cell + 0, 1, 0, // eta plus side of my cell + 0, 0,-1, // mu minus side of my cell + 0, 0, 1 // mu plus side of my cell + }; + + int num_dim_; + + int num_ref_nodes_1D_; + int num_ref_cells_1D_; + int num_ref_corners_1D_; + + int num_ref_surface_nodes_in_elem_; + int num_ref_inside_nodes_in_elem_; + + // Zones + int num_zones_1d_; + int num_zones_in_elem_; + + // cells + int num_ref_cells_in_elem_; + + CArray cells_in_zone_list_; + + // nodes + int num_ref_nodes_in_elem_; + int num_ref_nodes_in_cell_; + + CArray ref_nodes_in_cell_; + CArray ref_surface_nodes_in_elem_; + CArray ref_inside_nodes_in_elem_; + + CArray ref_node_positions_; + CArray ref_node_g_weights_; + + CArray cell_nodes_in_elem_list_; + + // Vertices + int num_ref_verts_1d_; + int num_ref_verts_in_elem_; + + // corners + int num_ref_corners_in_cell_; + int num_ref_corners_in_elem_; + + CArray ref_corners_in_cell_; + + CArray ref_corner_surf_normals_; + CArray ref_corner_g_weights_; + CArray ref_corner_surf_g_weights_; + + // patches and sides + int num_patches_in_elem_; + int num_sides_in_elem_; + + CArray ref_cell_positions_; + CArray ref_cell_g_weights_; + CArray ref_patch_positions_; + CArray ref_patch_g_weights_; + + CArray ref_patches_in_cell_list_; + + CArray ref_patch_basis_; + CArray ref_patch_gradient_; // grad basis at patch + + CArray ref_cell_basis_; + CArray ref_cell_gradient_; // grad basis at cell + + // Num basis functions + int num_basis_; + + // Basis evaluation at nodes + CArray ref_nodal_basis_; + + // Pointer to HexN object + HexN *elem_ptr; + + public: + + // Gradient of basis + CArray ref_nodal_gradient_; + //real_t * ref_nodal_gradient_; + + // Function Declarations + + // Default constructor + ref_element() : elem_ptr(nullptr) {}; + + // Initialize reference element information + void init(int poly_order, int num_dim, HexN &elem); + + int num_dim() const; + + int num_basis() const; + + int num_ref_nodes() const; + + int num_ref_cells_in_elem() const; + int num_ref_corners_in_cell() const; + + // local i,j,k indexing + int node_rid(int i, int j, int k) const; + int cell_rid(int i, int j, int k) const; + int corner_rid(int i, int j, int k) const; + + int ref_corners_in_cell(int cell_rid, int corner_rlid) const; + int ref_nodes_in_cell(int cell_rid, int node_rlid) const; + + int ref_surface_nodes_in_elem(int node_rlid) const; + int ref_inside_nodes_in_elem(int node_rlid) const; + int num_ref_surface_nodes_in_elem() const; + int num_ref_inside_nodes_in_elem() const; + + real_t ref_node_positions(int node_rid, int dim) const; + + real_t ref_corner_surface_normals(int corner_rid, int surf_rlid, int dim) const; + + real_t ref_corner_g_surface_weights(int corner_rid, int surf_rlid) const; + + real_t ref_node_g_weights(int node_rid) const; + + real_t ref_corner_g_weights(int corner_rid) const; + + real_t &ref_nodal_gradient(int node_rid, int basis_id, int dim) const; + + real_t &ref_nodal_basis(int node_rid, int basis_id) const; + + int& cell_lid_in_zone(int zone_lid, int cell_lid) const; + + real_t ref_cell_positions(int cell_rid, int dim) const; + real_t ref_cell_g_weights(int cell_rid) const; + real_t ref_cell_basis(int cell_rid, int basis_id) const; + real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; + + real_t cell_side_unit_normals(int side_rlid, int dim) const; + + int& cell_nodes_in_elem(int cell_lid, int node_lid) const; + + int node_in_patch_in_cell(int patch_lid, int node_lid) const; + + int patch_rlid_in_cell_neighbor(int patch_rlid) const; + + int ref_patches_in_cell(int cell_lid, int patch_rlid) const; + + real_t ref_patch_positions(int patch_rid, int dim) const; + real_t ref_patch_g_weights(int patch_rid) const; + real_t ref_patch_basis(int patch_rid, int basis_id) const; + real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; + + int vert_node_map(int vert_lid); + + // Deconstructor + ~ref_element(); + }; + +} +#endif // ELEMENTS_REF_ELEMENT_H From b630d675c396e365b00c5d737177de490dac463f Mon Sep 17 00:00:00 2001 From: Eric Collins Date: Thu, 9 Jun 2022 17:39:11 -0500 Subject: [PATCH 04/20] Initial stub-code for Kokkos implementations. --- .gitignore | 1 + elements-kokkos/include/HexRef.h | 8 +++++ elements-kokkos/src/HexRef.cpp | 2 ++ swage-kokkos/include/HexMesh.h | 13 +++++++ swage-kokkos/include/vect2d.h | 31 +++++++++++++++++ swage-kokkos/include/vect3d.h | 59 ++++++++++++++++++++++++++++++++ swage-kokkos/include/vect4d.h | 32 +++++++++++++++++ swage-kokkos/src/HexMesh.cpp | 2 ++ 8 files changed, 148 insertions(+) create mode 100644 elements-kokkos/include/HexRef.h create mode 100644 elements-kokkos/src/HexRef.cpp create mode 100644 swage-kokkos/include/HexMesh.h create mode 100644 swage-kokkos/include/vect2d.h create mode 100644 swage-kokkos/include/vect3d.h create mode 100644 swage-kokkos/include/vect4d.h create mode 100644 swage-kokkos/src/HexMesh.cpp diff --git a/.gitignore b/.gitignore index 9c6d4ac1..5b22c08e 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,4 @@ build Trilinos .vscode +*~ diff --git a/elements-kokkos/include/HexRef.h b/elements-kokkos/include/HexRef.h new file mode 100644 index 00000000..b1462b3e --- /dev/null +++ b/elements-kokkos/include/HexRef.h @@ -0,0 +1,8 @@ +#pramga once + +struct HexRef { + + HexRef() { + } + +}; diff --git a/elements-kokkos/src/HexRef.cpp b/elements-kokkos/src/HexRef.cpp new file mode 100644 index 00000000..a4222f02 --- /dev/null +++ b/elements-kokkos/src/HexRef.cpp @@ -0,0 +1,2 @@ +#include + diff --git a/swage-kokkos/include/HexMesh.h b/swage-kokkos/include/HexMesh.h new file mode 100644 index 00000000..4bb5833d --- /dev/null +++ b/swage-kokkos/include/HexMesh.h @@ -0,0 +1,13 @@ +#pragma once + +#include + +struct HexMesh { + enum { ND = 3 }; + + CArrayKokkos cpts; + + HexMesh() { + } + +}; diff --git a/swage-kokkos/include/vect2d.h b/swage-kokkos/include/vect2d.h new file mode 100644 index 00000000..721961bf --- /dev/null +++ b/swage-kokkos/include/vect2d.h @@ -0,0 +1,31 @@ +#pragma once + +template +struct Vector2D { + T x, y; + +public: + Vector2D(T _x=0, T _y=0) + : x(_x), y(_y) { } + +public: + T & operator[](const int idx) { + assert(idx<2); + return (&x)[idx]; + } + const T & operator[](const int idx) const { + assert(idx<2); + return (&x)[idx]; + } + T & operator()(const int idx) { + assert(idx<2); + return (&x)[idx]; + } + const T & operator()(const int idx) const { + assert(idx<2); + return (&x)[idx]; + } +}; + +typedef Vector2D vect2d; +typedef Vector2D vect2f; diff --git a/swage-kokkos/include/vect3d.h b/swage-kokkos/include/vect3d.h new file mode 100644 index 00000000..c601520a --- /dev/null +++ b/swage-kokkos/include/vect3d.h @@ -0,0 +1,59 @@ +#pragma once + +template +struct Vector3D { + T x, y, z; + +public: + Vector3D(T _x=0, T _y=0, T _z=0) + : x(_x), y(_y), z(_z) { } + +public: + T & operator[](const int idx) { + assert(idx<3); + return (&x)[idx]; + } + const T & operator[](const int idx) const { + assert(idx<3); + return (&x)[idx]; + } + T & operator()(const int idx) { + assert(idx<3); + return (&x)[idx]; + } + const T & operator()(const int idx) const { + assert(idx<3); + return (&x)[idx]; + } + +public: + template + Vector3D & operator=(const Vector3D & rhs) { + x = rhs.x; y = rhs.y; z = rhs.z; + return *this; + } + template + Vector3D & operator+=(const Vector3D & rhs) { + x += rhs.x; y += rhs.y; z += rhs.z; + return *this; + } + template + Vector3D & operator-=(const Vector3D & rhs) { + x -= rhs.x; y -= rhs.y; z -= rhs.z; + return *this; + } + template + Vector3D & operator*=(const S & rhs) { + x *= rhs; y *= rhs; z *= rhs; + return *this; + } + template + Vector3D & operator/=(const S & rhs) { + const T den(1.0/rhs); + x *= den; y *= den; z *= den; + return *this; + } +}; + +typedef Vector3D vect3d; +typedef Vector3D vect3f; diff --git a/swage-kokkos/include/vect4d.h b/swage-kokkos/include/vect4d.h new file mode 100644 index 00000000..be821e1a --- /dev/null +++ b/swage-kokkos/include/vect4d.h @@ -0,0 +1,32 @@ +#pragma once + +template +struct Vector4D { + T x, y, z, w; + +public: + Vector4D(T _x=0, T _y=0, T _z=0, T _w=0) + : x(_x), y(_y), z(_z), w(_w) { } + +public: + T & operator[](const int idx) { + assert(idx<4); + return (&x)[idx]; + } + const T & operator[](const int idx) const { + assert(idx<4); + return (&x)[idx]; + } + T & operator()(const int idx) { + assert(idx<4); + return (&x)[idx]; + } + const T & operator()(const int idx) const { + assert(idx<4); + return (&x)[idx]; + } +}; + + +typedef Vector4D vect4d; +typedef Vector4D vect4f; diff --git a/swage-kokkos/src/HexMesh.cpp b/swage-kokkos/src/HexMesh.cpp new file mode 100644 index 00000000..24fb0073 --- /dev/null +++ b/swage-kokkos/src/HexMesh.cpp @@ -0,0 +1,2 @@ +#include + From d0097a63ed06632eee0f783e208ede569061ad48 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Fri, 24 Jun 2022 14:56:06 -0500 Subject: [PATCH 05/20] Beginning consolidation of HexN and ref_element Starting out, all the source for from HexN::setup_HexN and ref_element::init is now in the constructor for HexRef. The basis and basis derivative evaluation routines from HexN have also been ported over. --- elements-kokkos/include/HexRef.h | 266 ++++++- elements-kokkos/include/changelog.md | 12 + elements-kokkos/src/HexRef.cpp | 1054 ++++++++++++++++++++++++++ 3 files changed, 1329 insertions(+), 3 deletions(-) create mode 100644 elements-kokkos/include/changelog.md diff --git a/elements-kokkos/include/HexRef.h b/elements-kokkos/include/HexRef.h index b1462b3e..963b03b2 100644 --- a/elements-kokkos/include/HexRef.h +++ b/elements-kokkos/include/HexRef.h @@ -1,8 +1,268 @@ -#pramga once +#pragma once struct HexRef { + + /* + * BEGIN FORMER REF_ELEMENT MEMBERS + */ + + // this assumes i,j,k structured indexing of nodes + const int node_rlid_in_patch_in_cell_[24] = { + // patches in xi-dir + 0,2,6,4, + 1,3,7,5, + // patches in eta-dir + 0,4,5,1, + 2,6,7,3, + // patches in mu-dir + 0,1,3,2, + 4,5,7,6 + }; + + // return the local ref id for the same patch in the cell-patch neighbor + const int patch_rlid_cell_neighbor_[6] = { + 1, // xi left side of my cell + 0, // xi right side of my cell + 3, // eta front side of my cell + 2, // eta bact side of my cell + 5, // mu bottom side of my cell + 4 // mu top side of my cell + }; + + // return the reference coordinate unit normal of the sides in a cell + const real_t cell_side_unit_normals_[18] = { + -1, 0, 0, // xi left side of my cell + 1, 0, 0, // xi right side of my cell + 0,-1, 0, // eta minus side of my cell + 0, 1, 0, // eta plus side of my cell + 0, 0,-1, // mu minus side of my cell + 0, 0, 1 // mu plus side of my cell + }; + + int num_ref_nodes_1D_; + int num_ref_cells_1D_; + int num_ref_corners_1D_; + + int num_ref_surface_nodes_in_elem_; + int num_ref_inside_nodes_in_elem_; + + // Zones + int num_zones_1d_; + int num_zones_in_elem_; + + // cells + int num_ref_cells_in_elem_; + + CArray cells_in_zone_list_; + + // nodes + int num_ref_nodes_in_elem_; + int num_ref_nodes_in_cell_; + + CArray ref_nodes_in_cell_; + CArray ref_surface_nodes_in_elem_; + CArray ref_inside_nodes_in_elem_; + + CArray ref_node_positions_; + CArray ref_node_g_weights_; + + CArray cell_nodes_in_elem_list_; + + // Vertices + int num_ref_verts_1d_; + int num_ref_verts_in_elem_; + + // corners + int num_ref_corners_in_cell_; + int num_ref_corners_in_elem_; + + CArray ref_corners_in_cell_; + + CArray ref_corner_surf_normals_; + CArray ref_corner_g_weights_; + CArray ref_corner_surf_g_weights_; + + // patches and sides + int num_patches_in_elem_; + int num_sides_in_elem_; + + CArray ref_cell_positions_; + CArray ref_cell_g_weights_; + CArray ref_patch_positions_; + CArray ref_patch_g_weights_; + + CArray ref_patches_in_cell_list_; + + CArray ref_patch_basis_; + CArray ref_patch_gradient_; // grad basis at patch + + CArray ref_cell_basis_; + CArray ref_cell_gradient_; // grad basis at cell + + // Num basis functions + int num_basis_; + + // Basis evaluation at nodes + CArray ref_nodal_basis_; + + // Pointer to HexN object + HexN *elem_ptr; + + // Gradient of basis + CArray ref_nodal_gradient_; + //real_t * ref_nodal_gradient_; + + // Function Declarations + + // Default constructor + ref_element() : elem_ptr(nullptr) {}; + + // Initialize reference element information + void init(int elem_order, HexN &elem); + + int num_dim() const; + + int num_basis() const; + + int num_ref_nodes() const; + + int num_ref_cells_in_elem() const; + int num_ref_corners_in_cell() const; + + // local i,j,k indexing + int node_rid(int i, int j, int k) const; + int cell_rid(int i, int j, int k) const; + int corner_rid(int i, int j, int k) const; + + int ref_corners_in_cell(int cell_rid, int corner_rlid) const; + int ref_nodes_in_cell(int cell_rid, int node_rlid) const; + + int ref_surface_nodes_in_elem(int node_rlid) const; + int ref_inside_nodes_in_elem(int node_rlid) const; + int num_ref_surface_nodes_in_elem() const; + int num_ref_inside_nodes_in_elem() const; + + real_t ref_node_positions(int node_rid, int dim) const; + + real_t ref_corner_surface_normals(int corner_rid, int surf_rlid, int dim) const; + + real_t ref_corner_g_surface_weights(int corner_rid, int surf_rlid) const; - HexRef() { - } + real_t ref_node_g_weights(int node_rid) const; + + real_t ref_corner_g_weights(int corner_rid) const; + + real_t &ref_nodal_gradient(int node_rid, int basis_id, int dim) const; + + real_t &ref_nodal_basis(int node_rid, int basis_id) const; + + int& cell_lid_in_zone(int zone_lid, int cell_lid) const; + + real_t ref_cell_positions(int cell_rid, int dim) const; + real_t ref_cell_g_weights(int cell_rid) const; + real_t ref_cell_basis(int cell_rid, int basis_id) const; + real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; + + real_t cell_side_unit_normals(int side_rlid, int dim) const; + + int& cell_nodes_in_elem(int cell_lid, int node_lid) const; + + int node_in_patch_in_cell(int patch_lid, int node_lid) const; + + int patch_rlid_in_cell_neighbor(int patch_rlid) const; + + int ref_patches_in_cell(int cell_lid, int patch_rlid) const; + + real_t ref_patch_positions(int patch_rid, int dim) const; + real_t ref_patch_g_weights(int patch_rid) const; + real_t ref_patch_basis(int patch_rid, int basis_id) const; + real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; + + int vert_node_map(int vert_lid); + + /* + * END FORMER REF_ELEMENT MEMBERS + */ + + + /* + * BEGIN FORMER HEXN MEMBERS + */ + + const static int num_dim_ = 3; + + // Nodes + int num_nodes_1d_; + int num_nodes_; + + MatarRealCArray HexN_Nodes_1d_; + MatarRealCArray HexN_Nodes_; + + // Vertices + int num_verts_1d_; + int num_verts_; + int num_basis_; + + MatarRealCArray HexN_Verts_1d_; + MatarRealCArray HexN_Verts_; + + MatarUIntCArray Vert_Node_map_; + + int order_; + + void setup_HexN(int elem_order); + + int num_verts(); + int num_nodes(); + int num_basis(); + int node_rid(int i, int j, int k) const; + int vert_rid(int i, int j, int k) const; + + // Return the noda coordinates in reference space + real_t &node_coords(int node_rlid, int dim); + + + int vert_node_map(int vert_rid) const; + + // Evaluate the basis at a given point + void evaluate_basis(MatarRealCArray &basis, MatarRealCArray &point); + + void build_nodal_gradient( + MatarRealCArray &gradient); + + // calculate the partial of the basis w.r.t xi at a given point + void evaluate_derivative_basis_xi( + MatarRealCArray &partial_xi, + MatarRealCArray &point); + + // calculate the partial of the basis w.r.t eta at a given point + void evaluate_derivative_basis_eta( + MatarRealCArray &partial_eta, + MatarRealCArray &point); + + // calculate the partial of the basis w.r.t mu at a given point + void evaluate_derivative_basis_zeta( + MatarRealCArray &partial_mu, + MatarRealCArray &point); + + void lagrange_basis_1D( + MatarRealCArray &interp, // interpolant + const real_t &x_point); // point of interest in element + + void lagrange_derivative_1D( + MatarRealCArray &partials, //derivative + const real_t &x_point); // point of interest in element + + void create_lobatto_nodes(int element_order); + + /* + * END FORMER HEXN MEMBERS + */ + + + HexRef(int elem_order); + ~HexRef(); + + }; diff --git a/elements-kokkos/include/changelog.md b/elements-kokkos/include/changelog.md new file mode 100644 index 00000000..4044aeae --- /dev/null +++ b/elements-kokkos/include/changelog.md @@ -0,0 +1,12 @@ +# Changelog + +Here I'll record changes that I make to the signatures while consolidating `ref_element` and `HexN` into `HexRef`. +I have a feeling this will be useful when I try to get something like the `Average` example or something in Fierro to use the `HexRef` element. + +* `num_dim_` is no longer set in the constructor/initialization routine; it is a static constant of 3 because the Hex element is assumed to be three-dimensional + +* The members `elem_order` and `p_order` have been consolidated into `elem_order` + +* `HexN::basis(...)` is now `HexRef::evaluate_basis(...)` + +* `HexN::partial_xi_basis`, `HexN::partial_eta_basis`, and `HexN::partial_mu_basis` are now `HexRef::evaluate_derivative_basis_xi`, `HexRef::evaluate_derivative_basis_eta`, and `HexRef::evaluate_derivative_basis_zeta` diff --git a/elements-kokkos/src/HexRef.cpp b/elements-kokkos/src/HexRef.cpp index a4222f02..c1a94a96 100644 --- a/elements-kokkos/src/HexRef.cpp +++ b/elements-kokkos/src/HexRef.cpp @@ -1,2 +1,1056 @@ #include +HexRef::HexRef(int elem_order) { + + + /* + * BEGIN ref_element::init source up to call to HexN::setup_HexN + */ + + + elem_ptr = &elem; + + int num_g_pts_1d; + + if(elem_order == 0){ + + num_g_pts_1d = 2; + num_ref_nodes_1D_ = num_g_pts_1d; + num_ref_verts_1d_ = 2; + num_zones_1d_ = 1; + num_zones_in_elem_ = num_zones_1d_*num_zones_1d_*num_zones_1d_; + + cells_in_zone_list_ = CArray (num_zones_in_elem_, 1); + + } + + else{ + + num_g_pts_1d = 2 * elem_order + 1; // num gauss points in 1d + num_ref_nodes_1D_ = num_g_pts_1d; + num_ref_verts_1d_ = elem_order+1; + num_zones_1d_ = (num_ref_nodes_1D_ - 1) / 2; + num_zones_in_elem_ = num_zones_1d_*num_zones_1d_*num_zones_1d_; + + cells_in_zone_list_ = CArray (num_zones_in_elem_, 8); + + + } + + + + num_ref_cells_1D_ = num_ref_nodes_1D_ - 1; + + num_ref_corners_1D_ = 2*(num_ref_nodes_1D_ - 2) + 2; + + + num_ref_nodes_in_elem_ = + num_ref_nodes_1D_*num_ref_nodes_1D_*num_ref_nodes_1D_; + + num_ref_verts_in_elem_ = num_ref_verts_1d_*num_ref_verts_1d_*num_ref_verts_1d_; + + num_ref_cells_in_elem_ = + (num_ref_nodes_1D_-1)*(num_ref_nodes_1D_-1)*(num_ref_nodes_1D_-1); + + std::cout<<"Num cells in element reference = "< (num_ref_cells_in_elem_, 8); + + num_ref_corners_in_cell_ = 8; + + num_ref_corners_in_elem_ = + num_ref_corners_1D_*num_ref_corners_1D_*num_ref_corners_1D_; + + num_basis_ = num_ref_verts_in_elem_; + + + + + + // allocate memory + ref_nodes_in_cell_ = CArray (num_ref_corners_in_elem_); + + ref_corners_in_cell_ = CArray (num_ref_corners_in_elem_); + + ref_corner_g_weights_ = CArray (num_ref_corners_in_elem_); + + ref_corner_surf_g_weights_ = CArray (num_ref_corners_in_elem_, num_dim_); + + ref_corner_surf_normals_ = CArray (num_ref_corners_in_elem_, num_dim_, num_dim_); + + ref_node_positions_ = CArray (num_ref_nodes_in_elem_, num_dim_); + + ref_node_g_weights_ = CArray (num_ref_nodes_in_elem_); + + // Memory for gradients + ref_nodal_gradient_ = CArray (num_ref_nodes_in_elem_, num_basis_, num_dim_); + + // Basis evaluation at the nodes + ref_nodal_basis_ = CArray (num_ref_nodes_in_elem_, num_basis_); + + + + // build reference index spaces + int N_1d = num_ref_nodes_1D_; // a temporary variable + num_ref_inside_nodes_in_elem_ = (N_1d - 2)*(N_1d - 2)*(N_1d - 2); + num_ref_surface_nodes_in_elem_ = N_1d*N_1d*N_1d - num_ref_inside_nodes_in_elem_; + ref_surface_nodes_in_elem_ = CArray (num_ref_surface_nodes_in_elem_); + ref_inside_nodes_in_elem_ = CArray (num_ref_inside_nodes_in_elem_); + + // --- build gauss nodal positions and weights --- + auto lob_nodes_1D = MatarRealCArray(num_ref_nodes_1D_); + lobatto_nodes_1D(lob_nodes_1D, num_ref_nodes_1D_); + + auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); + lobatto_weights_1D(lob_weights_1D, num_ref_nodes_1D_); + + for(int k = 0; k < num_ref_nodes_1D_; k++){ + for(int j = 0; j < num_ref_nodes_1D_; j++){ + for(int i = 0; i < num_ref_nodes_1D_; i++){ + + int n_rid = node_rid(i,j,k); + + ref_node_positions_(n_rid,0) = lob_nodes_1D(i); + ref_node_positions_(n_rid,1) = lob_nodes_1D(j); + ref_node_positions_(n_rid,2) = lob_nodes_1D(k); + + ref_node_g_weights_(n_rid) = lob_weights_1D(i)*lob_weights_1D(j)*lob_weights_1D(k); + } + } + } + + // must partition the nodal guass weights to the corners + auto corner_lob_weights_1D = CArray (num_ref_corners_1D_); + auto r_corner_part_g_weights = CArray (num_ref_corners_in_elem_, num_dim_); + + // loop over interior corners in 1D + corner_lob_weights_1D(0) = lob_weights_1D(0); + + for(int i = 1; i < num_ref_nodes_1D_ - 1; i++){ + + // get the corner_rid index in 1D for the left and right corners + int corner_left = (2*i) - 1; + int corner_right = 2*i; + + // WARNING WARNING WARNING: partitioning using an average + corner_lob_weights_1D(corner_left) = 0.5*lob_weights_1D(i); + corner_lob_weights_1D(corner_right) = 0.5*lob_weights_1D(i); + } + + corner_lob_weights_1D(num_ref_corners_1D_ - 1) = lob_weights_1D(num_ref_nodes_1D_ - 1); + + + // auto corner_lob_weights_1D = CArray (num_ref_corners_1D_); + // auto r_corner_part_g_weights = CArray (num_ref_corners_in_elem_, num_dim_); + + // // use geometric partition + // corner_lob_weights_1D(0) = lob_weights_1D(0); + + // for(int i = 1; i < num_ref_nodes_1D_ - 1; i++){ + + // // get the corner_rid index in 1D for the left and right corners + // int corner_left = (2*i) - 1; + // int corner_right = 2*i; + + // real_t bottom = ((lob_nodes_1D(i+1) - lob_nodes_1D(i))/2.0) + ((lob_nodes_1D(i) - lob_nodes_1D(i-1))/2.0); + + // real_t top = fabs( ((lob_nodes_1D(i) - lob_nodes_1D(i-1))/2.0) ); + + + // std::cout<<"ref 1d node = "< (num_sides_in_elem_); + + + // allocate memory for the 1D Gauss Legendre points and weights + auto leg_points_1D = CArray (num_ref_cells_1D_); + legendre_nodes_1D(leg_points_1D, num_ref_cells_1D_); + + auto leg_weights_1D = CArray (num_ref_cells_1D_); + legendre_weights_1D(leg_weights_1D, num_ref_cells_1D_); + + + // allocate memory for global variables related to Gauss Legendre points and weights + ref_cell_positions_ = CArray (num_ref_cells_in_elem_, 3); + ref_cell_g_weights_ = CArray (num_ref_cells_in_elem_); // this one + ref_patch_positions_ = CArray (num_patches_in_elem_, 3); + ref_patch_g_weights_ = CArray (num_patches_in_elem_); + + + + for (int side_rid = 0; side_rid < num_sides_in_elem_; side_rid++){ + ref_patches_in_cell_list_(side_rid) = -1; + } + + int patch_rid = 0; // the patch reference index + // loop over the cells + for (int k=0; k0){ + neighbor_cell_rid = cell_rid(i-1, j, k); + } // end xi minus direction + else if (side_lid == 1 && i0){ + neighbor_cell_rid = cell_rid(i, j-1, k); + } // end eta minus direction + else if (side_lid == 3 && j0){ + neighbor_cell_rid = cell_rid(i, j, k-1); + } // end mu minus direction + else if (side_lid == 5 && k= 0 && neighbor_cell_rid < num_ref_cells_in_elem_){ + + // get the patch_lid in the neighboring cell for this patch_lid + int neighbor_side_lid = patch_rlid_in_cell_neighbor(side_lid); + + // get the side index of cell for the same patch + int neighbor_side_rid = neighbor_side_lid + (neighbor_cell_rid)*6; // neighboring side index + + // save the patch_rid for this patch in the neighboring cell + ref_patches_in_cell_list_(neighbor_side_rid) = patch_rid; + + } // end if neighboring_cell_rid is valid + + + // increment the patch_rid index + patch_rid ++; + + } // end if the patch was saved + + } // end for sides in a cell + + } // end for i-dir cells + } // end for j-dir cells + } // end for k-dir cells + + std::cout << " patch_rid = " << patch_rid << " num_patches = " << num_patches_in_elem_ << "\n"; + std::cout << " num cells * 6 = " << num_ref_cells_in_elem_*6 << " and num_cells_1D = " << num_ref_cells_1D_ << std::endl; + + + // --- evaluate the Lagrange basis at the patch positions + ref_patch_basis_ = CArray (num_patches_in_elem_, num_ref_verts_in_elem_); + + for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ + + auto point = MatarRealCArray(3); + + // Get the patch coordinates + for(int dim = 0; dim < 3; dim++){ + point(dim) = ref_patch_positions(patch_rlid, dim); + } + + // the basis function values at the patch for each vertex + auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); + + // calculate the patch basis function values at the point, for each vertex + evaluate_basis(patch_basis, point); + + // save the basis values at the patch for each vertex + for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ + ref_patch_basis_(patch_rlid, vert_rlid) = patch_basis(vert_rlid); + } + + } // end for patch_rlid + + + + // --- evaluate grad_basis functions at the ref patches --- + ref_patch_gradient_ = CArray (num_patches_in_elem_, num_basis_, num_dim_); + + // loop over the patches + for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ + + auto point = MatarRealCArray(3); + + // Get the patch coordinates + for(int dim = 0; dim < 3; dim++){ + point(dim) = ref_patch_positions(patch_rlid, dim); + } + + // calculate the partials at the patch location for each vertex + evaluate_derivative_basis_xi(partial_xi, point); + evaluate_derivative_basis_eta(partial_eta, point); + evaluate_derivative_basis_zeta(partial_mu, point); + + // loop over the basis polynomials where there is one from each vertex + for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ + + ref_patch_gradient_(patch_rlid, basis_id, 0) = partial_xi(basis_id); + ref_patch_gradient_(patch_rlid, basis_id, 1) = partial_eta(basis_id); + ref_patch_gradient_(patch_rlid, basis_id, 2) = partial_mu(basis_id); + + partial_xi(basis_id) = 0.0; + partial_eta(basis_id) = 0.0; + partial_mu(basis_id) = 0.0; + } // end for basis_id + + } // end for patch_rlid + + + + // --- evaluate the Lagrange basis at the cell positions + ref_cell_basis_ = CArray (num_ref_cells_in_elem_, num_basis_, num_dim_); + + for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ + + auto point = MatarRealCArray(3); + + // Get the patch coordinates + for(int dim = 0; dim < 3; dim++){ + point(dim) = ref_cell_positions(cell_rlid, dim); + } + + // the basis function values at the patch for each vertex + auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); + + // calculate the cell basis function values at the point, for each vertex + evaluate_basis(cell_basis, point); + + // save the basis values at the patch for each vertex + for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ + ref_cell_basis_(cell_rlid, vert_rlid) = cell_basis(vert_rlid); + } + + } // end for cell_rlid + + + // --- evaluate grad_basis functions at the reference cell --- + ref_cell_gradient_ = CArray (num_ref_cells_in_elem_, num_basis_, num_dim_); + + // loop over the patches + for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ + + auto point = MatarRealCArray(3); + + // Get the cell coordinates + for(int dim = 0; dim < 3; dim++){ + point(dim) = ref_cell_positions_(cell_rlid, dim); + } + + // calculate the partials at the cell location for each vertex + evaluate_derivative_basis_xi(partial_xi, point); + evaluate_derivative_basis_eta(partial_eta, point); + evaluate_derivative_basis_zeta(partial_mu, point); + + // loop over the basis polynomials where there is one from each vertex + for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ + + ref_cell_gradient_(cell_rlid, basis_id, 0) = partial_xi(basis_id); + ref_cell_gradient_(cell_rlid, basis_id, 1) = partial_eta(basis_id); + ref_cell_gradient_(cell_rlid, basis_id, 2) = partial_mu(basis_id); + + partial_xi(basis_id) = 0.0; + partial_eta(basis_id) = 0.0; + partial_mu(basis_id) = 0.0; + } // end for basis_id + + } // end for patch_rlid + + + /* + * END ref_element::init source after call to HexN::setup_HexN + */ + +} + + +HexRef::evaluate_basis(MatarRealCArray &basis, MatarRealCArray &point) { + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); + + // Calculate 1D basis for the X coordinate of the point + lagrange_basis_1D(val_1d, point(0)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + val_3d(i, 0) = val_1d(i); + val_1d(i) = 0.0; + } + + // Calculate 1D basis for the Y coordinate of the point + lagrange_basis_1D(val_1d, point(1)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + val_3d(i, 1) = val_1d(i); + val_1d(i) = 0.0; + } + + // Calculate 1D basis for the Z coordinate of the point + lagrange_basis_1D(val_1d, point(2)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + val_3d(i, 2) = val_1d(i); + val_1d(i) = 0.0; + } + + // Multiply the i, j, k components of the basis from each node + // to get the tensor product basis for the node + for(int k = 0; k < num_verts_1d_; k++){ + for(int j = 0; j < num_verts_1d_; j++){ + for(int i = 0; i < num_verts_1d_; i++){ + + int vert_rlid = vert_rid(i,j,k); + basis(vert_rlid) = val_3d(i, 0)*val_3d(j, 1)*val_3d(k, 2); + } + } + } +} + + +HexRef::evaluate_derivative_basis_xi(MatarRealCArray &partial_xi, + MatarRealCArray &point) { + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); + + auto Dval_1d = MatarRealCArray (num_verts_1d_); + auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); + + // Calculate 1D partial w.r.t. xi for the X coordinate of the point + lagrange_derivative_1D(Dval_1d, point(0)); + + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + Dval_3d(i,0) = Dval_1d(i); + Dval_1d(i) = 0.0; + } + + + // Calculate 1D basis for the Y coordinate of the point + lagrange_basis_1D(val_1d, point(1)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + val_3d(i,1) = val_1d(i); + val_1d(i) = 0.0; + } + + + // Calculate 1D basis for the Z coordinate of the point + lagrange_basis_1D(val_1d, point(2)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + val_3d(i,2) = val_1d(i); + val_1d(i) = 0.0; + } + + // Multiply the i, j, k components of the basis and partial_xi from each node + // to get the tensor product partial derivatives of the basis at each node + for(int k = 0; k < num_verts_1d_; k++){ + for(int j = 0; j < num_verts_1d_; j++){ + for(int i = 0; i < num_verts_1d_; i++){ + + int vert_rlid = vert_rid(i,j,k); + + // Partial w.r.t xi + partial_xi(vert_rlid) = Dval_3d(i, 0)*val_3d(j, 1)*val_3d(k, 2); + + } + } + } +} + + +HexRef::evaluate_derivative_basis_eta(MatarRealCArray &partial_xi, + MatarRealCArray &point) { + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); + + auto Dval_1d = MatarRealCArray (num_verts_1d_); + auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); + + // Calculate 1D basis for the Y coordinate of the point + lagrange_basis_1D(val_1d, point(0)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + val_3d(i,0) = val_1d(i); + val_1d(i) = 0.0; + } + + + // Calculate 1D partial w.r.t. eta for the Y coordinate of the point + lagrange_derivative_1D(Dval_1d, point(1)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + Dval_3d(i,1) = Dval_1d(i); + Dval_1d(i) = 0.0; + } + + + // Calculate 1D basis for the Z coordinate of the point + lagrange_basis_1D(val_1d, point(2)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + val_3d(i,2) = val_1d(i); + val_1d(i) = 0.0; + } + + // Multiply the i, j, k components of the basis and partial_eta from each node + // to get the tensor product partial derivatives of the basis at each node + for(int k = 0; k < num_verts_1d_; k++){ + for(int j = 0; j < num_verts_1d_; j++){ + for(int i = 0; i < num_verts_1d_; i++){ + + int vert_rlid = vert_rid(i,j,k); + + // Partial w.r.t xi + partial_eta(vert_rlid) = val_3d(i, 0)*Dval_3d(j, 1)*val_3d(k, 2); + + } + } + } +} + + +HexRef::evaluate_derivative_basis_zeta(MatarRealCArray &partial_mu, + MatarRealCArray &point) { + auto val_1d = MatarRealCArray (num_verts_1d_); + auto val_3d = MatarRealCArray (num_verts_1d_, 3); + + auto Dval_1d = MatarRealCArray (num_verts_1d_); + auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); + + // Calculate 1D basis for the X coordinate of the point + lagrange_basis_1D(val_1d, point(0)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + val_3d(i,0) = val_1d(i); + val_1d(i) = 0.0; + } + + + // Calculate 1D basis for the Y coordinate of the point + lagrange_basis_1D(val_1d, point(1)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + val_3d(i,1) = val_1d(i); + val_1d(i) = 0.0; + } + + + // Calculate 1D partial w.r.t. mu for the Z coordinate of the point + lagrange_derivative_1D(Dval_1d, point(2)); + + // Save the basis value at the point to a temp array and zero out the temp array + for(int i = 0; i < num_verts_1d_; i++){ + + Dval_3d(i,2) = Dval_1d(i); + val_1d(i) = 0.0; + } + + // Multiply the i, j, k components of the basis and partial_xi from each node + // to get the tensor product partial derivatives of the basis at each node + for(int k = 0; k < num_verts_1d_; k++){ + for(int j = 0; j < num_verts_1d_; j++){ + for(int i = 0; i < num_verts_1d_; i++){ + + int vert_rlid = vert_rid(i,j,k); + + // Partial w.r.t mu + partial_mu(vert_rlid) = val_3d(i, 0)*val_3d(j, 1)*Dval_3d(k, 2); + + } + } + } +} From 757542204367b9f773f17d8b7ac1d6527368bfe3 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Thu, 7 Jul 2022 12:31:47 -0500 Subject: [PATCH 06/20] Building ELEMENTS-Kokkos No compile yet --- CMakeLists.txt | 16 +++++++++++- elements-kokkos/CMakeLists.txt | 3 +++ elements-kokkos/include/HexRef.h | 27 +++++++++++-------- elements-kokkos/include/changelog.md | 6 +++++ elements-kokkos/src/CMakeLists.txt | 39 ++++++++++++++++++++++++++++ elements-kokkos/src/HexRef.cpp | 1 + 6 files changed, 80 insertions(+), 12 deletions(-) create mode 100644 elements-kokkos/CMakeLists.txt create mode 100644 elements-kokkos/src/CMakeLists.txt diff --git a/CMakeLists.txt b/CMakeLists.txt index 6cd2999e..1f158181 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -17,6 +17,7 @@ set(CMAKE_Fortran_FLAGS_RELEASE "${CMAKE_Fortran_FLAGS_RELEASE} ${VECTOR_Fortran set(CMAKE_C_FLAGS_RELEASE "${CMAKE_C_FLAGS_RELEASE} ${VECTOR_C_FLAGS}") set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} ${VECTOR_CXX_FLAGS}") + ################################################################################ # Modules, macros, and packages ################################################################################ @@ -58,8 +59,9 @@ if (MATAR_WITH_KOKKOS) find_package(Kokkos REQUIRED) endif() + ################################################################################ -# Build organization +# ELEMENTS Build ################################################################################ # MATAR submodule # (Note: the way the MATAR submodule is handled may need to change in the @@ -95,6 +97,18 @@ add_subdirectory(examples) # mesh tools add_subdirectory(mesh_tools) + +################################################################################ +# ELEMENTS-Kokkos Build +################################################################################ +if (MATAR_WITH_KOKKOS) + add_subdirectory(elements-kokkos) +endif() + + +################################################################################ +# Installation +################################################################################ # Install headers in include/ subdirectory of the specified install directory # (Note: This is an inelegant way of installing the headers. Resursing through # subdirectories looking for anything that matches the pattern "*.h" is diff --git a/elements-kokkos/CMakeLists.txt b/elements-kokkos/CMakeLists.txt new file mode 100644 index 00000000..debdc8ff --- /dev/null +++ b/elements-kokkos/CMakeLists.txt @@ -0,0 +1,3 @@ +set(ELEMENTS_KOKKOS_INCLUDES ${CMAKE_CURRENT_SOURCE_DIR}/include) + +add_subdirectory(src) diff --git a/elements-kokkos/include/HexRef.h b/elements-kokkos/include/HexRef.h index 963b03b2..33f607fe 100644 --- a/elements-kokkos/include/HexRef.h +++ b/elements-kokkos/include/HexRef.h @@ -1,5 +1,21 @@ #pragma once + +// MATAR includes +#include "matar.h" + + +// Switch between MATAR Kokkos/non-Kokkos data structures, depending on +// availability of Kokkos +#ifdef MATAR_WITH_KOKKOS +typedef CArrayKokkos MatarRealCArray; +typedef CArrayKokkos MatarUIntCArray; +#else +typedef CArray MatarRealCArray; +typedef CArray MatarUIntCArray; +#endif // MATAR_WITH_KOKKOS + + struct HexRef { /* @@ -104,9 +120,6 @@ struct HexRef { // Basis evaluation at nodes CArray ref_nodal_basis_; - - // Pointer to HexN object - HexN *elem_ptr; // Gradient of basis CArray ref_nodal_gradient_; @@ -114,12 +127,6 @@ struct HexRef { // Function Declarations - // Default constructor - ref_element() : elem_ptr(nullptr) {}; - - // Initialize reference element information - void init(int elem_order, HexN &elem); - int num_dim() const; int num_basis() const; @@ -210,8 +217,6 @@ struct HexRef { int order_; - void setup_HexN(int elem_order); - int num_verts(); int num_nodes(); int num_basis(); diff --git a/elements-kokkos/include/changelog.md b/elements-kokkos/include/changelog.md index 4044aeae..1e7448de 100644 --- a/elements-kokkos/include/changelog.md +++ b/elements-kokkos/include/changelog.md @@ -10,3 +10,9 @@ I have a feeling this will be useful when I try to get something like the `Avera * `HexN::basis(...)` is now `HexRef::evaluate_basis(...)` * `HexN::partial_xi_basis`, `HexN::partial_eta_basis`, and `HexN::partial_mu_basis` are now `HexRef::evaluate_derivative_basis_xi`, `HexRef::evaluate_derivative_basis_eta`, and `HexRef::evaluate_derivative_basis_zeta` + + +# Notes + +* Look at SGH code to see what MATAR/Kokkos directives or decorators to use to get HexRef data and functions on the GPU. +Specifically look for `KOKKOS_FUNCTION`, e.g. in [these files](https://github.com/lanl/Fierro/search?q=KOKKOS_FUNCTION), and figure out what it does diff --git a/elements-kokkos/src/CMakeLists.txt b/elements-kokkos/src/CMakeLists.txt new file mode 100644 index 00000000..86e6dd58 --- /dev/null +++ b/elements-kokkos/src/CMakeLists.txt @@ -0,0 +1,39 @@ +add_library( + elements_kokkos + HexRef.cpp +) + +target_compile_definitions( + elements_kokkos + PUBLIC + MATAR_WITH_KOKKOS + HAVE_KOKKOS=1 + HAVE_OPENMP=1 +) + +target_include_directories( + elements_kokkos + PUBLIC + ${ELEMENTS_KOKKOS_INCLUDES} +) + + +if (CUDA) + target_compile_definitions(elements PUBLIC -DHAVE_CUDA=1) +elseif (HIP) + target_compile_definitions(elements PUBLIC -DHAVE_HIP=1) +elseif (OPENMP) + target_compile_definitions(elements PUBLIC -DHAVE_OPENMP=1) +elseif (THREADS) + target_compile_definitions(elements PUBLIC -DHAVE_THREADS=1) +else() + message(FATAL_ERROR "Please specify whether you are using CUDA, HIP, OPENMP, etc.") +endif() + +target_link_libraries( + elements_kokkos + PUBLIC + common + matar + Kokkos::kokkos +) diff --git a/elements-kokkos/src/HexRef.cpp b/elements-kokkos/src/HexRef.cpp index c1a94a96..778fd537 100644 --- a/elements-kokkos/src/HexRef.cpp +++ b/elements-kokkos/src/HexRef.cpp @@ -1,5 +1,6 @@ #include + HexRef::HexRef(int elem_order) { From 43236152962a4a91995756bc97b0bef84dcc8820 Mon Sep 17 00:00:00 2001 From: Steven Walton Date: Thu, 14 Jul 2022 07:24:15 -0600 Subject: [PATCH 07/20] removed inexplicable += from bernstein deriv in HexN --- .../CMakeDirectoryInformation.cmake | 16 + .../CMakeFiles/elements.dir/DependInfo.cmake | 28 + .../elements.dir/bernstein_polynomials.cpp.o | Bin 0 -> 47040 bytes .../bernstein_polynomials.cpp.o.d | 203 ++ elements/CMakeFiles/elements.dir/build.make | 239 ++ .../CMakeFiles/elements.dir/cmake_clean.cmake | 27 + .../elements.dir/cmake_clean_target.cmake | 3 + .../elements.dir/compiler_depend.internal | 2237 +++++++++++++ .../elements.dir/compiler_depend.make | 2762 +++++++++++++++++ .../elements.dir/compiler_depend.ts | 2 + elements/CMakeFiles/elements.dir/depend.make | 2 + .../CMakeFiles/elements.dir/elements.cpp.o | Bin 0 -> 3012512 bytes .../CMakeFiles/elements.dir/elements.cpp.o.d | 203 ++ elements/CMakeFiles/elements.dir/flags.make | 10 + .../gauss_jacobi_quadrature.cpp.o | Bin 0 -> 225872 bytes .../gauss_jacobi_quadrature.cpp.o.d | 208 ++ .../elements.dir/jacobi_polynomials.cpp.o | Bin 0 -> 76464 bytes .../elements.dir/jacobi_polynomials.cpp.o.d | 203 ++ .../elements.dir/lagrange_element.cpp.o | Bin 0 -> 271000 bytes .../elements.dir/lagrange_element.cpp.o.d | 204 ++ .../elements.dir/lagrange_polynomials.cpp.o | Bin 0 -> 168600 bytes .../elements.dir/lagrange_polynomials.cpp.o.d | 203 ++ .../elements.dir/legendre_element.cpp.o | Bin 0 -> 98688 bytes .../elements.dir/legendre_element.cpp.o.d | 204 ++ .../elements.dir/legendre_polynomials.cpp.o | Bin 0 -> 75272 bytes .../elements.dir/legendre_polynomials.cpp.o.d | 204 ++ elements/CMakeFiles/elements.dir/link.txt | 2 + .../elements.dir/point_distributions.cpp.o | Bin 0 -> 70384 bytes .../elements.dir/point_distributions.cpp.o.d | 203 ++ .../CMakeFiles/elements.dir/progress.make | 11 + elements/CMakeFiles/progress.marks | 1 + elements/CMakeLists.txt | 1 + elements/Makefile | 398 +++ elements/bernstein_element.cpp | 168 + elements/bernstein_element.h | 39 + elements/bernstein_polynomials.cpp | 50 + elements/bernstein_polynomials.h | 22 + elements/cmake_install.cmake | 44 + elements/elements.cpp | 259 +- elements/elements.h | 33 +- elements/libelements.a | Bin 0 -> 4064822 bytes 41 files changed, 8165 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+BernsteinElement::BernsteinElement(const SizeType order) : Np( order) { + N = Np + 1; + Ne = std::pow(N, Nd); + + rad[0] = N; + rad[1] = N; + rad[2] = N; + + //Allocate memory for intermediate coefficients + C = new NumType[2*N]; +} + +template +BernsteinElement::~BernsteinElement() { } + + +template +NumType BernsteinElement::eval_basis(const SizeType I, const NumType *X) { + //Decompose index of 3D tensor product basis function into indices of Bernstein polynomials + common::base_10_to_mixed_radix(Nd, rad, I, ijk); + + // Evaluate Bernstein polynomials + NumType Bi = bernstein::eval(N, int(ijk[0]), X[0]); + NumType Bj = bernstein::eval(N, int(ijk[1]), X[1]); + NumType Bk = bernstein::eval(N, int(ijk[2]), X[2]); + + return Bi*Bj*Bk; +} + +template +void BernsteinElement::eval_grad_basis(const SizeType I, const NumType *X, NumType *grad_phi) { + // Decompose index of 3D tensor product basis function into indices of Bernstein polynomials + + common::base_10_to_mized_radix(Nd, rad, I, ijk); + + // Evaluate Bernstein polynomials + NumType Bi = bernstein::eval(N, int(ijk[0]), X[0]); + NumType Bj = bernstein::eval(N, int(ijk[1]), X[1]); + NumType Bk = bernstein::eval(N, int(ijk[2]), X[2]); + + // Evaluate derivatives of Bernstein polynomials + NumType dBi = bernstein::eval_der(N, int(ijk[0]), X[0]); + NumType dBj = bernstein::eval_der(N, int(ijk[1]), X[1]); + NumType dBk = bernstein::eval_der(N, int(ijk[2]), X[2]); + + // Store partial derivatives in entries of gradient + grad_phi[0] = dBi*Bj*Bk; + grad_phi[1] = Bi*dBj*Bk; + grad_phi[3] = Bi*Bj*dBk; +} + +/* Return evaluation of local function approximation */ + +template +NumType BernsteinElement::eval_approx(const NumType *c, const NumType *X) { + for (int k = 0, k < N; k++) { + for (int j = 0; j < N; j++){ + // Collapse first dimension into coefficients for second dimension + C[j] = bernstein::eval_approx(N, &c[j*N+k*N*N], X[0]); + } + // Collapse second dimension into coefficients for third dimension + C[N+k] = bernstein::eval_approx(N, &C[N], X[2]); + } + // Collapse third dimension into approximation evaluation + return bernstein::eval_approx(N, &C[N], X[2]); +} + +/* Evaluate gradient of local function approximation, which is formed by the sum of the products of tensor-product Bernstein basis functions and the provided coefficients, at specified coordinates. */ +template +void BernsteinElement::eval_grad_approx(const NumType *c, const NumType *X, NumType *grad_f) { + for (int l = 0; l < Nd; l++) { + for (int k =0; k < N; k++) { + for (int j =0; j < N; j++) { + //Collapse first dimension into coefficients for second dimension + if (l==0) { + C[j] = bernstein::eval_der_approx(N, &c[j*N+k*N*N], X[0]); + } else { + C[j] = bernstein::eval_approx(N, &c[j*N+k*N*N], X[0]); + } + } + // Collapse second dimension into coefficients for third dimension + if ( l == 1) { + C[N+k] = bernstein::eval_der_approx(N, &C[N], X[2]); + } else { + C[N+k] = bernstein::eval_approx(N, C, X[1]); + } + } + + // Collapse third dimension into approximation evaluation + if ( l ==2 ) { + grad_f[l] = bernstein::eval_der_approx(N, &C[N], X[2]); + } else { + grad_f[l] = bernstein::eval_approx(N, &C[N], X[2]); + } + } +} + + +////////////////* Evaluate the Jacobian of the spatial mapping *//////////////////////// + +/* x, y, z in physical space. X in reference space. J = Jacobian (column major). */ + +template +void BernsteinElement::eval_jac(const NumType *x, const NumType *y, + const NumType *z, const NumType *X, NumType *J) { + // Evaluate gradient of x=x(X,Y,Z); + this->eval_grad_approx(x,X,J); + + // Evaluate gradient of y=y(X,Y,Z); + this->eval_grad_approx(y,X,J+3); + + // Evaluate gradient of z=z(X,Y,Z); + this->eval_grad_approx(z,X,J+6); +} + + +//////////////* Determinant of Jacobian *///////////////////////// + +/* x, y, z in physical space. X in reference space. */ + +template +NumType BernsteinElement::eval_det_jac(const NumType *x, const NumType *y, + const NumType *z, const NumType *X) { + NumType J[9]; + this->eval_jac(x, y, z, X, J); + + return J[0]*(J[4]*J[8]-J[5]*J[7]) - J[1]*(J[3]*J[8]-J[5]*J[6]) + J[2]*(J[3]*J[7]-J[4]*J[6]); +} + + +//////////////* Inverse Jacobian *////////////////////////////// + +/* x, y, z in physical space. X in reference space. Jinv = Invers Jacobian (column-major). */ + +template +void BernsteinElement::eval_inv_jac(const NumType *x, const Numtype *y, + const NumType *z, const NumType *X, NumType *Jinv) { + + // instantiate jacobian // + NumType J[9]; + + // get jacobian // + this->eval_jac(x,y,z,X,J); + + // invert determinant of J // + NumType d = 1.0/(this->eval_det_jac(x,y,z,X)); + + // get Jinv (Jinv = adj(J)/det(J) ) // + Jinv[0] = d*(J[4]*J[8]-J[5]*J[7]); + Jinv[1] = -d*(J[1]*J[8]-J[2]*J[7]); + Jinv[2] = d*(J[1]*J[5]-J[2]*J[4]); + Jinv[3] = -d*(J[3]*J[8]-J[5]*J[6]); + Jinv[4] = d*(J[0]*J[8]-J[2]*J[6]); + Jinv[5] = -d*(J[0]*J[5]-J[2]*J[3]); + Jinv[6] = d*(J[3]*J[7]-J[4]*J[6]); + Jinv[7] = -d*(J[0]*J[7]-J[1]*J[6]); + Jinv[8] = d*(J[0]*J[4]-J[1]*J[3]); +} + + +//////////////// Explicit instantiation of template class ////////////////////// +template class BernsteinElement; +template class BernsteinElement; diff --git a/elements/bernstein_element.h b/elements/bernstein_element.h new file mode 100644 index 00000000..e73ccb09 --- /dev/null +++ b/elements/bernstein_element.h @@ -0,0 +1,39 @@ +#pragma once + +#include "common.h" + +template +struct BernsteinElement { + // Element specifications // + static const SizeType Nd = 3; + SizeType Np; + SizeType N; + SizeType Ne; + + // Arrays for converting from flat to multidimensional indices// + SizeType ijk[Nd]; + SizeType rad[Nd]; + + // Work array for intermediate coefficients // + NumType *C; + + BernsteinElement(const SizeType); + ~BernsteinElement(); + + // Basis functions and basis function gradients// + NumType eval_basis(const SizeType, const NumType *); + void eval_grad_basis(const SizeType, const NumType *, NumType *); + + // Function approximation over element // + NumType eval_approx(const NumType *, const NumType *); + void eval_grad_approx(const NumType *, const NumType *, NumType *); + + // Jacobian of spatial mapping // + void eval_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); + + NumType eval_det_jac(const NumType *, const NumType *, const NumType *, const NumType *); + + void eval_inv_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); +}; diff --git a/elements/bernstein_polynomials.cpp b/elements/bernstein_polynomials.cpp new file mode 100644 index 00000000..0db1c057 --- /dev/null +++ b/elements/bernstein_polynomials.cpp @@ -0,0 +1,50 @@ +#include "bernstein_polynomials.h" + + +namespace bernstein { + template + NumType eval( const int n, const int v, const NumType X) { + if ( n == 0 && v != 0 ) return 0; + if ( n == 0 && v == 0 ) return 1; + if ( n < v ) return 0; + return 0.5*((1-double(X))*eval(n-1, v, X) + (1+double(X))*eval(n-1, v-1, X)); + }; + template + NumType eval_der( const int n, const int v, const NumType X) { + if ( n == 0) return 0; + if ( n < v) return 0; + if ( n == 1 && v == 0) return -0.5; + if ( n == 1 && v == 1) return 0.5; + return 0.5*( (1-double(X))*eval_der(n-1,v, X) + (1+double(X))*eval_der(n-1, v-1, X) + eval(n-1, v-1, X) - eval(n-1, v, X) ) ; + }; + + template + NumType eval_approx(const SizeType N, const NumType *c, const NumType X) { + NumType sum = 0.0; + for (SizeType j = 0; j < N; j++) { + sum += c[j]*eval(N, j, X); + } + return sum; + } + + template + NumType eval_der_approx(const SizeType N, const NumType *c, const NumType X) { + NumType sum = 0.0; + for (SizeType j = 0; j < N; j ++) { + sum += c[j]*eval_der( N, j, X); + } + return sum; + }; + + template Real eval(const int n, const int v, const Real X); + + + template Real eval_der(const int n, const int v, const Real X); + + + template Real eval_approx(const SizeType N, const Real *c, const Real X); + + + template Real eval_der_approx(const SizeType N, const Real *c, const Real X); + +} diff --git a/elements/bernstein_polynomials.h b/elements/bernstein_polynomials.h new file mode 100644 index 00000000..1f9de1e4 --- /dev/null +++ b/elements/bernstein_polynomials.h @@ -0,0 +1,22 @@ +#pragma once + +#include "common.h" + +// Bernstein polynomial of order n: +// B(n,v) = (0.5)^n * (C^n_v) * (1-x)^(n-v) * (1+x)^v +// for x \in [-1, 1] + +namespace bernstein{ + // Bernstein polynomials + // n is the order, v is the "index", X \in [-1, 1] + template NumType eval(const int n, const int v, const NumType X); + + template NumType eval_der(const int n, const int v, const NumType X); + + //Bernstein Approximations + template + NumType eval_approx(const SizeType N, const NumType *c, const NumType X); + + template + NumType eval_der_approx(const SizeType N, const NumType *c, const NumType X); +} diff --git a/elements/cmake_install.cmake b/elements/cmake_install.cmake new file mode 100644 index 00000000..09866067 --- /dev/null +++ b/elements/cmake_install.cmake @@ -0,0 +1,44 @@ +# Install script for directory: /home/xirhotopi/Fierro/Elements/elements + +# Set the install prefix +if(NOT DEFINED CMAKE_INSTALL_PREFIX) + set(CMAKE_INSTALL_PREFIX "/usr/local") +endif() +string(REGEX REPLACE "/$" "" CMAKE_INSTALL_PREFIX "${CMAKE_INSTALL_PREFIX}") + +# Set the install configuration name. +if(NOT DEFINED CMAKE_INSTALL_CONFIG_NAME) + if(BUILD_TYPE) + string(REGEX REPLACE "^[^A-Za-z0-9_]+" "" + CMAKE_INSTALL_CONFIG_NAME "${BUILD_TYPE}") + else() + set(CMAKE_INSTALL_CONFIG_NAME "RelWithDebInfo") + endif() + message(STATUS "Install configuration: \"${CMAKE_INSTALL_CONFIG_NAME}\"") +endif() + +# Set the component getting installed. +if(NOT CMAKE_INSTALL_COMPONENT) + if(COMPONENT) + message(STATUS "Install component: \"${COMPONENT}\"") + set(CMAKE_INSTALL_COMPONENT "${COMPONENT}") + else() + set(CMAKE_INSTALL_COMPONENT) + endif() +endif() + +# Install shared libraries without execute permission? +if(NOT DEFINED CMAKE_INSTALL_SO_NO_EXE) + set(CMAKE_INSTALL_SO_NO_EXE "1") +endif() + +# Is this installation the result of a crosscompile? +if(NOT DEFINED CMAKE_CROSSCOMPILING) + set(CMAKE_CROSSCOMPILING "FALSE") +endif() + +# Set default install directory permissions. +if(NOT DEFINED CMAKE_OBJDUMP) + set(CMAKE_OBJDUMP "/usr/bin/objdump") +endif() + diff --git a/elements/elements.cpp b/elements/elements.cpp index ec546b01..0625adca 100644 --- a/elements/elements.cpp +++ b/elements/elements.cpp @@ -55,6 +55,7 @@ ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #include "utilities.h" #include "elements.h" +#include "bernstein_polynomials.h" #define EPSILON 1.0e-12 @@ -2645,8 +2646,9 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } auto node_basis = CArray (num_ref_verts_in_elem_); - - elem.basis(node_basis, point); + + //elem.basis(node_basis,point); + elem.bernstein_basis(node_basis, point); for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ @@ -2672,10 +2674,13 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ for(int dim = 0; dim < 3; dim++){ point(dim) = ref_node_positions_(node_lid, dim); } - - elem.partial_xi_basis(partial_xi, point); - elem.partial_eta_basis(partial_eta, point); - elem.partial_mu_basis(partial_mu, point); + + //elem.partial_xi_basis(partial_xi,point); + elem.bernstein_partial_xi_basis(partial_xi, point); + //elem.partial_eta_basis(partial_eta, point); + elem.bernstein_partial_eta_basis(partial_eta, point); + //elem.partial_mu_basis(partial_mu, point); + elem.bernstein_partial_mu_basis(partial_mu, point); for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ @@ -2917,7 +2922,8 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ auto patch_basis = CArray (num_ref_verts_in_elem_); // calculate the patch basis function values at the point, for each vertex - elem.basis(patch_basis, point); + elem.bernstein_basis(patch_basis, point); + //elem.basis(patch_basis, point); // save the basis values at the patch for each vertex for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ @@ -2942,10 +2948,13 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // calculate the partials at the patch location for each vertex - elem.partial_xi_basis(partial_xi, point); - elem.partial_eta_basis(partial_eta, point); - elem.partial_mu_basis(partial_mu, point); - + elem.bernstein_partial_xi_basis(partial_xi, point); + //elem.partial_xi_basis(partial_xi, point); + elem.bernstein_partial_eta_basis(partial_eta, point); + //elem.partial_eta_basis(partial_eta, point); + elem.bernstein_partial_mu_basis(partial_mu, point); + //elem.partial_mu_basis(partial_mu, point); + // loop over the basis polynomials where there is one from each vertex for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ @@ -2978,8 +2987,9 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ auto cell_basis = CArray (num_ref_verts_in_elem_); // calculate the cell basis function values at the point, for each vertex - elem.basis(cell_basis, point); - + elem.bernstein_basis(cell_basis, point); + //elem.basis(cell_basis, point); + // save the basis values at the patch for each vertex for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ ref_cell_basis_(cell_rlid, vert_rlid) = cell_basis(vert_rlid); @@ -3002,10 +3012,13 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // calculate the partials at the cell location for each vertex - elem.partial_xi_basis(partial_xi, point); - elem.partial_eta_basis(partial_eta, point); - elem.partial_mu_basis(partial_mu, point); - + elem.bernstein_partial_xi_basis(partial_xi, point); + elem.bernstein_partial_eta_basis(partial_eta, point); + elem.bernstein_partial_mu_basis(partial_mu, point); + //elem.partial_xi_basis(partial_xi, point); + //elem.partial_eta_basis(partial_eta, point); + //elem.partial_mu_basis(partial_mu, point); + // loop over the basis polynomials where there is one from each vertex for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ @@ -4018,7 +4031,7 @@ void QuadN::lagrange_1D( } // end of Legrange_1D function -// Corners of Lagrange element for mapping +// Corners of Lagrange element for mappintein_basis void QuadN::corners ( ViewCArray &lag_nodes, // Nodes of Lagrange elements ViewCArray &lag_corner, // corner nodes of QuadN element @@ -5754,7 +5767,7 @@ representative linear element for visualization } // end looping over nodes != vert_i - // writing value to vectors for later use + // writing value to vectors for later use interp(vert_i) = interpolant; // Interpolant value at given point } // end loop over all nodes @@ -5771,10 +5784,10 @@ representative linear element for visualization real_t num_gradient = 0.0; // placeholder for numerator of the gradient real_t gradient = 0.0; - for(int vert_j = 0; vert_j < num_verts_1d_; vert_j++){ + //for(int vert_j = 0; vert_j < num_verts_1d_; vert_j++){ // std::cout<<"HexN 1D Vert "< (num_ref_nodes_in_elem_, num_dim_); + ref_node_g_weights_ = CArray (num_ref_nodes_in_elem_); - // allocate memory - ref_nodes_in_cell_ = CArray (num_ref_corners_in_elem_); - - ref_corners_in_cell_ = CArray (num_ref_corners_in_elem_); - + ref_corners_in_cell_ = MatarIntCArray (num_ref_corners_in_elem_); ref_corner_g_weights_ = CArray (num_ref_corners_in_elem_); - ref_corner_surf_g_weights_ = CArray (num_ref_corners_in_elem_, num_dim_); - ref_corner_surf_normals_ = CArray (num_ref_corners_in_elem_, num_dim_, num_dim_); - - ref_node_positions_ = CArray (num_ref_nodes_in_elem_, num_dim_); - - ref_node_g_weights_ = CArray (num_ref_nodes_in_elem_); - // Memory for gradients - ref_nodal_gradient_ = CArray (num_ref_nodes_in_elem_, num_basis_, num_dim_); + ref_nodes_in_cell_ = MatarIntCArray(num_ref_corners_in_elem_); - // Basis evaluation at the nodes ref_nodal_basis_ = CArray (num_ref_nodes_in_elem_, num_basis_); + ref_nodal_gradient_ = CArray (num_ref_nodes_in_elem_, num_basis_, num_dim_); + ref_surface_nodes_in_elem_ = MatarIntCArray(num_ref_surface_nodes_in_elem_); + ref_inside_nodes_in_elem_ = MatarIntCArray(num_ref_inside_nodes_in_elem_); - // build reference index spaces - int N_1d = num_ref_nodes_1D_; // a temporary variable - num_ref_inside_nodes_in_elem_ = (N_1d - 2)*(N_1d - 2)*(N_1d - 2); - num_ref_surface_nodes_in_elem_ = N_1d*N_1d*N_1d - num_ref_inside_nodes_in_elem_; - ref_surface_nodes_in_elem_ = CArray (num_ref_surface_nodes_in_elem_); - ref_inside_nodes_in_elem_ = CArray (num_ref_inside_nodes_in_elem_); - - // --- build gauss nodal positions and weights --- + /* Populate arrays containing quadrature points and weights */ auto lob_nodes_1D = MatarRealCArray(num_ref_nodes_1D_); lobatto_nodes_1D(lob_nodes_1D, num_ref_nodes_1D_); auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); lobatto_weights_1D(lob_weights_1D, num_ref_nodes_1D_); - for(int k = 0; k < num_ref_nodes_1D_; k++){ - for(int j = 0; j < num_ref_nodes_1D_; j++){ - for(int i = 0; i < num_ref_nodes_1D_; i++){ + for (int k = 0; k < num_ref_nodes_1D_; k++){ + for (int j = 0; j < num_ref_nodes_1D_; j++){ + for (int i = 0; i < num_ref_nodes_1D_; i++){ int n_rid = node_rid(i,j,k); @@ -120,9 +89,13 @@ HexRef::HexRef(int elem_order) { } } - // must partition the nodal guass weights to the corners - auto corner_lob_weights_1D = CArray (num_ref_corners_1D_); - auto r_corner_part_g_weights = CArray (num_ref_corners_in_elem_, num_dim_); + /* + * BEGIN ref_element::init source up to call to HexN::setup_HexN + */ + + // must partition the nodal gauss weights to the corners + auto corner_lob_weights_1D = CArray (num_ref_corners_1D_); + auto r_corner_part_g_weights = CArray (num_ref_corners_in_elem_, num_dim_); // loop over interior corners in 1D corner_lob_weights_1D(0) = lob_weights_1D(0); @@ -140,45 +113,7 @@ HexRef::HexRef(int elem_order) { corner_lob_weights_1D(num_ref_corners_1D_ - 1) = lob_weights_1D(num_ref_nodes_1D_ - 1); - - // auto corner_lob_weights_1D = CArray (num_ref_corners_1D_); - // auto r_corner_part_g_weights = CArray (num_ref_corners_in_elem_, num_dim_); - - // // use geometric partition - // corner_lob_weights_1D(0) = lob_weights_1D(0); - - // for(int i = 1; i < num_ref_nodes_1D_ - 1; i++){ - - // // get the corner_rid index in 1D for the left and right corners - // int corner_left = (2*i) - 1; - // int corner_right = 2*i; - - // real_t bottom = ((lob_nodes_1D(i+1) - lob_nodes_1D(i))/2.0) + ((lob_nodes_1D(i) - lob_nodes_1D(i-1))/2.0); - - // real_t top = fabs( ((lob_nodes_1D(i) - lob_nodes_1D(i-1))/2.0) ); - - - // std::cout<<"ref 1d node = "< &cheb_nodes_1D, // Chebyshev nodes + CArray &cheb_nodes_1D, // Chebyshev nodes (changed to CArray from ViewCArray --steven ) const int &order){ // Interpolation order real_t pi = 3.14159265358979323846; @@ -2647,8 +2647,11 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ auto node_basis = CArray (num_ref_verts_in_elem_); - //elem.basis(node_basis,point); - elem.bernstein_basis(node_basis, point); + #ifdef bern + elem.bernstein_basis(node_basis, point); + #else + elem.basis(node_basis, point); + #endif for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ @@ -2675,12 +2678,16 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ point(dim) = ref_node_positions_(node_lid, dim); } - //elem.partial_xi_basis(partial_xi,point); - elem.bernstein_partial_xi_basis(partial_xi, point); - //elem.partial_eta_basis(partial_eta, point); - elem.bernstein_partial_eta_basis(partial_eta, point); - //elem.partial_mu_basis(partial_mu, point); - elem.bernstein_partial_mu_basis(partial_mu, point); + + #ifdef bern + elem.bernstein_partial_xi_basis(partial_xi, point); + elem.bernstein_partial_eta_basis(partial_eta, point); + elem.bernstein_partial_mu_basis(partial_mu, point); + #else + elem.partial_xi_basis(partial_xi, point); + elem.partial_eta_basis(partial_eta, point); + elem.partial_mu_basis(partial_mu, point); + #endif for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ @@ -2922,9 +2929,13 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ auto patch_basis = CArray (num_ref_verts_in_elem_); // calculate the patch basis function values at the point, for each vertex - elem.bernstein_basis(patch_basis, point); - //elem.basis(patch_basis, point); - + + #ifdef bern + elem.bernstein_basis(patch_basis, point); + #else + elem.basis(patch_basis, point); + #endif + // save the basis values at the patch for each vertex for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ ref_patch_basis_(patch_rlid, vert_rlid) = patch_basis(vert_rlid); @@ -2948,12 +2959,16 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // calculate the partials at the patch location for each vertex - elem.bernstein_partial_xi_basis(partial_xi, point); - //elem.partial_xi_basis(partial_xi, point); - elem.bernstein_partial_eta_basis(partial_eta, point); - //elem.partial_eta_basis(partial_eta, point); - elem.bernstein_partial_mu_basis(partial_mu, point); - //elem.partial_mu_basis(partial_mu, point); + + #ifdef bern + elem.bernstein_partial_xi_basis(partial_xi, point); + elem.bernstein_partial_eta_basis(partial_eta, point); + elem.bernstein_partial_mu_basis(partial_mu, point); + #else + elem.partial_xi_basis(partial_xi, point); + elem.partial_eta_basis(partial_eta, point); + elem.partial_mu_basis(partial_mu, point); + #endif // loop over the basis polynomials where there is one from each vertex for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ @@ -2987,8 +3002,11 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ auto cell_basis = CArray (num_ref_verts_in_elem_); // calculate the cell basis function values at the point, for each vertex - elem.bernstein_basis(cell_basis, point); - //elem.basis(cell_basis, point); + #ifdef bern + elem.bernstein_basis(cell_basis, point); + #else + elem.basis(cell_basis, point); + #endif // save the basis values at the patch for each vertex for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ @@ -3012,12 +3030,15 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // calculate the partials at the cell location for each vertex - elem.bernstein_partial_xi_basis(partial_xi, point); - elem.bernstein_partial_eta_basis(partial_eta, point); - elem.bernstein_partial_mu_basis(partial_mu, point); - //elem.partial_xi_basis(partial_xi, point); - //elem.partial_eta_basis(partial_eta, point); - //elem.partial_mu_basis(partial_mu, point); + #ifdef bern + elem.bernstein_partial_xi_basis(partial_xi, point); + elem.bernstein_partial_eta_basis(partial_eta, point); + elem.bernstein_partial_mu_basis(partial_mu, point); + #else + elem.partial_xi_basis(partial_xi, point); + elem.partial_eta_basis(partial_eta, point); + elem.partial_mu_basis(partial_mu, point); + #endif // loop over the basis polynomials where there is one from each vertex for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ @@ -5822,65 +5843,6 @@ representative linear element for visualization } // end loop over all nodes } // end of Legrange_1D function - void HexN::create_lobatto_nodes(int element_order){ - - int num_nodes_1d = 0; - int num_nodes_3d = 0; - - if( element_order == 0){ - - num_nodes_1d = 2; - num_nodes_3d = pow(num_nodes_1d, 3); - - } - - else{ - num_nodes_1d = 2.0 * element_order + 1; - num_nodes_3d = pow(num_nodes_1d, 3); - } - - // --- build gauss nodal positions and weights --- - // std::cout<< "Num Nodes passed to create lobatto nodes "< &basis, CArray &point) { @@ -6069,7 +6031,7 @@ representative linear element for visualization // calculate the basis value associated with each node_i for( int vert_i = 0; vert_i < num_verts_1d_; vert_i++){ - interp(vert_i) = bernstein::eval(num_verts_1d_- 1, vert_i, point); + interp(vert_i) = bernstein::eval(num_verts_1d_-1, vert_i, point); } }//end of bernstein_basis_1D @@ -6079,11 +6041,71 @@ representative linear element for visualization const real_t &point){ for( int vert_i = 0; vert_i < num_verts_1d_; vert_i++){ - derivative(vert_i) = bernstein::eval_der(num_verts_1d_- 1, vert_i, point); + derivative(vert_i) = bernstein::eval_der(num_verts_1d_-1, vert_i, point); } }// end of bernstein_derivative_1D +void HexN::create_lobatto_nodes(int element_order){ + + int num_nodes_1d = 0; + int num_nodes_3d = 0; + + if( element_order == 0){ + + num_nodes_1d = 2; + num_nodes_3d = pow(num_nodes_1d, 3); + + } + + else{ + num_nodes_1d = 2.0 * element_order + 1; + num_nodes_3d = pow(num_nodes_1d, 3); + } + + // --- build gauss nodal positions and weights --- + // std::cout<< "Num Nodes passed to create lobatto nodes "< &cheb_nodes_1D, // Chebyshev nodes + CArray &cheb_nodes_1D, // Chebyshev nodes (changed to CArray from ViewCArray --steven) const int &order); // Interpolation order diff --git a/tests/test_bernstein_polynomials.cpp b/tests/test_bernstein_polynomials.cpp new file mode 100644 index 00000000..14c16cd5 --- /dev/null +++ b/tests/test_bernstein_polynomials.cpp @@ -0,0 +1,209 @@ +#include "bernstein_polynomials.h" +#include "point_distributions.h" + +#include +#include + +// Test Parameters +template +struct TestParams { + SizeType Np; + SizeType N; + + NumType X; + NumType *c; + + TestParams(SizeType order){ + Np = order; + N = Np + 1; + + // Generating coefficients for bernstein polynomial expansion + c = new NumType[N]; + for (SizeType i = 0; i &p){ + Real tol = 1e-15; + + bool pass = false; + + Real sum1 = 0.0; + for (SizeType i = 0; i < p.N; i++){ + Real Bi = bernstein::eval(p.N, i, p.X); + sum1 += p.c[i]*Bi; + }; + + Real sum2 = bernstein::eval_approx(p.N, p.c, p.X); + + Real rel_error = common::abs((sum1-sum2)/sum1); + + if (rel_error < tol ){ + pass = true; + } + else{ + std::cout << "Test 1, error: " << rel_error << std::endl; + } + + return pass; +}; + +// Test 2: Checking consistency of the first derivative of the polynomials with derivative of the Bernstein Approximation + +bool test2(TestParams &p) { + Real tol = 1e-15; + + bool pass = false; + Real sum1 = 0.0; + + for (SizeType i = 0; i < p.N; i++) { + Real dBi = bernstein::eval_der(p.N, i, p.X); + sum1 += p.c[i]*dBi; + } + + Real sum2 = bernstein::eval_der_approx(p.N, p.c, p.X); + + Real rel_error = common::abs((sum1 - sum2)/sum1); + + if (rel_error < tol) { + pass = true; + } + else { + std::cout << "Test 2, error: " << rel_error << std::endl; + } + + return pass; +} + +// Test 3: This test ensures the a property of the bernstein polynomials where the +// the sum of the nth degree polynomials from v equals 0 to n-1 is equal to 1. + +bool test3(TestParams &p){ + Real tol = 1e-15; + bool pass = false; + + // Establishes random number between -1 and 1 to use for each Bernstein test + Real Zl = -1.0; + Real Zr = 1.0; + + Real rand_X = Zl + (Zr - Zl)*Real(rand())/Real(RAND_MAX); + + // Sums bernstein polynomials at value rand_X + Real sum = 0.0; + for (SizeType i = 0; i < p.N; i++) { + sum += bernstein::eval(p.N, i, rand_X); + } + Real error = common::abs( sum - 1 ); + if (error< tol) { + pass = true; + } + else { + std::cout << "Test 3, error: " << error << std::endl; + } + + return pass; +} + +// Test 4: Checks for the positivity of the Bernstein polynomials generated by the code + +bool test4(TestParams &p){ + + bool pass = false; + SizeType NumTests = 1000; + for ( SizeType i = 0; i < NumTests + 1; i ++){ + + Real Zl = -1.0; + Real Zr = 1.0; + + Real rand_X = Zl + (Zr - Zl)*Real(rand())/Real(RAND_MAX); + for (SizeType j=0; j < p.N; j++){ + Real val = bernstein::eval(p.N, j, rand_X); + if (0 <= val){ + pass = true; + } + else { + std::cout << "Test 4 Error: At least one of the values tested is negative" << std::endl; + } + } + } + return pass; +} + +bool test5(TestParams &p){ + Real tol = 1e-15; + bool pass = false; + + Real Zl = -1.0; + Real Zr = 1.0; + + Real rand_X = Zl + (Zr - Zl)*Real(rand())/Real(RAND_MAX); + + //Sums bernstein polynomial derivatives at value rand_X + Real sum = 0.0; + for (SizeType i = 0; i < p.N; i++) { + sum += bernstein::eval_der(p.N, i, rand_X); + } + Real error = common::abs( sum ); + if (error< tol) { + pass = true; + } + else { + std::cout << "Test 3, error: " << error << std::endl; + } + return pass; +} + + int main(){ + std::cout.precision(15); + + std::cout << "TEST BERNSTEIN POLYNOMIALS\n" + <<"----------------------------" + << std::endl; + + // Initialize Random Seed + srand(time(NULL)); + + // Generate the Parameters + TestParams rp(8); + + // Run Test 1 + bool pass1 = test1(rp); + std::cout << "Test 1 " << (pass1 ? "PASSED" : "FAILED") << std::endl; + + // Run Test 2 + bool pass2 = test2(rp); + std::cout << "Test 2 " << (pass2 ? "PASSED" : "FAILED") << std::endl; + + // Run Test 3 + bool pass3 = test3(rp); + std::cout << "Test 3 " << (pass3 ? "PASSED" : "FAILED") << std::endl; + + // Run Test 4 + bool pass4 = test4(rp); + std::cout << "Test 4 " << (pass4 ? "PASSED" : "FAILED") << std::endl; + bool pass5 = test5(rp); + std::cout << "Test 5 " << (pass5 ? "PASSED" : "FAILED") << std::endl; + + std::cout << std::endl; + std::cout << "PASSED " + << int(pass1) + int(pass2) + int(pass3) + int(pass4) + int(pass5) + << "/5" << std::endl; + + return 0; + + } + + + From 747e107ec89b29f1fbfe10c30029c453668838ce Mon Sep 17 00:00:00 2001 From: steven-t-walton Date: Mon, 29 Aug 2022 15:21:39 -0600 Subject: [PATCH 10/20] " " --- .../elements.dir/bernstein_polynomials.cpp.o | Bin 47040 -> 47040 bytes .../bernstein_polynomials.cpp.o.d | 1 + .../elements.dir/compiler_depend.internal | 9 +++++++ .../elements.dir/compiler_depend.make | 23 +++++++++++++----- .../CMakeFiles/elements.dir/elements.cpp.o | Bin 3012512 -> 3013744 bytes .../CMakeFiles/elements.dir/elements.cpp.o.d | 1 + .../gauss_jacobi_quadrature.cpp.o | Bin 225872 -> 225864 bytes .../gauss_jacobi_quadrature.cpp.o.d | 1 + .../elements.dir/jacobi_polynomials.cpp.o | Bin 76464 -> 76464 bytes .../elements.dir/jacobi_polynomials.cpp.o.d | 1 + .../elements.dir/lagrange_element.cpp.o | Bin 271000 -> 271000 bytes .../elements.dir/lagrange_element.cpp.o.d | 1 + .../elements.dir/lagrange_polynomials.cpp.o | Bin 168600 -> 168600 bytes .../elements.dir/lagrange_polynomials.cpp.o.d | 1 + .../elements.dir/legendre_element.cpp.o | Bin 98688 -> 98688 bytes .../elements.dir/legendre_element.cpp.o.d | 1 + .../elements.dir/legendre_polynomials.cpp.o | Bin 75272 -> 75272 bytes .../elements.dir/legendre_polynomials.cpp.o.d | 1 + .../elements.dir/point_distributions.cpp.o | Bin 70384 -> 70384 bytes .../elements.dir/point_distributions.cpp.o.d | 1 + .../CMakeFiles/elements.dir/progress.make | 20 +++++++-------- elements/libelements.a | Bin 4064822 -> 4066042 bytes tests/CMakeLists.txt | 10 ++++++++ 23 files changed, 55 insertions(+), 16 deletions(-) diff --git a/elements/CMakeFiles/elements.dir/bernstein_polynomials.cpp.o b/elements/CMakeFiles/elements.dir/bernstein_polynomials.cpp.o index 22cd8f850344134d315a4f1f6f3086b1450c3e19..2a673e9d9b26b43ea73404424f28462df4212a0a 100644 GIT binary patch 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/usr/include/x86_64-linux-gnu/bits/stdlib-bsearch.h \ diff --git a/elements/CMakeFiles/elements.dir/compiler_depend.internal b/elements/CMakeFiles/elements.dir/compiler_depend.internal index 4dc8028a..5583afc2 100644 --- a/elements/CMakeFiles/elements.dir/compiler_depend.internal +++ b/elements/CMakeFiles/elements.dir/compiler_depend.internal @@ -66,6 +66,7 @@ Elements/elements/CMakeFiles/elements.dir/bernstein_polynomials.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/alloca.h @@ -352,6 +353,7 @@ Elements/elements/CMakeFiles/elements.dir/elements.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/x86_64-linux-gnu/bits/setjmp.h @@ -564,6 +566,7 @@ Elements/elements/CMakeFiles/elements.dir/gauss_jacobi_quadrature.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/alloca.h @@ -815,6 +818,7 @@ Elements/elements/CMakeFiles/elements.dir/jacobi_polynomials.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/alloca.h @@ -1062,6 +1066,7 @@ Elements/elements/CMakeFiles/elements.dir/lagrange_element.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/alloca.h @@ -1310,6 +1315,7 @@ Elements/elements/CMakeFiles/elements.dir/lagrange_polynomials.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/alloca.h @@ -1557,6 +1563,7 @@ Elements/elements/CMakeFiles/elements.dir/legendre_element.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/alloca.h @@ -1805,6 +1812,7 @@ Elements/elements/CMakeFiles/elements.dir/legendre_polynomials.cpp.o /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h /usr/include/x86_64-linux-gnu/bits/struct_mutex.h /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h /usr/include/alloca.h @@ -2053,6 +2061,7 @@ 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/usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h \ /usr/include/x86_64-linux-gnu/bits/struct_mutex.h \ /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h \ /usr/include/alloca.h \ @@ -350,6 +351,7 @@ Elements/elements/CMakeFiles/elements.dir/elements.cpp.o: Elements/elements/elem /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h \ /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h \ /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h \ + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h \ /usr/include/x86_64-linux-gnu/bits/struct_mutex.h \ /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h \ /usr/include/x86_64-linux-gnu/bits/setjmp.h \ @@ -561,6 +563,7 @@ Elements/elements/CMakeFiles/elements.dir/gauss_jacobi_quadrature.cpp.o: Element /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h \ /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h \ /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h \ + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h \ /usr/include/x86_64-linux-gnu/bits/struct_mutex.h \ /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h \ /usr/include/alloca.h \ @@ -811,6 +814,7 @@ Elements/elements/CMakeFiles/elements.dir/jacobi_polynomials.cpp.o: Elements/ele /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h \ /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h \ /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h \ + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h \ /usr/include/x86_64-linux-gnu/bits/struct_mutex.h \ /usr/include/x86_64-linux-gnu/bits/struct_rwlock.h \ /usr/include/alloca.h \ @@ -1057,6 +1061,7 @@ Elements/elements/CMakeFiles/elements.dir/lagrange_element.cpp.o: Elements/eleme /usr/include/x86_64-linux-gnu/bits/pthreadtypes.h \ /usr/include/x86_64-linux-gnu/bits/thread-shared-types.h \ /usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h \ + /usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h \ /usr/include/x86_64-linux-gnu/bits/struct_mutex.h \ 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z_~+yn`p?PI(uP!1tHbhus8;*(dKh^#hUv|pmIuiT;!>jKRB59;a8#bBStw7b)OXDV zg|+h3y+V09oji3|1aAeVz{_v z+p3tc*u(Agpr7m?CjZSgZ5wsIT}KU{ueUhuJljT{KQB-H>a*=U+eV#Vp67hM6>sO+ zR{f=p-SF7bQ_cVD=Wx=z;dGqrC<~8eJ>K5)Pn5hmPNUA}`gp%s&Q;b$2Ye`5{pPRj zPt>&Id!_u(SO2_}&t>h@`qh@X{s)EStN*Qb*1t{8&sV=Z zUEQT{{V^e2|0lv+{XTp4uU!wb`OXfo{y&lfu71ma?Ml=i?teX(>(}{Pw(vyt%t=1Jz z#|g+Me-Y&WOb4hWwIB6=Rz@%-|E>O%u>I*zZMgobi25%a< z&o-Bo_)ni&N8x~EcgeOlM4X?#(C5?nDV*#)+x{5mhx6#?^*EooooD=40uGQJntp@v+I6v8zVkOj{+)CJ?FRo1Qu=|3 diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt index bedfa95e..399ebf49 100644 --- a/tests/CMakeLists.txt +++ b/tests/CMakeLists.txt @@ -76,3 +76,13 @@ if (ENABLE_BLAS_LAPACK) ${LAPACK_LIBRARIES} ) endif() + +#test Bernstein polynomials +add_executable( + test_bernstein_polynomials + test_bernstein_polynomials.cpp +) +target_link_libraries( + test_bernstein_polynomials + elements +) From 2a6c4615c2213121f5bc2ea800f5ac066e5d15ec Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Thu, 8 Sep 2022 17:29:43 -0500 Subject: [PATCH 11/20] Reorganization of HexRef; progress on constructor - Interface is more or less set - Data structures holding quadrature points in "cells" and on "patches" - Still need to finish data structures holding evaluations of basis functions and their gradients in "cells" and on "patches" --- elements-kokkos/include/HexRef.h | 298 ++----- elements-kokkos/src/HexRef.cpp | 1251 +++++++----------------------- 2 files changed, 345 insertions(+), 1204 deletions(-) diff --git a/elements-kokkos/include/HexRef.h b/elements-kokkos/include/HexRef.h index 1a370419..e17fa17d 100644 --- a/elements-kokkos/include/HexRef.h +++ b/elements-kokkos/include/HexRef.h @@ -19,267 +19,89 @@ typedef CArray MatarIntCArray; enum BasisType { - LAGRANGE, - LEGENDRE, - BEZIER -}; - - -enum QuadratureType { - GAUSS_LOBATTO, - GAUSS_LEGENDRE + LAGRANGE, + LEGENDRE, + BEZIER }; struct HexRef { + HexRef(int order_basis, BasisType type_basis); + ~HexRef(); - /* - * BEGIN FORMER REF_ELEMENT MEMBERS - */ - - // this assumes i,j,k structured indexing of nodes - const int node_rlid_in_patch_in_cell_[24] = { - // patches in xi-dir - 0,2,6,4, - 1,3,7,5, - // patches in eta-dir - 0,4,5,1, - 2,6,7,3, - // patches in zeta-dir - 0,1,3,2, - 4,5,7,6 - }; - - // return the local ref id for the same patch in the cell-patch neighbor - const int patch_rlid_cell_neighbor_[6] = { - 1, // xi left side of my cell - 0, // xi right side of my cell - 3, // eta front side of my cell - 2, // eta bact side of my cell - 5, // zeta bottom side of my cell - 4 // zeta top side of my cell - }; - - // return the reference coordinate unit normal of the sides in a cell - const real_t cell_side_unit_normals_[18] = { - -1, 0, 0, // xi left side of my cell - 1, 0, 0, // xi right side of my cell - 0,-1, 0, // eta minus side of my cell - 0, 1, 0, // eta plus side of my cell - 0, 0,-1, // zeta minus side of my cell - 0, 0, 1 // zeta plus side of my cell - }; - - int num_ref_nodes_1D_; - int num_ref_cells_1D_; - int num_ref_corners_1D_; - - int num_ref_surface_nodes_in_elem_; - int num_ref_inside_nodes_in_elem_; - - // Zones - int num_zones_1d_; - int num_zones_in_elem_; - - // cells - int num_ref_cells_in_elem_; - - MatarIntCArray cells_in_zone_list_; - - // nodes - int num_ref_nodes_in_elem_; - int num_ref_nodes_in_cell_; - - MatarIntCArray ref_nodes_in_cell_; - MatarIntCArray ref_surface_nodes_in_elem_; - MatarIntCArray ref_inside_nodes_in_elem_; - - CArray ref_node_positions_; - CArray ref_node_g_weights_; - - MatarIntCArray cell_nodes_in_elem_list_; - - // Vertices - int num_ref_verts_1d_; - int num_ref_verts_in_elem_; - - // corners - int num_ref_corners_in_cell_; - int num_ref_corners_in_elem_; - - MatarIntCArray ref_corners_in_cell_; - - CArray ref_corner_surf_normals_; - CArray ref_corner_g_weights_; - CArray ref_corner_surf_g_weights_; - - // patches and sides - int num_patches_in_elem_; - int num_sides_in_elem_; - - CArray ref_cell_positions_; - CArray ref_cell_g_weights_; - CArray ref_patch_positions_; - CArray ref_patch_g_weights_; - - MatarIntCArray ref_patches_in_cell_list_; - - CArray ref_patch_basis_; - CArray ref_patch_gradient_; // grad basis at patch - - CArray ref_cell_basis_; - CArray ref_cell_gradient_; // grad basis at cell - - // Num basis functions - int num_basis_; - - // Basis evaluation at nodes - CArray ref_nodal_basis_; - - // Gradient of basis - CArray ref_nodal_gradient_; - //real_t * ref_nodal_gradient_; - - // Function Declarations - - int num_dim() const; - - int num_basis() const; - - int num_ref_nodes() const; - - int num_ref_cells_in_elem() const; - int num_ref_corners_in_cell() const; - - // local i,j,k indexing - int node_rid(int i, int j, int k) const; - int cell_rid(int i, int j, int k) const; - int corner_rid(int i, int j, int k) const; - - int ref_corners_in_cell(int cell_rid, int corner_rlid) const; - int ref_nodes_in_cell(int cell_rid, int node_rlid) const; - - int ref_surface_nodes_in_elem(int node_rlid) const; - int ref_inside_nodes_in_elem(int node_rlid) const; - int num_ref_surface_nodes_in_elem() const; - int num_ref_inside_nodes_in_elem() const; - - real_t ref_node_positions(int node_rid, int dim) const; - - real_t ref_corner_surface_normals(int corner_rid, int surf_rlid, int dim) const; - - real_t ref_corner_g_surface_weights(int corner_rid, int surf_rlid) const; - - real_t ref_node_g_weights(int node_rid) const; - - real_t ref_corner_g_weights(int corner_rid) const; - - real_t &ref_nodal_gradient(int node_rid, int basis_id, int dim) const; - - real_t &ref_nodal_basis(int node_rid, int basis_id) const; - - int& cell_lid_in_zone(int zone_lid, int cell_lid) const; - - real_t ref_cell_positions(int cell_rid, int dim) const; - real_t ref_cell_g_weights(int cell_rid) const; - real_t ref_cell_basis(int cell_rid, int basis_id) const; - real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; - - real_t cell_side_unit_normals(int side_rlid, int dim) const; - - int& cell_nodes_in_elem(int cell_lid, int node_lid) const; - - int node_in_patch_in_cell(int patch_lid, int node_lid) const; - - int patch_rlid_in_cell_neighbor(int patch_rlid) const; - - int ref_patches_in_cell(int cell_lid, int patch_rlid) const; - - real_t ref_patch_positions(int patch_rid, int dim) const; - real_t ref_patch_g_weights(int patch_rid) const; - real_t ref_patch_basis(int patch_rid, int basis_id) const; - real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; - - int vert_node_map(int vert_lid); - /* - * END FORMER REF_ELEMENT MEMBERS - */ + // Cells (subelements used in volume integration) + int num_ref_cells_1D_; + int num_ref_cells_in_elem() const; + int cell_rid(int i, int j, int k) const; - /* - * BEGIN FORMER HEXN MEMBERS - */ - - const static int num_dim_ = 3; + MatarRealCArray ref_cell_positions_; + real_t ref_cell_positions(int cell_rid, int dim) const; - // Nodes - int num_nodes_1d_; - int num_nodes_; + MatarRealCArray ref_cell_g_weights_; + real_t ref_cell_g_weights(int cell_rid) const; - MatarRealCArray HexN_Nodes_1d_; - MatarRealCArray HexN_Nodes_; - // Vertices - int num_verts_1d_; - int num_verts_; - int num_basis_; + // Patches (subelement faces used in surface integration) + int num_patches_in_elem_; + int num_sides_in_elem_; - MatarRealCArray HexN_Verts_1d_; - MatarRealCArray HexN_Verts_; + const int patch_rlid_cell_neighbor_[6] = { + 1, // side in neighbor cell mated with -xi side in this cell + 0, // side in neighbor cell mated with +xi side in this cell + 3, // side in neighbor cell mated with -eta side in this cell + 2, // side in neighbor cell mated with +eta side in this cell + 5, // side in neighbor cell mated with -zeta side in this cell + 4 // side in neighbor cell mated with +zeta side in this cell + }; + int patch_rlid_in_cell_neighbor(int patch_rlid) const; - MatarUIntCArray Vert_Node_map_; - - int order_; + MatarIntCArray ref_patches_in_cell_list_; + int ref_patches_in_cell(int cell_lid, int patch_rlid) const; - int num_verts(); - int num_nodes(); - int num_basis(); - int node_rid(int i, int j, int k) const; - int vert_rid(int i, int j, int k) const; + MatarRealCArray ref_patch_positions_; + real_t ref_patch_positions(int patch_rid, int dim) const; - // Return the noda coordinates in reference space - real_t &node_coords(int node_rlid, int dim); + MatarRealCArray ref_patch_g_weights_; + real_t ref_patch_g_weights(int patch_rid) const; + const real_t cell_side_unit_normals_[18] = { + -1, 0, 0, // -xi + 1, 0, 0, // +xi + 0, -1, 0, // -eta + 0, 1, 0, // +eta + 0, 0, -1, // -zeta + 0, 0, 1 // +zeta + }; + real_t cell_side_unit_normals(int side_rlid, int dim) const; - int vert_node_map(int vert_rid) const; - - // Evaluate the basis at a given point - void evaluate_basis(MatarRealCArray &basis, MatarRealCArray &point); - void build_nodal_gradient( - MatarRealCArray &gradient); + // Nodes (quadrature points) and vertices (degrees of freedom) + int num_ref_nodes_in_elem_; + int num_ref_nodes() const; - // calculate the partial of the basis w.r.t xi at a given point - void evaluate_derivative_basis_xi( - MatarRealCArray &partial_xi, - MatarRealCArray &point); + int num_ref_verts_1D_; + int num_ref_verts_in_elem_; - // calculate the partial of the basis w.r.t eta at a given point - void evaluate_derivative_basis_eta( - MatarRealCArray &partial_eta, - MatarRealCArray &point); - // calculate the partial of the basis w.r.t zeta at a given point - void evaluate_derivative_basis_zeta( - MatarRealCArray &partial_zeta, - MatarRealCArray &point); + // Evaluations of basis functions and their gradients at quadrature points + // in cells and on patches + static const int num_dim_ = 3; + int num_dim() const; - void lagrange_basis_1D( - MatarRealCArray &interp, // interpolant - const real_t &x_point); // point of interest in element - - void lagrange_derivative_1D( - MatarRealCArray &partials, //derivative - const real_t &x_point); // point of interest in element + int num_basis_; + int num_basis() const; + + MatarRealCArray ref_cell_basis_; + real_t ref_cell_basis(int cell_rid, int basis_id) const; - void create_lobatto_nodes(int element_order); + MatarRealCArray ref_cell_gradient_; + real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; - /* - * END FORMER HEXN MEMBERS - */ - + MatarRealCArray ref_patch_basis_; + real_t ref_patch_basis(int patch_rid, int basis_id) const; - HexRef(int orderBasis, BasisType typeBasis, QuadratureType typeQuad, bool verbose); - ~HexRef(); + MatarRealCArray ref_patch_gradient_; + real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; }; diff --git a/elements-kokkos/src/HexRef.cpp b/elements-kokkos/src/HexRef.cpp index c06180f8..cb3fea38 100644 --- a/elements-kokkos/src/HexRef.cpp +++ b/elements-kokkos/src/HexRef.cpp @@ -1,991 +1,310 @@ -#include - -HexRef::HexRef(int orderBasis, BasisType typeBasis=LAGRANGE, - QuadratureType typeQuad=GAUSS_LOBATTO, bool verbose=false) { - - /* Determine sizes of data structures based on the order of the basis */ - int numGaussPts1d = 2; - if(orderBasis == 0){ - numGaussPts1d = 2; - - num_ref_nodes_1D_ = numGaussPts1d; - num_ref_verts_1d_ = 2; - num_zones_1d_ = 1; - - cells_in_zone_list_ = MatarIntCArray(num_zones_in_elem_, 1); - } else if (orderBasis > 0) { - numGaussPts1d = 2*orderBasis + 1; - - num_ref_nodes_1D_ = numGaussPts1d; - num_ref_verts_1d_ = orderBasis+1; - num_zones_1d_ = (num_ref_nodes_1D_ - 1) / 2; - - cells_in_zone_list_ = MatarIntCArray(num_zones_in_elem_, 8); - } else { - std::cout << "Error: element order must be positive" << std::endl; - } - - num_ref_cells_1D_ = num_ref_nodes_1D_ - 1; - num_ref_corners_1D_ = 2*(num_ref_nodes_1D_ - 2) + 2; - - num_zones_in_elem_ = num_zones_1d_*num_zones_1d_*num_zones_1d_; - num_ref_nodes_in_elem_ = num_ref_nodes_1D_*num_ref_nodes_1D_*num_ref_nodes_1D_; - num_ref_verts_in_elem_ = num_ref_verts_1d_*num_ref_verts_1d_*num_ref_verts_1d_; - num_ref_cells_in_elem_ = num_ref_cells_1D_*num_ref_cells_*num_ref_cells_1D; - - if (verbose) { - std::cout << "Num cells in reference element: " - << num_ref_cells_in_elem_ - << std::endl; - } - - cell_nodes_in_elem_list_ = MatarIntCArray (num_ref_cells_in_elem_, 8); - num_ref_corners_in_cell_ = 8; - num_ref_corners_in_elem_ = num_ref_corners_1D_*num_ref_corners_1D_*num_ref_corners_1D_; - num_basis_ = num_ref_verts_in_elem_; - - num_ref_inside_nodes_in_elem_ = (num_ref_nodes_1D_ - 2)*(num_ref_nodes_1D_ - 2)*(num_ref_nodes_1D_ - 2); - num_ref_surface_nodes_in_elem_ = num_ref_nodes_1D_*num_ref_nodes_1D_*num_ref_nodes_1D_ - num_ref_inside_nodes_in_elem_; - - - /* Allocate arrays */ - - ref_node_positions_ = CArray (num_ref_nodes_in_elem_, num_dim_); - ref_node_g_weights_ = CArray (num_ref_nodes_in_elem_); - - ref_corners_in_cell_ = MatarIntCArray (num_ref_corners_in_elem_); - ref_corner_g_weights_ = CArray (num_ref_corners_in_elem_); - ref_corner_surf_g_weights_ = CArray (num_ref_corners_in_elem_, num_dim_); - ref_corner_surf_normals_ = CArray (num_ref_corners_in_elem_, num_dim_, num_dim_); - - ref_nodes_in_cell_ = MatarIntCArray(num_ref_corners_in_elem_); - - ref_nodal_basis_ = CArray (num_ref_nodes_in_elem_, num_basis_); - ref_nodal_gradient_ = CArray (num_ref_nodes_in_elem_, num_basis_, num_dim_); - - ref_surface_nodes_in_elem_ = MatarIntCArray(num_ref_surface_nodes_in_elem_); - ref_inside_nodes_in_elem_ = MatarIntCArray(num_ref_inside_nodes_in_elem_); - - - /* Populate arrays containing quadrature points and weights */ - auto lob_nodes_1D = MatarRealCArray(num_ref_nodes_1D_); - lobatto_nodes_1D(lob_nodes_1D, num_ref_nodes_1D_); - - auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); - lobatto_weights_1D(lob_weights_1D, num_ref_nodes_1D_); - - for (int k = 0; k < num_ref_nodes_1D_; k++){ - for (int j = 0; j < num_ref_nodes_1D_; j++){ - for (int i = 0; i < num_ref_nodes_1D_; i++){ - - int n_rid = node_rid(i,j,k); - - ref_node_positions_(n_rid,0) = lob_nodes_1D(i); - ref_node_positions_(n_rid,1) = lob_nodes_1D(j); - ref_node_positions_(n_rid,2) = lob_nodes_1D(k); - - ref_node_g_weights_(n_rid) = lob_weights_1D(i)*lob_weights_1D(j)*lob_weights_1D(k); - } - } - } - - /* - * BEGIN ref_element::init source up to call to HexN::setup_HexN - */ - - // must partition the nodal gauss weights to the corners - auto corner_lob_weights_1D = CArray (num_ref_corners_1D_); - auto r_corner_part_g_weights = CArray (num_ref_corners_in_elem_, num_dim_); - - // loop over interior corners in 1D - corner_lob_weights_1D(0) = lob_weights_1D(0); - - for(int i = 1; i < num_ref_nodes_1D_ - 1; i++){ - - // get the corner_rid index in 1D for the left and right corners - int corner_left = (2*i) - 1; - int corner_right = 2*i; - - // WARNING WARNING WARNING: partitioning using an average - corner_lob_weights_1D(corner_left) = 0.5*lob_weights_1D(i); - corner_lob_weights_1D(corner_right) = 0.5*lob_weights_1D(i); - } - - corner_lob_weights_1D(num_ref_corners_1D_ - 1) = lob_weights_1D(num_ref_nodes_1D_ - 1); - - if(orderBasis == 0){ - - cell_lid_in_zone(0, 0) = 0; - } - - else{ - // Save the Cell_lid to the zones - int zone_rid = 0; - for(int k = 0; k < num_zones_1d_; k++){ - for(int j = 0; j < num_zones_1d_; j++){ - for(int i = 0; i < num_zones_1d_; i++){ - - - cell_lid_in_zone(zone_rid, 0) = cell_rid(2*i , 2*j , 2*k ); - cell_lid_in_zone(zone_rid, 1) = cell_rid(2*i+1, 2*j , 2*k ); - cell_lid_in_zone(zone_rid, 2) = cell_rid(2*i , 2*j+1, 2*k ); - cell_lid_in_zone(zone_rid, 3) = cell_rid(2*i+1, 2*j+1, 2*k ); - cell_lid_in_zone(zone_rid, 4) = cell_rid(2*i , 2*j , 2*k+1); - cell_lid_in_zone(zone_rid, 5) = cell_rid(2*i+1, 2*j , 2*k+1); - cell_lid_in_zone(zone_rid, 6) = cell_rid(2*i , 2*j+1, 2*k+1); - cell_lid_in_zone(zone_rid, 7) = cell_rid(2*i+1, 2*j+1, 2*k+1); - - zone_rid++; - } - } - } - - } - - // Save the node in cell lid to node rid in elem map - int cell_lid = 0; - int num_ref_cells_1d = (num_ref_nodes_1D_-1); - for(int k = 0; k < num_ref_cells_1d; k++){ - for(int j = 0; j < num_ref_cells_1d; j++){ - for(int i = 0; i < num_ref_cells_1d; i++){ - - cell_nodes_in_elem(cell_lid, 0) = node_rid(i , j, k); - cell_nodes_in_elem(cell_lid, 1) = node_rid(i+1, j, k); - cell_nodes_in_elem(cell_lid, 2) = node_rid(i , j+1, k); - cell_nodes_in_elem(cell_lid, 3) = node_rid(i+1, j+1, k); - cell_nodes_in_elem(cell_lid, 4) = node_rid(i , j, k+1); - cell_nodes_in_elem(cell_lid, 5) = node_rid(i+1, j, k+1); - cell_nodes_in_elem(cell_lid, 6) = node_rid(i , j+1, k+1); - cell_nodes_in_elem(cell_lid, 7) = node_rid(i+1, j+1, k+1); - - cell_lid++; - } - } - } - - // i,j,k indicies are for corners - for(int k = 0; k < num_ref_corners_1D_; k++){ - for(int j = 0; j < num_ref_corners_1D_; j++){ - for(int i = 0; i < num_ref_corners_1D_; i++){ - - int crn_rid = corner_rid(i, j, k); // the ref space id - - r_corner_part_g_weights(crn_rid, 0) = corner_lob_weights_1D(i); - r_corner_part_g_weights(crn_rid, 1) = corner_lob_weights_1D(j); - r_corner_part_g_weights(crn_rid, 2) = corner_lob_weights_1D(k); - - ref_corner_g_weights_(crn_rid) = - corner_lob_weights_1D(i)*corner_lob_weights_1D(j)*corner_lob_weights_1D(k); - - } - } - } // end loop over i,j,k for corners in element - - - - // --- build corners --- - auto unit_normals = CArray (num_ref_corners_in_cell_, num_dim_); - - set_unit_normals(unit_normals); - - - // loop over the cells in the elem (i,j,k are ref cell indices) - int index = 0; // index = num_cells*num_corners_in_cell + corner_lid - for(int k = 0; k < num_ref_cells_1D_; k++){ - for(int j = 0; j < num_ref_cells_1D_; j++){ - for(int i = 0; i < num_ref_cells_1D_; i++){ - - int corner_rid_in_cell_0 = 2*i + 2*(num_ref_corners_1D_)*j - + 2*(num_ref_corners_1D_)*(num_ref_corners_1D_)*k; - - // loop over the corners in the cell - int corner_rlid = 0; - for(int k_rlid = 0; k_rlid < 2; k_rlid++){ - for(int j_rlid = 0; j_rlid < 2; j_rlid++){ - for(int i_rlid = 0; i_rlid < 2; i_rlid++){ - - // calculate the reference corner index from the rlid's - int crn_rid = corner_rid_in_cell_0 - + i_rlid + (num_ref_corners_1D_)*j_rlid - + (num_ref_corners_1D_)*(num_ref_corners_1D_)*k_rlid; - - ref_corners_in_cell_(index) = crn_rid; // save the rid - - // node ref index - ref_nodes_in_cell_(index) = node_rid(i + i_rlid, j + j_rlid, k + k_rlid); - int n_rid = node_rid(i + i_rlid, j + j_rlid, k + k_rlid); - - - // 3 surfaces vectors in each ref corner that have 3 components - real_t surf_vec0[3] = {unit_normals(corner_rlid,0), 0.0, 0.0}; // s_0 - real_t surf_vec1[3] = {0.0, unit_normals(corner_rlid,1), 0.0}; // s_1 - real_t surf_vec2[3] = {0.0, 0.0, unit_normals(corner_rlid,2)}; // s_2 - - - // surface unit normal 0 and surface quadrature 0 - int surf_rlid = 0; - for(int dim = 0; dim < num_dim_; dim++){ - ref_corner_surf_normals_(crn_rid, surf_rlid, dim) = surf_vec0[dim]; - } - - // power coef is =1 for the quadrature values for the surf normal else =0 - ref_corner_surf_g_weights_(crn_rid, surf_rlid) = - pow( r_corner_part_g_weights(crn_rid, 0), (1.0 - fabs(surf_vec0[0])) ) - * pow( r_corner_part_g_weights(crn_rid, 1), (1.0 - fabs(surf_vec0[1])) ) - * pow( r_corner_part_g_weights(crn_rid, 2), (1.0 - fabs(surf_vec0[2])) ); - - - surf_rlid = 1; - - for(int dim = 0; dim < num_dim_; dim++){ - ref_corner_surf_normals_(crn_rid, surf_rlid, dim) = surf_vec1[dim]; - } - - // power coef is =1 for the quadrature values for the surf normal else =0 - ref_corner_surf_g_weights_(crn_rid, surf_rlid) = - pow( r_corner_part_g_weights(crn_rid, 0), (1.0 - fabs(surf_vec1[0])) ) - * pow( r_corner_part_g_weights(crn_rid, 1), (1.0 - fabs(surf_vec1[1])) ) - * pow( r_corner_part_g_weights(crn_rid, 2), (1.0 - fabs(surf_vec1[2])) ); - - surf_rlid = 2; - - for (int dim = 0; dim < num_dim_; dim++){ - ref_corner_surf_normals_(crn_rid, surf_rlid, dim) = surf_vec2[dim]; - } - - // power coef is =1 for the quadrature values for the surf normal else =0 - ref_corner_surf_g_weights_(crn_rid, surf_rlid) = - pow( r_corner_part_g_weights(crn_rid, 0), (1.0 - fabs(surf_vec2[0])) ) - * pow( r_corner_part_g_weights(crn_rid, 1), (1.0 - fabs(surf_vec2[1])) ) - * pow( r_corner_part_g_weights(crn_rid, 2), (1.0 - fabs(surf_vec2[2])) ); - - - index++; // increment the index in the ref element - corner_rlid++; // increment the corner index in the ref cell - - } - } - } // end of loop over corners in ref cell - } - } - } // end of loop over the ref cells in element - - - /* - * END ref_element::init source up to call to HexN::setup_HexN - */ - - - /* - * BEGIN HexN::setup_HexN source - */ - - if (orderBasis == 0) { - - num_nodes_1d_ = 2; - num_nodes_ = pow(num_nodes_1d_, 3); - - HexN_Nodes_1d_ = MatarRealCArray (num_nodes_); - HexN_Nodes_ = MatarRealCArray (num_nodes_, 3); - - - // Vertices - num_verts_1d_ = 2; - num_verts_ = pow(num_verts_1d_, 3); - num_basis_ = pow(num_verts_1d_, 3); - - HexN_Verts_1d_ = MatarRealCArray (num_verts_); - HexN_Verts_ = MatarRealCArray (num_verts_, 3); - - - Vert_Node_map_ = MatarUIntCArray (num_verts_); - - order_ = orderBasis+1; - - - } - - - else{ - - // Nodes - num_nodes_1d_ = 2 * orderBasis + 1; - num_nodes_ = pow(num_nodes_1d_, 3); - - HexN_Nodes_1d_ = MatarRealCArray (num_nodes_); - HexN_Nodes_ = MatarRealCArray (num_nodes_, 3); - - - // Vertices - num_verts_1d_ = orderBasis + 1; - num_verts_ = pow(num_verts_1d_, 3); - num_basis_ = pow(num_verts_1d_, 3); - - HexN_Verts_1d_ = MatarRealCArray (num_verts_); - HexN_Verts_ = MatarRealCArray (num_verts_, 3); - - - Vert_Node_map_ = MatarUIntCArray (num_verts_); - - order_ = orderBasis; - - } - - create_lobatto_nodes(orderBasis); - - - // Set the vertex to node map (every other node) - if (orderBasis == 0) { - - int vert_rid = 0; - for(int k = 0; k < num_nodes_1d_; k++){ - for(int j = 0; j < num_nodes_1d_; j++){ - for(int i = 0; i < num_nodes_1d_; i++){ - - int node_id = node_rid(i, j, k); - - Vert_Node_map_(vert_rid) = node_id; - - vert_rid++; - } - } - } - - - } - - - if (orderBasis >= 1){ - - int vert_rid = 0; - for(int k = 0; k < num_nodes_1d_; k=k+2){ - for(int j = 0; j < num_nodes_1d_; j=j+2){ - for(int i = 0; i < num_nodes_1d_; i=i+2){ +#include "HexRef.h" + + +HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { + // Determine sizes of data structures based on the order of the basis + assert(order_basis >= 0 && "Error: order of basis must be positive"); + if (order_basis == 0){ + num_ref_nodes_1D_ = 2; + num_ref_verts_1D_ = 2; + } else if (order_basis > 0) { + num_ref_nodes_1D_ = 2*order_basis + 1; + num_ref_verts_1D_ = order_basis + 1; + } + + num_ref_cells_1D_ = num_ref_nodes_1D_ - 1; + num_ref_cells_in_elem_ = (num_ref_nodes_1D_ - 1)*(num_ref_nodes_1D_ - 1) + *(num_ref_nodes_1D_ - 1); + + num_patches_in_elem_ = (num_ref_cells_1D_ + 1) + *(num_ref_cells_1D_*num_ref_cells_1D_)*3; + num_sides_in_elem_ = num_ref_cells_in_elem_*6; + + num_ref_verts_in_elem_ = num_ref_verts_1d_*num_ref_verts_1d_ + *num_ref_verts_1d_; + num_basis_ = num_ref_verts_in_elem_; + + + // Allocate memory for data structures + ref_cell_positions_ = MatarRealCArray(num_ref_cells_in_elem_, 3); + ref_cell_g_weights_ = MatarRealCArray(num_ref_cells_in_elem_); + + ref_patches_in_cell_list_ = MatarIntCArray(num_sides_in_elem_); + ref_patch_positions_ = MatarRealCArray(num_patches_in_elem_, 3); + ref_patch_g_weights_ = MatarRealCArray(num_patches_in_elem_); + + ref_cell_basis_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); + ref_cell_gradient_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); + + ref_patch_basis_ = MatarRealCArray(num_patches_in_elem_, num_ref_verts_in_elem_); + ref_patch_gradient_ = MatarRealCArray(num_patches_in_elem_, num_basis_, num_dim_); + + + // Retrieve Gauss-Legendre and Gauss-Lobatto quadrature points and weights + auto leg_weights_1D = MatarRealCArray(num_ref_cells_1D_); + legendre_weights_1D(leg_weights_1D, num_ref_cells_1D_); + + auto leg_points_1D = MatarRealCArray(num_ref_cells_1D_); + legendre_nodes_1D(leg_points_1D, num_ref_cells_1D_); + + auto lob_nodes_1D = MatarRealCArray(num_ref_nodes_1D_); + lobatto_nodes_1D(lob_nodes_1D, num_ref_nodes_1D_); + + auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); + lobatto_weights_1D(lob_weights_1D, num_ref_nodes_1D_); + + + // Fill in cell data structures + for (int k = 0; k < num_ref_cells_1D_; k++) { + for (int j = 0; j < num_ref_cells_1D_; j++) { + for (int i = 0; i < num_ref_cells_1D_; i++) { + int this_cell_rid = cell_rid(i, j, k); + + ref_cell_positions_(this_cell_rid, 0) = leg_points_1D(i); + ref_cell_positions_(this_cell_rid, 1) = leg_points_1D(j); + ref_cell_positions_(this_cell_rid, 2) = leg_points_1D(k); + + ref_cell_g_weights_(this_cell_rid) = leg_weights_1D(i) + *leg_weights_1D(j)*leg_weights_1D(k); + } + } + } + + + // Fill in patch data structures + for (int side_rid = 0; side_rid < num_sides_in_elem_; side_rid++){ + ref_patches_in_cell_list_(side_rid) = -1; + } + + int patch_rid = 0; + for (int k = 0; k < num_ref_cells_1D_; k++) { + for (int j = 0; j < num_ref_cells_1D_; j++) { + for (int i = 0; i < num_ref_cells_1D_; i++) { + int this_cell_rid = cell_rid(i, j, k); + + for (int side_lid = 0; side_lid < 6; side_lid++) { + int side_rid = side_lid + this_cell_rid*6; + + // Check to see that this patch has not been seen already + if (ref_patches_in_cell_list_(side_rid) == -1) { + // Store the index for this patch in the cell + ref_patches_in_cell_list_(side_rid) = patch_rid; + + // Store the quadrature point area values on the patch + switch (side_lid) { + case 0: // patch with -xi normal + ref_patch_positions_(patch_rid,0) = lob_nodes_1D(i); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(j)*leg_weights_1D(k); + break; + case 1: // patch with +xi normal + ref_patch_positions_(patch_rid,0) = lob_nodes_1D(i+1); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(j)*leg_weights_1D(k); + break; + case 2: // patch with -eta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = lob_nodes_1D(j); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(k); + break; + case 3: // patch with +eta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = lob_nodes_1D(j+1); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(k); + break; + case 4: // patch with -zeta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = lob_nodes_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(j); + break; + case 5: // patch with +zeta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = lob_nodes_1D(k+1); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(j); + break; + } + + // Get the rID for the neighboring cell in the element + // that communicates with this cell across this patch + if (side_lid == 0 && 0 < i) { + neighbor_cell_rid = cell_rid(i-1, j, k); + } else if (side_lid == 1 && i < num_ref_cells_1D_ - 1) { + neighbor_cell_rid = cell_rid(i+1, j, k); + } else if (side_lid == 2 && 0 < j) { + neighbor_cell_rid = cell_rid(i, j-1, k); + } else if (side_lid == 3 && j < num_ref_cells_1D_ - 1) { + neighbor_cell_rid = cell_rid(i, j+1, k); + } else if (side_lid == 4 && 0 < k) { + neighbor_cell_rid = cell_rid(i, j, k-1); + } else if (side_lid == 5 && k < num_ref_cells_1D_ - 1) { + neighbor_cell_rid = cell_rid(i, j, k+1); + } else { + neighbor_cell_rid = -1; // no neighboring cell in element + } + + // If there is a neighboring cell, set this patch rID in its list + if (0 <= neighbor_cell_rid && neighbor_cell_rid < num_ref_cells_in_elem_) { + // Get the side lid for this patch in the neighboring cell + int neighbor_side_lid = patch_rlid_in_cell_neighbor(side_lid); + + // Get side rID from that side lid + int neighbor_side_rid = neighbor_side_lid + (neighbor_cell_rid)*6; + + // Store the patch rID for this patch in the neighboring cell + ref_patches_in_cell_list_(neighbor_side_rid) = patch_rid; + } + + // Increment the patch index + patch_rid ++; + } + } + } + } + } + + + // Fill in evaluations of basis functions and their gradients in cells + for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++) { + + auto point = MatarRealCArray(3); + + // Get the patch coordinates + for(int dim = 0; dim < 3; dim++){ + point(dim) = ref_cell_positions(cell_rlid, dim); + } + + // the basis function values at the patch for each vertex + auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); + + // calculate the cell basis function values at the point, for each vertex + elem.basis(cell_basis, point); + + // save the basis values at the patch for each vertex + for (int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++) { + ref_cell_basis_(cell_rlid, vert_rlid) = cell_basis(vert_rlid); + } + + // calculate the partials at the cell location for each vertex + elem.partial_xi_basis(partial_xi, point); + elem.partial_eta_basis(partial_eta, point); + elem.partial_mu_basis(partial_mu, point); + + // loop over the basis polynomials where there is one from each vertex + for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ + + ref_cell_gradient_(cell_rlid, basis_id, 0) = partial_xi(basis_id); + ref_cell_gradient_(cell_rlid, basis_id, 1) = partial_eta(basis_id); + ref_cell_gradient_(cell_rlid, basis_id, 2) = partial_mu(basis_id); + + partial_xi(basis_id) = 0.0; + partial_eta(basis_id) = 0.0; + partial_mu(basis_id) = 0.0; + } + } + + + // Fill in evaluations of basis functions and their gradients on patches + for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ + + auto point = MatarRealCArray(3); + + // Get the patch coordinates + for(int dim = 0; dim < 3; dim++){ + point(dim) = ref_patch_positions(patch_rlid, dim); + } + + // the basis function values at the patch for each vertex + auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); + + // calculate the patch basis function values at the point, for each vertex + elem.basis(patch_basis, point); + + // save the basis values at the patch for each vertex + for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ + ref_patch_basis_(patch_rlid, vert_rlid) = patch_basis(vert_rlid); + } + + // calculate the partials at the patch location for each vertex + elem.partial_xi_basis(partial_xi, point); + elem.partial_eta_basis(partial_eta, point); + elem.partial_mu_basis(partial_mu, point); + + // loop over the basis polynomials where there is one from each vertex + for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ + + ref_patch_gradient_(patch_rlid, basis_id, 0) = partial_xi(basis_id); + ref_patch_gradient_(patch_rlid, basis_id, 1) = partial_eta(basis_id); + ref_patch_gradient_(patch_rlid, basis_id, 2) = partial_mu(basis_id); + + partial_xi(basis_id) = 0.0; + partial_eta(basis_id) = 0.0; + partial_mu(basis_id) = 0.0; + } + } +} - int node_id = node_rid(i, j, k); - Vert_Node_map_(vert_rid) = node_id; - vert_rid++; - } - } - } - } +int HexRef::cell_rid(int i, int j, int k) const { + return i + j*num_ref_cells_1D_ + k*num_ref_cells_1D_*num_ref_cells_1D_; +}; - /* - * END HexN::setup_HexN source - */ +real_t HexRef::ref_cell_positions(int cell_rid, int dim) const { + return ref_cell_positions_(cell_rid, dim); +} - /* - * BEGIN ref_element::init source after call to HexN::setup_HexN - */ +real_t HexRef::ref_cell_g_weights(int cell_rid) const { + return ref_cell_g_weights_(cell_rid); +} - // --- evaluate the basis at the nodal positions - for(int node_rlid = 0; node_rlid < num_ref_nodes_in_elem_; node_rlid++){ - auto point = MatarRealCArray(3); +int HexRef::ref_patches_in_cell(int cell_rid, int patch_rlid) const { + int index = patch_rlid + cell_rid*6; + return ref_patches_in_cell_list_(index); +} - // Get the nodal coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_node_positions_(node_rlid, dim); - } - - auto node_basis = MatarRealCArray(num_ref_verts_in_elem_); - evaluate_basis(node_basis, point); +real_t HexRef::ref_patch_g_weights(int patch_rid) const { + return ref_patch_g_weights_(patch_rid); +} - for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ - ref_nodal_basis_(node_rlid, vert_rlid) = node_basis(vert_rlid); - } - - } - - - // --- evaluate grad_basis functions at the ref nodes --- - - auto partial_xi = MatarRealCArray(num_ref_nodes_in_elem_); - auto partial_eta = MatarRealCArray(num_ref_nodes_in_elem_); - auto partial_zeta = MatarRealCArray(num_ref_nodes_in_elem_); - - - - for(int node_lid = 0; node_lid < num_ref_nodes_in_elem_; node_lid++){ - - auto point = MatarRealCArray(3); - - // Get the nodal coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_node_positions_(node_lid, dim); - } - - evaluate_derivative_basis_xi(partial_xi, point); - evaluate_derivative_basis_eta(partial_eta, point); - evaluate_derivative_basis_zeta(partial_zeta, point); - - for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ - - - ref_nodal_gradient_(node_lid, basis_id, 0) = partial_xi(basis_id); - ref_nodal_gradient_(node_lid, basis_id, 1) = partial_eta(basis_id); - ref_nodal_gradient_(node_lid, basis_id, 2) = partial_zeta(basis_id); - - partial_xi(basis_id) = 0.0; - partial_eta(basis_id) = 0.0; - partial_zeta(basis_id) = 0.0; - } - } - - // build a local rlid for the interior and surface nodes of the ref element - int count_surf = 0; - int count_inside = 0; - for (int k=0; k0 && i0 && j0 && k (num_ref_cells_1D_); - legendre_nodes_1D(leg_points_1D, num_ref_cells_1D_); - - auto leg_weights_1D = CArray (num_ref_cells_1D_); - legendre_weights_1D(leg_weights_1D, num_ref_cells_1D_); - - - // allocate memory for global variables related to Gauss Legendre points and weights - ref_cell_positions_ = CArray (num_ref_cells_in_elem_, 3); - ref_cell_g_weights_ = CArray (num_ref_cells_in_elem_); // this one - ref_patch_positions_ = CArray (num_patches_in_elem_, 3); - ref_patch_g_weights_ = CArray (num_patches_in_elem_); - - - - for (int side_rid = 0; side_rid < num_sides_in_elem_; side_rid++){ - ref_patches_in_cell_list_(side_rid) = -1; - } - - int patch_rid = 0; // the patch reference index - // loop over the cells - for (int k=0; k0){ - neighbor_cell_rid = cell_rid(i-1, j, k); - } // end xi minus direction - else if (side_lid == 1 && i0){ - neighbor_cell_rid = cell_rid(i, j-1, k); - } // end eta minus direction - else if (side_lid == 3 && j0){ - neighbor_cell_rid = cell_rid(i, j, k-1); - } // end zeta minus direction - else if (side_lid == 5 && k= 0 && neighbor_cell_rid < num_ref_cells_in_elem_){ - - // get the patch_lid in the neighboring cell for this patch_lid - int neighbor_side_lid = patch_rlid_in_cell_neighbor(side_lid); - - // get the side index of cell for the same patch - int neighbor_side_rid = neighbor_side_lid + (neighbor_cell_rid)*6; // neighboring side index - - // save the patch_rid for this patch in the neighboring cell - ref_patches_in_cell_list_(neighbor_side_rid) = patch_rid; - - } // end if neighboring_cell_rid is valid - - - // increment the patch_rid index - patch_rid ++; - - } // end if the patch was saved - - } // end for sides in a cell - - } // end for i-dir cells - } // end for j-dir cells - } // end for k-dir cells - - std::cout << " patch_rid = " << patch_rid << " num_patches = " << num_patches_in_elem_ << "\n"; - std::cout << " num cells * 6 = " << num_ref_cells_in_elem_*6 << " and num_cells_1D = " << num_ref_cells_1D_ << std::endl; - - - // --- evaluate the Lagrange basis at the patch positions - ref_patch_basis_ = CArray (num_patches_in_elem_, num_ref_verts_in_elem_); - - for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ - - auto point = MatarRealCArray(3); - - // Get the patch coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_patch_positions(patch_rlid, dim); - } - - // the basis function values at the patch for each vertex - auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); - - // calculate the patch basis function values at the point, for each vertex - evaluate_basis(patch_basis, point); - - // save the basis values at the patch for each vertex - for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ - ref_patch_basis_(patch_rlid, vert_rlid) = patch_basis(vert_rlid); - } - - } // end for patch_rlid - - - - // --- evaluate grad_basis functions at the ref patches --- - ref_patch_gradient_ = CArray (num_patches_in_elem_, num_basis_, num_dim_); - - // loop over the patches - for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ - - auto point = MatarRealCArray(3); - - // Get the patch coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_patch_positions(patch_rlid, dim); - } - - // calculate the partials at the patch location for each vertex - evaluate_derivative_basis_xi(partial_xi, point); - evaluate_derivative_basis_eta(partial_eta, point); - evaluate_derivative_basis_zeta(partial_zeta, point); - - // loop over the basis polynomials where there is one from each vertex - for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ - - ref_patch_gradient_(patch_rlid, basis_id, 0) = partial_xi(basis_id); - ref_patch_gradient_(patch_rlid, basis_id, 1) = partial_eta(basis_id); - ref_patch_gradient_(patch_rlid, basis_id, 2) = partial_zeta(basis_id); - - partial_xi(basis_id) = 0.0; - partial_eta(basis_id) = 0.0; - partial_zeta(basis_id) = 0.0; - } // end for basis_id - - } // end for patch_rlid - - - - // --- evaluate the Lagrange basis at the cell positions - ref_cell_basis_ = CArray (num_ref_cells_in_elem_, num_basis_, num_dim_); - - for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ - - auto point = MatarRealCArray(3); - - // Get the patch coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_cell_positions(cell_rlid, dim); - } - - // the basis function values at the patch for each vertex - auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); - - // calculate the cell basis function values at the point, for each vertex - evaluate_basis(cell_basis, point); - - // save the basis values at the patch for each vertex - for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ - ref_cell_basis_(cell_rlid, vert_rlid) = cell_basis(vert_rlid); - } - - } // end for cell_rlid - - - // --- evaluate grad_basis functions at the reference cell --- - ref_cell_gradient_ = CArray (num_ref_cells_in_elem_, num_basis_, num_dim_); - - // loop over the patches - for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ - - auto point = MatarRealCArray(3); - - // Get the cell coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_cell_positions_(cell_rlid, dim); - } - - // calculate the partials at the cell location for each vertex - evaluate_derivative_basis_xi(partial_xi, point); - evaluate_derivative_basis_eta(partial_eta, point); - evaluate_derivative_basis_zeta(partial_zeta, point); - - // loop over the basis polynomials where there is one from each vertex - for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ - - ref_cell_gradient_(cell_rlid, basis_id, 0) = partial_xi(basis_id); - ref_cell_gradient_(cell_rlid, basis_id, 1) = partial_eta(basis_id); - ref_cell_gradient_(cell_rlid, basis_id, 2) = partial_zeta(basis_id); - - partial_xi(basis_id) = 0.0; - partial_eta(basis_id) = 0.0; - partial_zeta(basis_id) = 0.0; - } // end for basis_id - - } // end for patch_rlid - - - /* - * END ref_element::init source after call to HexN::setup_HexN - */ - +int ref_element::patch_rlid_in_cell_neighbor(int patch_rlid) const +{ + return patch_rlid_cell_neighbor_[patch_rlid]; } -HexRef::evaluate_basis(MatarRealCArray &basis, MatarRealCArray &point) { - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); - - // Calculate 1D basis for the X coordinate of the point - lagrange_basis_1D(val_1d, point(0)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - val_3d(i, 0) = val_1d(i); - val_1d(i) = 0.0; - } - - // Calculate 1D basis for the Y coordinate of the point - lagrange_basis_1D(val_1d, point(1)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - val_3d(i, 1) = val_1d(i); - val_1d(i) = 0.0; - } - - // Calculate 1D basis for the Z coordinate of the point - lagrange_basis_1D(val_1d, point(2)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - val_3d(i, 2) = val_1d(i); - val_1d(i) = 0.0; - } - - // Multiply the i, j, k components of the basis from each node - // to get the tensor product basis for the node - for(int k = 0; k < num_verts_1d_; k++){ - for(int j = 0; j < num_verts_1d_; j++){ - for(int i = 0; i < num_verts_1d_; i++){ - - int vert_rlid = vert_rid(i,j,k); - basis(vert_rlid) = val_3d(i, 0)*val_3d(j, 1)*val_3d(k, 2); - } - } - } +real_t HexRef::cell_side_unit_normals(int side_rlid, int dim) const { + int index = side_rlid*3 + dim; + return cell_side_unit_normals_[index]; } -HexRef::evaluate_derivative_basis_xi(MatarRealCArray &partial_xi, - MatarRealCArray &point) { - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); - - auto Dval_1d = MatarRealCArray (num_verts_1d_); - auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); - - // Calculate 1D partial w.r.t. xi for the X coordinate of the point - lagrange_derivative_1D(Dval_1d, point(0)); - - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - Dval_3d(i,0) = Dval_1d(i); - Dval_1d(i) = 0.0; - } - - - // Calculate 1D basis for the Y coordinate of the point - lagrange_basis_1D(val_1d, point(1)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - val_3d(i,1) = val_1d(i); - val_1d(i) = 0.0; - } - - - // Calculate 1D basis for the Z coordinate of the point - lagrange_basis_1D(val_1d, point(2)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - val_3d(i,2) = val_1d(i); - val_1d(i) = 0.0; - } - - // Multiply the i, j, k components of the basis and partial_xi from each node - // to get the tensor product partial derivatives of the basis at each node - for(int k = 0; k < num_verts_1d_; k++){ - for(int j = 0; j < num_verts_1d_; j++){ - for(int i = 0; i < num_verts_1d_; i++){ - - int vert_rlid = vert_rid(i,j,k); - - // Partial w.r.t xi - partial_xi(vert_rlid) = Dval_3d(i, 0)*val_3d(j, 1)*val_3d(k, 2); - - } - } - } +int ref_element::num_ref_nodes() const { + return num_ref_nodes_in_elem_; } -HexRef::evaluate_derivative_basis_eta(MatarRealCArray &partial_xi, - MatarRealCArray &point) { - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); - - auto Dval_1d = MatarRealCArray (num_verts_1d_); - auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); - - // Calculate 1D basis for the Y coordinate of the point - lagrange_basis_1D(val_1d, point(0)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - val_3d(i,0) = val_1d(i); - val_1d(i) = 0.0; - } - - - // Calculate 1D partial w.r.t. eta for the Y coordinate of the point - lagrange_derivative_1D(Dval_1d, point(1)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - Dval_3d(i,1) = Dval_1d(i); - Dval_1d(i) = 0.0; - } - - - // Calculate 1D basis for the Z coordinate of the point - lagrange_basis_1D(val_1d, point(2)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - val_3d(i,2) = val_1d(i); - val_1d(i) = 0.0; - } - - // Multiply the i, j, k components of the basis and partial_eta from each node - // to get the tensor product partial derivatives of the basis at each node - for(int k = 0; k < num_verts_1d_; k++){ - for(int j = 0; j < num_verts_1d_; j++){ - for(int i = 0; i < num_verts_1d_; i++){ - - int vert_rlid = vert_rid(i,j,k); - - // Partial w.r.t xi - partial_eta(vert_rlid) = val_3d(i, 0)*Dval_3d(j, 1)*val_3d(k, 2); - - } - } - } +int ref_element::num_dim() const +{ + return num_dim_; } -HexRef::evaluate_derivative_basis_zeta(MatarRealCArray &partial_zeta, - MatarRealCArray &point) { - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); - - auto Dval_1d = MatarRealCArray (num_verts_1d_); - auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); - - // Calculate 1D basis for the X coordinate of the point - lagrange_basis_1D(val_1d, point(0)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - val_3d(i,0) = val_1d(i); - val_1d(i) = 0.0; - } - - - // Calculate 1D basis for the Y coordinate of the point - lagrange_basis_1D(val_1d, point(1)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - val_3d(i,1) = val_1d(i); - val_1d(i) = 0.0; - } - - - // Calculate 1D partial w.r.t. zeta for the Z coordinate of the point - lagrange_derivative_1D(Dval_1d, point(2)); - - // Save the basis value at the point to a temp array and zero out the temp array - for(int i = 0; i < num_verts_1d_; i++){ - - Dval_3d(i,2) = Dval_1d(i); - val_1d(i) = 0.0; - } - - // Multiply the i, j, k components of the basis and partial_xi from each node - // to get the tensor product partial derivatives of the basis at each node - for(int k = 0; k < num_verts_1d_; k++){ - for(int j = 0; j < num_verts_1d_; j++){ - for(int i = 0; i < num_verts_1d_; i++){ - - int vert_rlid = vert_rid(i,j,k); - - // Partial w.r.t zeta - partial_zeta(vert_rlid) = val_3d(i, 0)*val_3d(j, 1)*Dval_3d(k, 2); - - } - } - } +int ref_element::num_basis() const { + return num_basis_; } From 865505526ca082074b61b67ede291ae1166a17a0 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Wed, 14 Sep 2022 16:22:48 -0500 Subject: [PATCH 12/20] TensorProductBasis interface class for basis evals - Created TensorProductBasis class as an interface for evaluations of tensor products of different types of basis function over the hexahedral element - Copied LagrangeElement and LegendreElement classes over from elements/ directory and made them TensorProductBasis derived classes - Copied over quadrature point and weight routines over from elements/ directory and reorganized them --- common/error.h | 5 + elements-kokkos/include/HexRef.h | 114 +- .../include/LagrangeProductBasis.h | 35 + .../include/LegendreProductBasis.h | 25 + elements-kokkos/include/TensorProductBasis.h | 35 + elements-kokkos/include/changelog.md | 18 - elements-kokkos/include/jacobi_polynomials.h | 35 + .../include/lagrange_polynomials.h | 35 + .../include/legendre_polynomials.h | 20 + elements-kokkos/include/points_and_weights.h | 20 + elements-kokkos/src/HexRef.cpp | 474 ++++--- elements-kokkos/src/LagrangeProductBasis.cpp | 288 +++++ elements-kokkos/src/LegendreProductBasis.cpp | 168 +++ elements-kokkos/src/TensorProductBasis.cpp | 30 + elements-kokkos/src/jacobi_polynomials.cpp | 33 + elements-kokkos/src/lagrange_polynomials.cpp | 295 +++++ elements-kokkos/src/legendre_polynomials.cpp | 95 ++ elements-kokkos/src/points_and_weights.cpp | 1103 +++++++++++++++++ 18 files changed, 2513 insertions(+), 315 deletions(-) create mode 100644 elements-kokkos/include/LagrangeProductBasis.h create mode 100644 elements-kokkos/include/LegendreProductBasis.h create mode 100644 elements-kokkos/include/TensorProductBasis.h delete mode 100644 elements-kokkos/include/changelog.md create mode 100644 elements-kokkos/include/jacobi_polynomials.h create mode 100644 elements-kokkos/include/lagrange_polynomials.h create mode 100644 elements-kokkos/include/legendre_polynomials.h create mode 100644 elements-kokkos/include/points_and_weights.h create mode 100644 elements-kokkos/src/LagrangeProductBasis.cpp create mode 100644 elements-kokkos/src/LegendreProductBasis.cpp create mode 100644 elements-kokkos/src/TensorProductBasis.cpp create mode 100644 elements-kokkos/src/jacobi_polynomials.cpp create mode 100644 elements-kokkos/src/lagrange_polynomials.cpp create mode 100644 elements-kokkos/src/legendre_polynomials.cpp create mode 100644 elements-kokkos/src/points_and_weights.cpp diff --git a/common/error.h b/common/error.h index ee33c36e..e93b26c5 100644 --- a/common/error.h +++ b/common/error.h @@ -19,3 +19,8 @@ class VtkGridError : public std::runtime_error { public: VtkGridError(const std::string info) : std::runtime_error(info) {} }; + +class NotImplementedError : public std::runtime_error { + public: + NotImplementedError(const std::string info) : std::runtime_error(info) {} +}; diff --git a/elements-kokkos/include/HexRef.h b/elements-kokkos/include/HexRef.h index e17fa17d..34ff495e 100644 --- a/elements-kokkos/include/HexRef.h +++ b/elements-kokkos/include/HexRef.h @@ -26,82 +26,82 @@ enum BasisType { struct HexRef { - HexRef(int order_basis, BasisType type_basis); - ~HexRef(); + HexRef(int order_basis, BasisType type_basis); + ~HexRef(); - // Cells (subelements used in volume integration) - int num_ref_cells_1D_; - int num_ref_cells_in_elem() const; + // Cells (subelements used in volume integration) + int num_ref_cells_1D_; + int num_ref_cells_in_elem() const; - int cell_rid(int i, int j, int k) const; + int cell_rid(int i, int j, int k) const; - MatarRealCArray ref_cell_positions_; - real_t ref_cell_positions(int cell_rid, int dim) const; + MatarRealCArray ref_cell_positions_; + real_t ref_cell_positions(int cell_rid, int dim) const; - MatarRealCArray ref_cell_g_weights_; - real_t ref_cell_g_weights(int cell_rid) const; + MatarRealCArray ref_cell_g_weights_; + real_t ref_cell_g_weights(int cell_rid) const; - // Patches (subelement faces used in surface integration) - int num_patches_in_elem_; - int num_sides_in_elem_; + // Patches (subelement faces used in surface integration) + int num_patches_in_elem_; + int num_sides_in_elem_; - const int patch_rlid_cell_neighbor_[6] = { - 1, // side in neighbor cell mated with -xi side in this cell - 0, // side in neighbor cell mated with +xi side in this cell - 3, // side in neighbor cell mated with -eta side in this cell - 2, // side in neighbor cell mated with +eta side in this cell - 5, // side in neighbor cell mated with -zeta side in this cell - 4 // side in neighbor cell mated with +zeta side in this cell - }; - int patch_rlid_in_cell_neighbor(int patch_rlid) const; + const int patch_rlid_cell_neighbor_[6] = { + 1, // side in neighbor cell mated with -xi side in this cell + 0, // side in neighbor cell mated with +xi side in this cell + 3, // side in neighbor cell mated with -eta side in this cell + 2, // side in neighbor cell mated with +eta side in this cell + 5, // side in neighbor cell mated with -zeta side in this cell + 4 // side in neighbor cell mated with +zeta side in this cell + }; + int patch_rlid_in_cell_neighbor(int patch_rlid) const; - MatarIntCArray ref_patches_in_cell_list_; - int ref_patches_in_cell(int cell_lid, int patch_rlid) const; + MatarIntCArray ref_patches_in_cell_list_; + int ref_patches_in_cell(int cell_lid, int patch_rlid) const; - MatarRealCArray ref_patch_positions_; - real_t ref_patch_positions(int patch_rid, int dim) const; + MatarRealCArray ref_patch_positions_; + real_t ref_patch_positions(int patch_rid, int dim) const; - MatarRealCArray ref_patch_g_weights_; - real_t ref_patch_g_weights(int patch_rid) const; + MatarRealCArray ref_patch_g_weights_; + real_t ref_patch_g_weights(int patch_rid) const; - const real_t cell_side_unit_normals_[18] = { - -1, 0, 0, // -xi - 1, 0, 0, // +xi - 0, -1, 0, // -eta - 0, 1, 0, // +eta - 0, 0, -1, // -zeta - 0, 0, 1 // +zeta - }; - real_t cell_side_unit_normals(int side_rlid, int dim) const; + const real_t cell_side_unit_normals_[18] = { + -1, 0, 0, // -xi + 1, 0, 0, // +xi + 0, -1, 0, // -eta + 0, 1, 0, // +eta + 0, 0, -1, // -zeta + 0, 0, 1 // +zeta + }; + real_t cell_side_unit_normals(int side_rlid, int dim) const; - // Nodes (quadrature points) and vertices (degrees of freedom) - int num_ref_nodes_in_elem_; - int num_ref_nodes() const; + // Nodes (quadrature points) and vertices (degrees of freedom) + int num_ref_nodes_in_elem_; + int num_ref_nodes() const; - int num_ref_verts_1D_; - int num_ref_verts_in_elem_; + int num_ref_verts_1D_; + int num_ref_verts_in_elem_; - // Evaluations of basis functions and their gradients at quadrature points - // in cells and on patches - static const int num_dim_ = 3; - int num_dim() const; + // Evaluations of basis functions and their gradients at quadrature points + // in cells and on patches + static const int num_dim_ = 3; + int num_dim() const; - int num_basis_; - int num_basis() const; - - MatarRealCArray ref_cell_basis_; - real_t ref_cell_basis(int cell_rid, int basis_id) const; + int num_basis_; + int num_basis() const; + + MatarRealCArray ref_cell_basis_; + real_t ref_cell_basis(int cell_rid, int basis_id) const; - MatarRealCArray ref_cell_gradient_; - real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; + MatarRealCArray ref_cell_gradient_; + real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; - MatarRealCArray ref_patch_basis_; - real_t ref_patch_basis(int patch_rid, int basis_id) const; + MatarRealCArray ref_patch_basis_; + real_t ref_patch_basis(int patch_rid, int basis_id) const; - MatarRealCArray ref_patch_gradient_; - real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; + MatarRealCArray ref_patch_gradient_; + real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; }; diff --git a/elements-kokkos/include/LagrangeProductBasis.h b/elements-kokkos/include/LagrangeProductBasis.h new file mode 100644 index 00000000..738bcee7 --- /dev/null +++ b/elements-kokkos/include/LagrangeProductBasis.h @@ -0,0 +1,35 @@ +#pragma once + +#include "TensorProductBasis.h" +#include "common.h" + + +template +struct LagrangeProductBasis : public TensorProductBasis { + SizeType N; + SizeType Ne; + const NumType *Z; + NumType *w; + + // Work array for intermediate coefficients + NumType *C; + + LagrangeProductBasis(const SizeType, const NumType *); + ~LagrangeProductBasis(); + + // Basis functions and basis function gradients + NumType eval_basis(const SizeType, const NumType *); + void eval_grad_basis(const SizeType, const NumType *, NumType *); + + // Function approximation over element + NumType eval_approx(const NumType *, const NumType *); + void eval_grad_approx(const NumType *, const NumType *, NumType *); + + // Jacobian of spatial mapping + void eval_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); + NumType eval_det_jac(const NumType *, const NumType *, const NumType *, + const NumType *); + void eval_inv_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); +}; diff --git a/elements-kokkos/include/LegendreProductBasis.h b/elements-kokkos/include/LegendreProductBasis.h new file mode 100644 index 00000000..7f376ba6 --- /dev/null +++ b/elements-kokkos/include/LegendreProductBasis.h @@ -0,0 +1,25 @@ +#pragma once + +#include "TensorProductBasis.h" +#include "common.h" + + +template +struct LegendreProductBasis : public TensorProductBasis { + SizeType N; + SizeType Ne; + + // Work array for intermediate coefficients + NumType *C; + + LegendreProductBasis(SizeType); + ~LegendreProductBasis(); + + // Basis functions and basis function gradients + NumType eval_basis(const SizeType, const NumType *); + void eval_grad_basis(const SizeType, const NumType *, NumType *); + + // Function approximation over element + NumType eval_approx(const NumType *, const NumType *); + void eval_grad_approx(const NumType *, const NumType *, NumType *); +}; diff --git a/elements-kokkos/include/TensorProductBasis.h b/elements-kokkos/include/TensorProductBasis.h new file mode 100644 index 00000000..b5833e22 --- /dev/null +++ b/elements-kokkos/include/TensorProductBasis.h @@ -0,0 +1,35 @@ +#pragma once + + +/* + * Interface class for 3D tensor product basis, to be called for evaluating: + * - basis functions and their gradients; + * - approximations in the basis and their derivatives; and, + * - for choices of basis that are typically used to represent the geometry of + * the mesh (Lagrange and Bernstein), the Jacobian of the spatial mapping. + */ +template +struct TensorProductBasis { + static const SizeType Nd = 3; + SizeType Np; + + // Arrays for converting from flat to multidimensional indices + SizeType ijk[Nd]; + SizeType rad[Nd]; + + // Basis functions and basis function gradients + virtual NumType eval_basis(const SizeType, const NumType *) = 0; + virtual void eval_grad_basis(const SizeType, const NumType *, NumType *) = 0; + + // Function approximation over element + virtual NumType eval_approx(const NumType *, const NumType *) = 0; + virtual void eval_grad_approx(const NumType *, const NumType *, NumType *) = 0; + + // Jacobian of spatial mapping + virtual void eval_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); + virtual NumType eval_det_jac(const NumType *, const NumType *, const NumType *, + const NumType *); + virtual void eval_inv_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); +}; diff --git a/elements-kokkos/include/changelog.md b/elements-kokkos/include/changelog.md deleted file mode 100644 index 1e7448de..00000000 --- a/elements-kokkos/include/changelog.md +++ /dev/null @@ -1,18 +0,0 @@ -# Changelog - -Here I'll record changes that I make to the signatures while consolidating `ref_element` and `HexN` into `HexRef`. -I have a feeling this will be useful when I try to get something like the `Average` example or something in Fierro to use the `HexRef` element. - -* `num_dim_` is no longer set in the constructor/initialization routine; it is a static constant of 3 because the Hex element is assumed to be three-dimensional - -* The members `elem_order` and `p_order` have been consolidated into `elem_order` - -* `HexN::basis(...)` is now `HexRef::evaluate_basis(...)` - -* `HexN::partial_xi_basis`, `HexN::partial_eta_basis`, and `HexN::partial_mu_basis` are now `HexRef::evaluate_derivative_basis_xi`, `HexRef::evaluate_derivative_basis_eta`, and `HexRef::evaluate_derivative_basis_zeta` - - -# Notes - -* Look at SGH code to see what MATAR/Kokkos directives or decorators to use to get HexRef data and functions on the GPU. -Specifically look for `KOKKOS_FUNCTION`, e.g. in [these files](https://github.com/lanl/Fierro/search?q=KOKKOS_FUNCTION), and figure out what it does diff --git a/elements-kokkos/include/jacobi_polynomials.h b/elements-kokkos/include/jacobi_polynomials.h new file mode 100644 index 00000000..f076ceb7 --- /dev/null +++ b/elements-kokkos/include/jacobi_polynomials.h @@ -0,0 +1,35 @@ +#pragma once + +#include "common.h" + +namespace jacobi { + /* Recurrence relation parameters */ + inline Real a(Real alpha, Real beta, int n) { + if (n == 1) return 0.5*(alpha + beta) + 1.0; + return (2.0*Real(n) + alpha + beta - 1.0)*(2.0*Real(n) + alpha + beta) + /(2.0*Real(n)*(Real(n) + alpha + beta)); + }; + + inline Real b(Real alpha, Real beta, int n) { + if (n == 1) return 0.5*(alpha - beta); + return (alpha*alpha - beta*beta)*(2*Real(n) + alpha + beta - 1.0) + /(2.0*Real(n)*(Real(n) + alpha + beta) + *(2.0*Real(n) + alpha + beta - 2.0)); + }; + + inline Real c(Real alpha, Real beta, int n) { + if (n == 1) return 0.0; + return (Real(n) + alpha - 1.0)*(Real(n) + beta - 1.0) + *(2.0*Real(n) + alpha + beta) + /(Real(n)*(Real(n) + alpha + beta) + *(2.0*Real(n) + alpha + beta - 2.0)); + }; + + /* Polynomial and polynomial derivative evaluation */ + template + NumType eval(int n, Real alpha, Real beta, NumType X); + + template + NumType eval_der(const int n, const int k, const Real alpha, + const Real beta, const NumType X); +} diff --git a/elements-kokkos/include/lagrange_polynomials.h b/elements-kokkos/include/lagrange_polynomials.h new file mode 100644 index 00000000..7a124b61 --- /dev/null +++ b/elements-kokkos/include/lagrange_polynomials.h @@ -0,0 +1,35 @@ +#pragma once + +#include "common.h" + +namespace lagrange { + // Identifying singularities + template + SizeType find_coincident_vertex(const SizeType &, const NumType *, + const NumType &); + + // Barycentric weights + template + void compute_barycentric_weights(const SizeType &, const NumType *, + NumType *); + + // Lagrange polynomials (basis functions) + template + NumType eval(const SizeType Nv, const SizeType i, const SizeType ic, + const NumType *Z, const NumType *w, const NumType X); + + template + NumType eval_der(const SizeType Nv, const SizeType n, + const SizeType i, const SizeType ic, const NumType *Z, + const NumType *w, const NumType X, NumType *c); + + // Lagrange interpolants (sums of products of bases and coefficients) + template + NumType eval_interp(const SizeType Nv, const SizeType i, + const NumType *Z, const NumType *w, const NumType X, const NumType *c); + + template + NumType eval_der_interp(const SizeType Nv, const SizeType n, + const SizeType i, const NumType *Z, const NumType *w, const NumType X, + NumType *c); +} diff --git a/elements-kokkos/include/legendre_polynomials.h b/elements-kokkos/include/legendre_polynomials.h new file mode 100644 index 00000000..526def45 --- /dev/null +++ b/elements-kokkos/include/legendre_polynomials.h @@ -0,0 +1,20 @@ +#pragma once + +#include "common.h" + +namespace legendre { + // Legendre polynomials (basis functions) + template + NumType eval(const int n, const NumType X); + + template + NumType eval_der(const int n, const int k, const NumType X); + + // Legendre approximations (sums of products of bases and coefficients) + template + NumType eval_approx(const SizeType N, const NumType *c, const NumType X); + + template + NumType eval_der_approx(const SizeType N, const SizeType k, const NumType *c, + const NumType X); +} diff --git a/elements-kokkos/include/points_and_weights.h b/elements-kokkos/include/points_and_weights.h new file mode 100644 index 00000000..e24d3f87 --- /dev/null +++ b/elements-kokkos/include/points_and_weights.h @@ -0,0 +1,20 @@ +#pragma once + + +#include "common.h" + + +/* Equispaced and Chebyshev point distributions */ +template +void equispaced_points(SizeType N, NumType &zl, NumType &zr, NumType *z); + +template +void chebyshev_points(SizeType N, NumType &zl, NumType &zr, NumType *z); + + +/* Hard-coded Gauss-Lobatto and Gauss-Legendre quadrature points and weights */ +void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num); +void lobatto_weights_1D(MatarRealCArray &lob_weights_1D, const int &num); + +void legendre_nodes_1D(CArray &leg_nodes_1D, const int &num); +void legendre_weights_1D(CArray &leg_weights_1D, const int &num); diff --git a/elements-kokkos/src/HexRef.cpp b/elements-kokkos/src/HexRef.cpp index cb3fea38..db6bebcd 100644 --- a/elements-kokkos/src/HexRef.cpp +++ b/elements-kokkos/src/HexRef.cpp @@ -2,309 +2,303 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { - // Determine sizes of data structures based on the order of the basis - assert(order_basis >= 0 && "Error: order of basis must be positive"); - if (order_basis == 0){ - num_ref_nodes_1D_ = 2; - num_ref_verts_1D_ = 2; - } else if (order_basis > 0) { - num_ref_nodes_1D_ = 2*order_basis + 1; - num_ref_verts_1D_ = order_basis + 1; - } + // Determine sizes of data structures based on the order of the basis + assert(order_basis >= 0 && "Error: order of basis must be positive"); + if (order_basis == 0){ + num_ref_nodes_1D_ = 2; + num_ref_verts_1D_ = 2; + } else if (order_basis > 0) { + num_ref_nodes_1D_ = 2*order_basis + 1; + num_ref_verts_1D_ = order_basis + 1; + } - num_ref_cells_1D_ = num_ref_nodes_1D_ - 1; - num_ref_cells_in_elem_ = (num_ref_nodes_1D_ - 1)*(num_ref_nodes_1D_ - 1) - *(num_ref_nodes_1D_ - 1); + num_ref_cells_1D_ = num_ref_nodes_1D_ - 1; + num_ref_cells_in_elem_ = (num_ref_nodes_1D_ - 1)*(num_ref_nodes_1D_ - 1) + *(num_ref_nodes_1D_ - 1); - num_patches_in_elem_ = (num_ref_cells_1D_ + 1) - *(num_ref_cells_1D_*num_ref_cells_1D_)*3; - num_sides_in_elem_ = num_ref_cells_in_elem_*6; + num_patches_in_elem_ = (num_ref_cells_1D_ + 1) + *(num_ref_cells_1D_*num_ref_cells_1D_)*3; + num_sides_in_elem_ = num_ref_cells_in_elem_*6; - num_ref_verts_in_elem_ = num_ref_verts_1d_*num_ref_verts_1d_ - *num_ref_verts_1d_; - num_basis_ = num_ref_verts_in_elem_; + num_ref_verts_in_elem_ = num_ref_verts_1d_*num_ref_verts_1d_ + *num_ref_verts_1d_; + num_basis_ = num_ref_verts_in_elem_; - // Allocate memory for data structures - ref_cell_positions_ = MatarRealCArray(num_ref_cells_in_elem_, 3); - ref_cell_g_weights_ = MatarRealCArray(num_ref_cells_in_elem_); + // Allocate memory for data structures + ref_cell_positions_ = MatarRealCArray(num_ref_cells_in_elem_, 3); + ref_cell_g_weights_ = MatarRealCArray(num_ref_cells_in_elem_); - ref_patches_in_cell_list_ = MatarIntCArray(num_sides_in_elem_); - ref_patch_positions_ = MatarRealCArray(num_patches_in_elem_, 3); - ref_patch_g_weights_ = MatarRealCArray(num_patches_in_elem_); + ref_patches_in_cell_list_ = MatarIntCArray(num_sides_in_elem_); + ref_patch_positions_ = MatarRealCArray(num_patches_in_elem_, 3); + ref_patch_g_weights_ = MatarRealCArray(num_patches_in_elem_); - ref_cell_basis_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); - ref_cell_gradient_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); + ref_cell_basis_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); + ref_cell_gradient_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); - ref_patch_basis_ = MatarRealCArray(num_patches_in_elem_, num_ref_verts_in_elem_); - ref_patch_gradient_ = MatarRealCArray(num_patches_in_elem_, num_basis_, num_dim_); + ref_patch_basis_ = MatarRealCArray(num_patches_in_elem_, num_ref_verts_in_elem_); + ref_patch_gradient_ = MatarRealCArray(num_patches_in_elem_, num_basis_, num_dim_); - // Retrieve Gauss-Legendre and Gauss-Lobatto quadrature points and weights - auto leg_weights_1D = MatarRealCArray(num_ref_cells_1D_); - legendre_weights_1D(leg_weights_1D, num_ref_cells_1D_); + // Retrieve Gauss-Legendre and Gauss-Lobatto quadrature points and weights + auto leg_points_1D = MatarRealCArray(num_ref_cells_1D_); + legendre_points(leg_points_1D, num_ref_cells_1D_); - auto leg_points_1D = MatarRealCArray(num_ref_cells_1D_); - legendre_nodes_1D(leg_points_1D, num_ref_cells_1D_); + auto leg_weights_1D = MatarRealCArray(num_ref_cells_1D_); + legendre_weights(leg_weights_1D, num_ref_cells_1D_); - auto lob_nodes_1D = MatarRealCArray(num_ref_nodes_1D_); - lobatto_nodes_1D(lob_nodes_1D, num_ref_nodes_1D_); - - auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); - lobatto_weights_1D(lob_weights_1D, num_ref_nodes_1D_); + auto lob_points_1D = MatarRealCArray(num_ref_nodes_1D_); + lobatto_points(lob_points_1D, num_ref_nodes_1D_); + + auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); + lobatto_weights(lob_weights_1D, num_ref_nodes_1D_); - // Fill in cell data structures - for (int k = 0; k < num_ref_cells_1D_; k++) { - for (int j = 0; j < num_ref_cells_1D_; j++) { - for (int i = 0; i < num_ref_cells_1D_; i++) { - int this_cell_rid = cell_rid(i, j, k); - - ref_cell_positions_(this_cell_rid, 0) = leg_points_1D(i); - ref_cell_positions_(this_cell_rid, 1) = leg_points_1D(j); - ref_cell_positions_(this_cell_rid, 2) = leg_points_1D(k); - - ref_cell_g_weights_(this_cell_rid) = leg_weights_1D(i) - *leg_weights_1D(j)*leg_weights_1D(k); - } - } + // Fill in cell data structures + for (int k = 0; k < num_ref_cells_1D_; k++) { + for (int j = 0; j < num_ref_cells_1D_; j++) { + for (int i = 0; i < num_ref_cells_1D_; i++) { + int this_cell_rid = cell_rid(i, j, k); + + ref_cell_positions_(this_cell_rid, 0) = leg_points_1D(i); + ref_cell_positions_(this_cell_rid, 1) = leg_points_1D(j); + ref_cell_positions_(this_cell_rid, 2) = leg_points_1D(k); + + ref_cell_g_weights_(this_cell_rid) = leg_weights_1D(i) + *leg_weights_1D(j)*leg_weights_1D(k); + } } + } - // Fill in patch data structures - for (int side_rid = 0; side_rid < num_sides_in_elem_; side_rid++){ - ref_patches_in_cell_list_(side_rid) = -1; - } + // Fill in patch data structures + for (int side_rid = 0; side_rid < num_sides_in_elem_; side_rid++) { + ref_patches_in_cell_list_(side_rid) = -1; + } + + int patch_rid = 0; + for (int k = 0; k < num_ref_cells_1D_; k++) { + for (int j = 0; j < num_ref_cells_1D_; j++) { + for (int i = 0; i < num_ref_cells_1D_; i++) { + int this_cell_rid = cell_rid(i, j, k); + + for (int side_lid = 0; side_lid < 6; side_lid++) { + int side_rid = side_lid + this_cell_rid*6; - int patch_rid = 0; - for (int k = 0; k < num_ref_cells_1D_; k++) { - for (int j = 0; j < num_ref_cells_1D_; j++) { - for (int i = 0; i < num_ref_cells_1D_; i++) { - int this_cell_rid = cell_rid(i, j, k); - - for (int side_lid = 0; side_lid < 6; side_lid++) { - int side_rid = side_lid + this_cell_rid*6; - - // Check to see that this patch has not been seen already - if (ref_patches_in_cell_list_(side_rid) == -1) { - // Store the index for this patch in the cell - ref_patches_in_cell_list_(side_rid) = patch_rid; - - // Store the quadrature point area values on the patch - switch (side_lid) { - case 0: // patch with -xi normal - ref_patch_positions_(patch_rid,0) = lob_nodes_1D(i); - ref_patch_positions_(patch_rid,1) = leg_points_1D(j); - ref_patch_positions_(patch_rid,2) = leg_points_1D(k); - - ref_patch_g_weights_(patch_rid) = leg_weights_1D(j)*leg_weights_1D(k); - break; - case 1: // patch with +xi normal - ref_patch_positions_(patch_rid,0) = lob_nodes_1D(i+1); - ref_patch_positions_(patch_rid,1) = leg_points_1D(j); - ref_patch_positions_(patch_rid,2) = leg_points_1D(k); - - ref_patch_g_weights_(patch_rid) = leg_weights_1D(j)*leg_weights_1D(k); - break; - case 2: // patch with -eta normal - ref_patch_positions_(patch_rid,0) = leg_points_1D(i); - ref_patch_positions_(patch_rid,1) = lob_nodes_1D(j); - ref_patch_positions_(patch_rid,2) = leg_points_1D(k); - - ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(k); - break; - case 3: // patch with +eta normal - ref_patch_positions_(patch_rid,0) = leg_points_1D(i); - ref_patch_positions_(patch_rid,1) = lob_nodes_1D(j+1); - ref_patch_positions_(patch_rid,2) = leg_points_1D(k); - - ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(k); - break; - case 4: // patch with -zeta normal - ref_patch_positions_(patch_rid,0) = leg_points_1D(i); - ref_patch_positions_(patch_rid,1) = leg_points_1D(j); - ref_patch_positions_(patch_rid,2) = lob_nodes_1D(k); - - ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(j); - break; - case 5: // patch with +zeta normal - ref_patch_positions_(patch_rid,0) = leg_points_1D(i); - ref_patch_positions_(patch_rid,1) = leg_points_1D(j); - ref_patch_positions_(patch_rid,2) = lob_nodes_1D(k+1); - - ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(j); - break; - } - - // Get the rID for the neighboring cell in the element - // that communicates with this cell across this patch - if (side_lid == 0 && 0 < i) { - neighbor_cell_rid = cell_rid(i-1, j, k); - } else if (side_lid == 1 && i < num_ref_cells_1D_ - 1) { - neighbor_cell_rid = cell_rid(i+1, j, k); - } else if (side_lid == 2 && 0 < j) { - neighbor_cell_rid = cell_rid(i, j-1, k); - } else if (side_lid == 3 && j < num_ref_cells_1D_ - 1) { - neighbor_cell_rid = cell_rid(i, j+1, k); - } else if (side_lid == 4 && 0 < k) { - neighbor_cell_rid = cell_rid(i, j, k-1); - } else if (side_lid == 5 && k < num_ref_cells_1D_ - 1) { - neighbor_cell_rid = cell_rid(i, j, k+1); - } else { - neighbor_cell_rid = -1; // no neighboring cell in element - } - - // If there is a neighboring cell, set this patch rID in its list - if (0 <= neighbor_cell_rid && neighbor_cell_rid < num_ref_cells_in_elem_) { - // Get the side lid for this patch in the neighboring cell - int neighbor_side_lid = patch_rlid_in_cell_neighbor(side_lid); - - // Get side rID from that side lid - int neighbor_side_rid = neighbor_side_lid + (neighbor_cell_rid)*6; - - // Store the patch rID for this patch in the neighboring cell - ref_patches_in_cell_list_(neighbor_side_rid) = patch_rid; - } - - // Increment the patch index - patch_rid ++; - } - } + // Check to see that this patch has not been seen already + if (ref_patches_in_cell_list_(side_rid) == -1) { + // Store the index for this patch in the cell + ref_patches_in_cell_list_(side_rid) = patch_rid; + + // Store the quadrature point area values on the patch + switch (side_lid) { + case 0: // patch with -xi normal + ref_patch_positions_(patch_rid,0) = lob_points_1D(i); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(j)*leg_weights_1D(k); + break; + case 1: // patch with +xi normal + ref_patch_positions_(patch_rid,0) = lob_points_1D(i+1); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(j)*leg_weights_1D(k); + break; + case 2: // patch with -eta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = lob_points_1D(j); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(k); + break; + case 3: // patch with +eta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = lob_points_1D(j+1); + ref_patch_positions_(patch_rid,2) = leg_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(k); + break; + case 4: // patch with -zeta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = lob_points_1D(k); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(j); + break; + case 5: // patch with +zeta normal + ref_patch_positions_(patch_rid,0) = leg_points_1D(i); + ref_patch_positions_(patch_rid,1) = leg_points_1D(j); + ref_patch_positions_(patch_rid,2) = lob_points_1D(k+1); + + ref_patch_g_weights_(patch_rid) = leg_weights_1D(i)*leg_weights_1D(j); + break; } + + // Get the rID for the neighboring cell in the element + // that communicates with this cell across this patch + if (side_lid == 0 && 0 < i) { + neighbor_cell_rid = cell_rid(i-1, j, k); + } else if (side_lid == 1 && i < num_ref_cells_1D_ - 1) { + neighbor_cell_rid = cell_rid(i+1, j, k); + } else if (side_lid == 2 && 0 < j) { + neighbor_cell_rid = cell_rid(i, j-1, k); + } else if (side_lid == 3 && j < num_ref_cells_1D_ - 1) { + neighbor_cell_rid = cell_rid(i, j+1, k); + } else if (side_lid == 4 && 0 < k) { + neighbor_cell_rid = cell_rid(i, j, k-1); + } else if (side_lid == 5 && k < num_ref_cells_1D_ - 1) { + neighbor_cell_rid = cell_rid(i, j, k+1); + } else { + neighbor_cell_rid = -1; // no neighboring cell in element + } + + // If there is a neighboring cell, set this patch rID in its list + if (0 <= neighbor_cell_rid && neighbor_cell_rid < num_ref_cells_in_elem_) { + // Get the side lid for this patch in the neighboring cell + int neighbor_side_lid = patch_rlid_in_cell_neighbor(side_lid); + + // Get side rID from that side lid + int neighbor_side_rid = neighbor_side_lid + (neighbor_cell_rid)*6; + + // Store the patch rID for this patch in the neighboring cell + ref_patches_in_cell_list_(neighbor_side_rid) = patch_rid; + } + + // Increment the patch index + patch_rid ++; + } } + } } + } - // Fill in evaluations of basis functions and their gradients in cells - for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++) { - - auto point = MatarRealCArray(3); - - // Get the patch coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_cell_positions(cell_rlid, dim); - } - - // the basis function values at the patch for each vertex - auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); - - // calculate the cell basis function values at the point, for each vertex - elem.basis(cell_basis, point); - - // save the basis values at the patch for each vertex - for (int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++) { - ref_cell_basis_(cell_rlid, vert_rlid) = cell_basis(vert_rlid); - } + // Fill in evaluations of basis functions and their gradients in cells + for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++) { + auto point = MatarRealCArray(3); + + // Get the patch coordinates + for (int dim = 0; dim < 3; dim++){ + point(dim) = ref_cell_positions(cell_rlid, dim); + } + + // the basis function values at the patch for each vertex + auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); + + // calculate the cell basis function values at the point, for each vertex + elem.basis(cell_basis, point); + + // save the basis values at the patch for each vertex + for (int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++) { + ref_cell_basis_(cell_rlid, vert_rlid) = cell_basis(vert_rlid); + } - // calculate the partials at the cell location for each vertex - elem.partial_xi_basis(partial_xi, point); - elem.partial_eta_basis(partial_eta, point); - elem.partial_mu_basis(partial_mu, point); - - // loop over the basis polynomials where there is one from each vertex - for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ - - ref_cell_gradient_(cell_rlid, basis_id, 0) = partial_xi(basis_id); - ref_cell_gradient_(cell_rlid, basis_id, 1) = partial_eta(basis_id); - ref_cell_gradient_(cell_rlid, basis_id, 2) = partial_mu(basis_id); - - partial_xi(basis_id) = 0.0; - partial_eta(basis_id) = 0.0; - partial_mu(basis_id) = 0.0; - } + // calculate the partials at the cell location for each vertex + elem.partial_xi_basis(partial_xi, point); + elem.partial_eta_basis(partial_eta, point); + elem.partial_mu_basis(partial_mu, point); + + // loop over the basis polynomials where there is one from each vertex + for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++) { + ref_cell_gradient_(cell_rlid, basis_id, 0) = partial_xi(basis_id); + ref_cell_gradient_(cell_rlid, basis_id, 1) = partial_eta(basis_id); + ref_cell_gradient_(cell_rlid, basis_id, 2) = partial_mu(basis_id); + + partial_xi(basis_id) = 0.0; + partial_eta(basis_id) = 0.0; + partial_mu(basis_id) = 0.0; } + } - // Fill in evaluations of basis functions and their gradients on patches - for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ - - auto point = MatarRealCArray(3); - - // Get the patch coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_patch_positions(patch_rlid, dim); - } - - // the basis function values at the patch for each vertex - auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); - - // calculate the patch basis function values at the point, for each vertex - elem.basis(patch_basis, point); - - // save the basis values at the patch for each vertex - for(int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++){ - ref_patch_basis_(patch_rlid, vert_rlid) = patch_basis(vert_rlid); - } + // Fill in evaluations of basis functions and their gradients on patches + for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++) { + auto point = MatarRealCArray(3); + + // Get the patch coordinates + for(int dim = 0; dim < 3; dim++){ + point(dim) = ref_patch_positions(patch_rlid, dim); + } + + // the basis function values at the patch for each vertex + auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); + + // calculate the patch basis function values at the point, for each vertex + elem.basis(patch_basis, point); + + // save the basis values at the patch for each vertex + for (int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++) { + ref_patch_basis_(patch_rlid, vert_rlid) = patch_basis(vert_rlid); + } - // calculate the partials at the patch location for each vertex - elem.partial_xi_basis(partial_xi, point); - elem.partial_eta_basis(partial_eta, point); - elem.partial_mu_basis(partial_mu, point); - - // loop over the basis polynomials where there is one from each vertex - for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++){ - - ref_patch_gradient_(patch_rlid, basis_id, 0) = partial_xi(basis_id); - ref_patch_gradient_(patch_rlid, basis_id, 1) = partial_eta(basis_id); - ref_patch_gradient_(patch_rlid, basis_id, 2) = partial_mu(basis_id); - - partial_xi(basis_id) = 0.0; - partial_eta(basis_id) = 0.0; - partial_mu(basis_id) = 0.0; - } + // calculate the partials at the patch location for each vertex + elem.partial_xi_basis(partial_xi, point); + elem.partial_eta_basis(partial_eta, point); + elem.partial_mu_basis(partial_mu, point); + + // loop over the basis polynomials where there is one from each vertex + for (int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++) { + ref_patch_gradient_(patch_rlid, basis_id, 0) = partial_xi(basis_id); + ref_patch_gradient_(patch_rlid, basis_id, 1) = partial_eta(basis_id); + ref_patch_gradient_(patch_rlid, basis_id, 2) = partial_mu(basis_id); + + partial_xi(basis_id) = 0.0; + partial_eta(basis_id) = 0.0; + partial_mu(basis_id) = 0.0; } + } } int HexRef::cell_rid(int i, int j, int k) const { - return i + j*num_ref_cells_1D_ + k*num_ref_cells_1D_*num_ref_cells_1D_; + return i + j*num_ref_cells_1D_ + k*num_ref_cells_1D_*num_ref_cells_1D_; }; real_t HexRef::ref_cell_positions(int cell_rid, int dim) const { - return ref_cell_positions_(cell_rid, dim); + return ref_cell_positions_(cell_rid, dim); } real_t HexRef::ref_cell_g_weights(int cell_rid) const { - return ref_cell_g_weights_(cell_rid); + return ref_cell_g_weights_(cell_rid); } int HexRef::ref_patches_in_cell(int cell_rid, int patch_rlid) const { - int index = patch_rlid + cell_rid*6; - return ref_patches_in_cell_list_(index); + int index = patch_rlid + cell_rid*6; + return ref_patches_in_cell_list_(index); } real_t HexRef::ref_patch_g_weights(int patch_rid) const { - return ref_patch_g_weights_(patch_rid); + return ref_patch_g_weights_(patch_rid); } -int ref_element::patch_rlid_in_cell_neighbor(int patch_rlid) const -{ - return patch_rlid_cell_neighbor_[patch_rlid]; +int HexRef::patch_rlid_in_cell_neighbor(int patch_rlid) const { + return patch_rlid_cell_neighbor_[patch_rlid]; } real_t HexRef::cell_side_unit_normals(int side_rlid, int dim) const { - int index = side_rlid*3 + dim; - return cell_side_unit_normals_[index]; + int index = side_rlid*3 + dim; + return cell_side_unit_normals_[index]; } -int ref_element::num_ref_nodes() const { - return num_ref_nodes_in_elem_; +int HexRef::num_ref_nodes() const { + return num_ref_nodes_in_elem_; } -int ref_element::num_dim() const -{ - return num_dim_; +int HexRef::num_dim() const { + return num_dim_; } -int ref_element::num_basis() const { - return num_basis_; +int HexRef::num_basis() const { + return num_basis_; } diff --git a/elements-kokkos/src/LagrangeProductBasis.cpp b/elements-kokkos/src/LagrangeProductBasis.cpp new file mode 100644 index 00000000..5fb2221c --- /dev/null +++ b/elements-kokkos/src/LagrangeProductBasis.cpp @@ -0,0 +1,288 @@ +#include "LagrangeProductBasis.h" +#include "lagrange_polynomials.h" + + +template +LagrangeProductBasis::LagrangeProductBasis(const SizeType order, + const NumType *vert_coords) : Np(order), Z(vert_coords) { + N = Np + 1; + Ne = std::pow(N, Nd); + + rad[0] = N; + rad[1] = N; + rad[2] = N; + + // Allocate memory for weights and compute + w = new NumType[N]; + lagrange::compute_barycentric_weights(N, Z, w); + + // Allocate memory for intermediate coefficients + C = new NumType[3*N]; +} + +template +LagrangeProductBasis::~LagrangeProductBasis() { + delete [] w, C; +} + +/* + * Return evaluation of basis function, which is the tensor product of Lagrange + * polynomials, at specified coordinates. + * + * Parameters + * ---------- + * I : index of basis function + * X : coordinates (in reference space) + */ +template +NumType LagrangeProductBasis::eval_basis(const SizeType I, const NumType *X) { + // Decompose index of 3D tensor product basis function into indices of + // Lagrange polynomials + common::base_10_to_mixed_radix(Nd, rad, I, ijk); + + // Check coincidence of coordinates with vertex coordinates + SizeType ix = lagrange::find_coincident_vertex(N, Z, X[0]); + SizeType iy = lagrange::find_coincident_vertex(N, Z, X[1]); + SizeType iz = lagrange::find_coincident_vertex(N, Z, X[2]); + + // Evaluate Lagrange polynomials + NumType li = lagrange::eval(N, ijk[0], ix, Z, w, X[0]); + NumType lj = lagrange::eval(N, ijk[1], iy, Z, w, X[1]); + NumType lk = lagrange::eval(N, ijk[2], iz, Z, w, X[2]); + + return li*lj*lk; +} + +/* + * Evaluate gradient of basis function + * + * Parameters + * ---------- + * I : index of basis function + * X : coordinates (in reference space) + * + * Returns + * ------- + * grad_phi : gradient of the basis function + */ +template +void LagrangeProductBasis::eval_grad_basis(const SizeType I, + const NumType *X, NumType *grad_phi) { + // Decompose index of 3D tensor product basis function into indices of + // Lagrange polynomials + common::base_10_to_mixed_radix(Nd, rad, I, ijk); + + // Check coincidence of coordinates with vertex coordinates + SizeType ix = lagrange::find_coincident_vertex(N, Z, X[0]); + SizeType iy = lagrange::find_coincident_vertex(N, Z, X[1]); + SizeType iz = lagrange::find_coincident_vertex(N, Z, X[2]); + + // Evaluate Lagrange polynomials + NumType li = lagrange::eval(N, ijk[0], ix, Z, w, X[0]); + NumType lj = lagrange::eval(N, ijk[1], iy, Z, w, X[1]); + NumType lk = lagrange::eval(N, ijk[2], iz, Z, w, X[2]); + + // Evaluate Lagrange polynomial derivatives + SizeType n = 1; // order of derivative + NumType dli = lagrange::eval_der(N, n, ijk[0], ix, Z, w, X[0], C); + NumType dlj = lagrange::eval_der(N, n, ijk[1], iy, Z, w, X[1], C); + NumType dlk = lagrange::eval_der(N, n, ijk[2], iz, Z, w, X[2], C); + + // Store partial derivatives in entries of gradient + grad_phi[0] = dli*lj*lk; + grad_phi[1] = li*dlj*lk; + grad_phi[2] = li*lj*dlk; +} + +/* + * Return evaluation of local function approximation, which is formed by + * the sum of the products of tensor-product Lagrange basis functions and the + * provided coefficients, at specified coordinates + * + * Parameters + * ---------- + * c : coefficients + * X : coordinates (in reference space) + * + * Note + * ---- + * The intermediate coefficients or workspace array is divided into 3 lines of + * length equal to the number of vertices. In the dimension-by-dimension + * approach used for the approximation evaluation, each line is filled by + * evaluations at the previous dimensional level. The initial coefficients are + * cycled through in the X-dimension loop to produce coefficients, stored in + * the workspace array, to be used in the Y-dimension loop. The output from the + * Y-dimension loop is coefficients, stored again in the workspace array, to be + * used in the final Z-dimension evaluation. This process, as described, only + * requires 2 lines of workspace. The extra line of workspace is needed for + * derivative evaluations, and so it is unused here. + */ +template +NumType LagrangeProductBasis::eval_approx(const NumType *c, + const NumType *X) { + // Check the coincidence of the coordinates with vertex coordinates + SizeType ix = lagrange::find_coincident_vertex(N, Z, X[0]); + SizeType iy = lagrange::find_coincident_vertex(N, Z, X[1]); + SizeType iz = lagrange::find_coincident_vertex(N, Z, X[2]); + + for (int k = 0; k < N; k++) { + for (int j = 0; j < N; j++) { + // Collapse first dimension into coefficients for second dimension + C[j] = lagrange::eval_interp(N, ix, Z, w, X[0], &c[j*N+k*N*N]); + } + + // Collapse second dimension into coefficients for third dimension + C[N+k] = lagrange::eval_interp(N, iy, Z, w, X[1], C); + } + + // Collapse third dimension into interpolant evaluation + return lagrange::eval_interp(N, iz, Z, w, X[2], &C[N]); +} + +/* + * Evaluate gradient of the local function approximation, which is formed by + * the sum of the products of tensor-product Lagrange basis functions and the + * provided coefficients, at specified coordinates + * + * Parameters + * ---------- + * c : coefficients + * X : coordinates (in reference space) + * + * Returns + * ------- + * grad_f : gradient of the interpolant + * + * Note + * ---- + * This routine uses a dimension-by-dimension approach as in the approximation + * routine. See the documentation of that routine for details. This routine + * differs from that one in that the first line of the workspace array is + * reserved for the derivative evaluations. These derivative evaluations use + * the first line to store divided differences. + */ +template +void LagrangeProductBasis::eval_grad_approx(const NumType *c, + const NumType *X, NumType *grad_f) { + const SizeType n = 1; // order of partial derivative + + // Check the coincidence of the coordinates with vertex coordinates + SizeType ix = lagrange::find_coincident_vertex(N, Z, X[0]); + SizeType iy = lagrange::find_coincident_vertex(N, Z, X[1]); + SizeType iz = lagrange::find_coincident_vertex(N, Z, X[2]); + + for (int l = 0; l < Nd; l++) { + for (int k = 0; k < N; k++) { + for (int j = 0; j < N; j++) { + // Collapse first dimension into coefficients for second dimension + std::copy(c+j*N+k*N*N, c+j*N+k*N*N+N, C); // load first line + if (l == 0) { + C[N+j] = lagrange::eval_der_interp(N, n, ix, Z, w, X[0], C); + } else { + C[N+j] = lagrange::eval_interp(N, ix, Z, w, X[0], C); + } + } + + // Collapse second dimension into coefficients for third dimension + std::copy(C+N, C+2*N, C); // second line back into first line + if (l == 1) { + C[2*N+k] = lagrange::eval_der_interp(N, n, iy, Z, w, X[1], C); + } else { + C[2*N+k] = lagrange::eval_interp(N, iy, Z, w, X[1], C); + } + } + + // Collapse third dimension into interpolant evaluation + std::copy(C+2*N, C+3*N, C); // third line back into first line + if (l == 2) { + grad_f[l] = lagrange::eval_der_interp(N, n, iz, Z, w, X[2], C); + } else { + grad_f[l] = lagrange::eval_interp(N, iz, Z, w, X[2], C); + } + } +} + +/* + * Evaluate the Jacobian of the spatial mapping + * + * Parameters + * ---------- + * x : x coordinates in physical space + * y : y coordinates in physical space + * z : z coordinates in physical space + * X : coordinates in reference space at which to evaluate + * + * Returns + * ------- + * J : Jacobian (stored in column-major order) + */ +template +void LagrangeProductBasis::eval_jac(const NumType *x, const NumType *y, + const NumType *z, const NumType *X, NumType *J) { + // Evaluate the gradient of x = x(X, Y, Z) + this->eval_grad_approx(x, X, J); + + // Evaluate the gradient of y = y(X, Y, Z) + this->eval_grad_approx(y, X, J+3); + + // Evaluate the gradient of z = z(X, Y, Z) + this->eval_grad_approx(z, X, J+6); +} + +/* + * Return the determinant of the Jacobian of the spatial mapping + * + * Parameters + * ---------- + * x : x coordinates in physical space + * y : y coordinates in physical space + * z : z coordinates in physical space + * X : coordinates in reference space at which to evaluate + */ +template +NumType LagrangeProductBasis::eval_det_jac(const NumType *x, + const NumType *y, const NumType *z, const NumType *X) { + NumType J[9]; + this->eval_jac(x, y, z, X, J); + + return J[0]*(J[4]*J[8] - J[5]*J[7]) - J[1]*(J[3]*J[8] - J[5]*J[6]) + + J[2]*(J[3]*J[7] - J[4]*J[6]); +} + +/* Evaluate the inverse of the Jacobian of the spatial mapping + * + * Parameters + * ---------- + * x : x coordinates in physical space + * y : y coordinates in physical space + * z : z coordinates in physical space + * X : coordinates in reference space at which to evaluate + * + * Returns + * ------- + * Jinv : Jacobian inverse (stored in column-major order) + */ +template +void LagrangeProductBasis::eval_inv_jac(const NumType *x, const NumType *y, + const NumType *z, const NumType *X, NumType *Jinv) { + NumType J[9]; + this->eval_jac(x, y, z, X, J); + + NumType d = 1.0/(this->eval_det_jac(x, y, z, X)); + + Jinv[0] = d*(J[4]*J[8] - J[5]*J[7]); + Jinv[1] = -d*(J[1]*J[8] - J[2]*J[7]); + Jinv[2] = d*(J[1]*J[5] - J[2]*J[4]); + + Jinv[3] = -d*(J[3]*J[8] - J[5]*J[6]); + Jinv[4] = d*(J[0]*J[8] - J[2]*J[6]); + Jinv[5] = -d*(J[0]*J[5] - J[2]*J[3]); + + Jinv[6] = d*(J[3]*J[7] - J[4]*J[6]); + Jinv[7] = -d*(J[0]*J[7] - J[1]*J[6]); + Jinv[8] = d*(J[0]*J[4] - J[1]*J[3]); +} + +// Explicit instantiation of template class +template class LagrangeProductBasis; +template class LagrangeProductBasis; diff --git a/elements-kokkos/src/LegendreProductBasis.cpp b/elements-kokkos/src/LegendreProductBasis.cpp new file mode 100644 index 00000000..5c23419a --- /dev/null +++ b/elements-kokkos/src/LegendreProductBasis.cpp @@ -0,0 +1,168 @@ +#include "LegendreProductBasis.h" +#include "legendre_polynomials.h" + + +template +LegendreProductBasis::LegendreProductBasis(const SizeType order) + : Np(order) { + N = Np + 1; + Ne = std::pow(N, Nd); + + rad[0] = N; + rad[1] = N; + rad[2] = N; + + // Allocate memory for intermediate coefficients + C = new NumType[2*N]; +} + +template +LegendreProductBasis::~LegendreProductBasis() {} + +/* + * Return evaluation of basis function, which is the tensor product of Legendre + * polynomials, at specified coordinates. + * + * Parameters + * ---------- + * I : index of basis function + * X : coordinates (in reference space) + */ +template +NumType LegendreProductBasis::eval_basis(const SizeType I, + const NumType *X) { + // Decompose index of 3D tensor product basis function into indices of + // Legendre polynomials + common::base_10_to_mixed_radix(Nd, rad, I, ijk); + + // Evaluate Legendre polynomials + NumType Pi = legendre::eval(int(ijk[0]), X[0]); + NumType Pj = legendre::eval(int(ijk[1]), X[1]); + NumType Pk = legendre::eval(int(ijk[2]), X[2]); + + return Pi*Pj*Pk; +} + +/* + * Evaluate gradient of basis function + * + * Parameters + * ---------- + * I : index of basis function + * X : coordinates (in reference space) + * + * Returns + * ------- + * grad_phi : gradient of the basis function + */ +template +void LegendreProductBasis::eval_grad_basis(const SizeType I, + const NumType *X, NumType *grad_phi) { + // Decompose index of 3D tensor product basis function into indices of + // Legendre polynomials + common::base_10_to_mixed_radix(Nd, rad, I, ijk); + + // Evaluate Legendre polynomials + NumType Pi = legendre::eval(int(ijk[0]), X[0]); + NumType Pj = legendre::eval(int(ijk[1]), X[1]); + NumType Pk = legendre::eval(int(ijk[2]), X[2]); + + // Evaluate Legendre polynomial derivatives + SizeType q = 1; // order of derivative + NumType dPi = legendre::eval_der(int(ijk[0]), q, X[0]); + NumType dPj = legendre::eval_der(int(ijk[1]), q, X[1]); + NumType dPk = legendre::eval_der(int(ijk[2]), q, X[2]); + + // Store partial derivatives in entries of gradient + grad_phi[0] = dPi*Pj*Pk; + grad_phi[1] = Pi*dPj*Pk; + grad_phi[2] = Pi*Pj*dPk; +} + +/* + * Return evaluation of local function approximation, which is formed by the + * sum of the products of tensor-product Legendre basis functions and the + * provided coefficients, at specified coordinates + * + * Parameters + * ---------- + * c : coefficients + * X : coordinates (in reference space) + * + * Note + * ---- + * The intermediate coefficients or workspace array is divided into 2 lines of + * length equal to the number of vertices. In the dimension-by-dimension + * approach used for the approximation evaluation, each line is filled by + * evaluations at the previous dimensional level. The initial coefficients are + * cycled through in the X-dimension loop to produce coefficients, stored in + * the workspace array, to be used in the Y-dimension loop. The output from the + * Y-dimension loop is coefficients, stored again in the workspace array, to be + * used in the final Z-dimension evaluation. + */ +template +NumType LegendreProductBasis::eval_approx(const NumType *c, + const NumType *X) { + for (int k = 0; k < N; k++) { + for (int j = 0; j < N; j++) { + // Collapse first dimension into coefficients for second dimension + C[j] = legendre::eval_approx(N, &c[j*N+k*N*N], X[0]); + } + + // Collapse second dimension into coefficients for third dimension + C[N+k] = legendre::eval_approx(N, C, X[1]); + } + + // Collapse third dimension into approximation evaluation + return legendre::eval_approx(N, &C[N], X[2]); +} + +/* + * Evaluate gradient of the local function approximation, which is formed by + * the sum of the products of tensor-product Legendre basis functions and the + * provided coefficients, at specified coordinates + * + * Parameters + * ---------- + * c : coefficients + * X : coordinates (in reference space) + * + * Returns + * ------- + * grad_f : gradient of the approximation + */ +template +void LegendreProductBasis::eval_grad_approx(const NumType *c, + const NumType *X, NumType *grad_f) { + SizeType q = 1; // order of derivative + for (int l = 0; l < Nd; l++) { + for (int k = 0; k < N; k++) { + for (int j = 0; j < N; j++) { + // Collapse first dimension into coefficients for second dimension + if (l == 0) { + C[j] = legendre::eval_der_approx(N, 1, &c[j*N+k*N*N], X[0]); + } else { + C[j] = legendre::eval_approx(N, &c[j*N+k*N*N], X[0]); + } + } + + // Collapse second dimension into coefficients for third dimension + if (l == 1) { + C[N+k] = legendre::eval_der_approx(N, q, C, X[1]); + } else { + C[N+k] = legendre::eval_approx(N, C, X[1]); + } + } + + // Collapse third dimension into approximation evaluation + if (l == 2) { + grad_f[l] = legendre::eval_der_approx(N, q, &C[N], X[2]); + } else { + grad_f[l] = legendre::eval_approx(N, &C[N], X[2]); + } + } +} + +// Explicit instantiation of template class +template class LegendreProductBasis; +template class LegendreProductBasis; diff --git a/elements-kokkos/src/TensorProductBasis.cpp b/elements-kokkos/src/TensorProductBasis.cpp new file mode 100644 index 00000000..70b5f024 --- /dev/null +++ b/elements-kokkos/src/TensorProductBasis.cpp @@ -0,0 +1,30 @@ +#include "TensorProductBasis.h" + +#include "error.h" + + +void TensorProductBasis::eval_jac(const NumType *, const NumType *, + const NumType *, const NumType *, NumType *) { + std::string err_msg( + "Error: Jacobian routines not implemented for this basis type.") + throw NotImplementedError(err_msg); +}; + +NumType TensorProductBasis::eval_det_jac(const NumType *, const NumType *, + const NumType *, const NumType *) { + std::string err_msg( + "Error: Jacobian routines not implemented for this basis type.") + throw NotImplementedError(err_msg); + return 0.0; +} + +void TensorProductBasis::eval_inv_jac(const NumType *, const NumType *, + const NumType *, const NumType *, NumType *) { + std::string err_msg( + "Error: Jacobian routines not implemented for this basis type.") + throw NotImplementedError(err_msg); +} + +// Explicit instantiation of template class +template class TensorProductBasis; +template class LegendreProductBasis; diff --git a/elements-kokkos/src/jacobi_polynomials.cpp b/elements-kokkos/src/jacobi_polynomials.cpp new file mode 100644 index 00000000..98e4df68 --- /dev/null +++ b/elements-kokkos/src/jacobi_polynomials.cpp @@ -0,0 +1,33 @@ +#include "jacobi_polynomials.h" + +namespace jacobi { + template + NumType eval(const int n, const Real alpha, const Real beta, + const NumType X) { + if (n == -1) return 0.0; + if (n == 0) return 1.0; + return (a(alpha, beta, n)*X + b(alpha, beta, n)) + *eval(n - 1, alpha, beta, X) + - c(alpha, beta, n)*eval(n - 2, alpha, beta, X); + } + + template + NumType eval_der(const int n, const int k, const Real alpha, + const Real beta, const NumType X) { + if (n == 0 || k > n) return 0.0; + Real theta = Real(n) + Real(alpha + alpha) + 1.0; + return std::pow(0.5, k)*std::tgamma(theta + Real(k)) + *eval(n - k, alpha + Real(k), beta + Real(k), X)/std::tgamma(theta); + } + + // Explicit instantiations of template functions + template Real eval(const int n, const Real alpha, const Real beta, + const Real X); + template Complex eval(const int n, const Real alpha, const Real beta, + const Complex X); + + template Real eval_der(const int n, const int k, const Real alpha, + const Real beta, const Real X); + template Complex eval_der(const int n, const int k, const Real alpha, + const Real beta, const Complex X); +} diff --git a/elements-kokkos/src/lagrange_polynomials.cpp b/elements-kokkos/src/lagrange_polynomials.cpp new file mode 100644 index 00000000..28ccb511 --- /dev/null +++ b/elements-kokkos/src/lagrange_polynomials.cpp @@ -0,0 +1,295 @@ +#include "lagrange_polynomials.h" + +namespace lagrange { + /* + * If the input coordinate is coincident with any of the input vertices, + * return the index of the vertex with which it coincides + * + * It is typically bad practice to check if two floating point numbers, say x + * and y, are equal by evaluating x - y == 0. But that is precisely what the + * authors suggest to do in "Barycentric Lagrange Interpolation" (Berrut and + * Trefethen, 2004). It is also what the authors of Nektar++ do in their + * implementation of barycentric Lagrange interpolation. I'm not sure what to + * do + * + * Parameters + * ---------- + * N : number of vertices + * z : vertex coordinates + * x : coordinate to test + */ + template + SizeType find_coincident_vertex(const SizeType &N, const NumType *z, + const NumType &x) { + // The largest number an unsigned integer can be + SizeType k = -1; + + // Adding to -1 in unsigned rolls over zero + for (SizeType j = 0; j < N; j++) { + //k += (j + 1)*SizeType(z[j] - x == 0.0); + k += (j + 1)*SizeType(common::almost_equal(z[j], x)); + } + + return k; + } + + /* + * Calculation of barycentric weights of Lagrange interpolant vertices + * + * Parameters + * ---------- + * N : number of vertices + * z : vertex coordinates + * + * Returns + * ------- + * w : barycentric vertex weights + * + * Notes + * ----- + * If one evaluates the interpolant using the barycentric formula of the + * second kind, the barycentric weights may be scaled by an arbitrary scalar + * (the maximum weight, for example). Since I am using the barycentric + * formula of the first kind (also called the modified Lagrange formula), I + * cannot and do not scale the weights + */ + template + void compute_barycentric_weights(const SizeType &N, const NumType *z, + NumType *w) { + // Compute weights + for (SizeType j = 0; j < N; j++) { + w[j] = 1.0; + for (SizeType k = 0; k < N; k++) { + // TODO optimization: make branchless? Trefethen uses log o exp trick + if (j != k) w[j] *= 1.0/(z[j] - z[k]); + } + } + }; + + /* + * Return evaluation of Lagrange polynomial associated with a given vertex at + * a given coordinate + * + * Parameters + * ---------- + * Nv : number of vertices + * i : index of vertex + * ic : index of vertex coincident with X (-1 if not coincident) + * Z : vertex coordinates + * w : barycentric weights + * X : coordinate at which to evaluate + */ + template + NumType eval(const SizeType Nv, const SizeType i, const SizeType ic, + const NumType *Z, const NumType *w, const NumType X) { + if (ic < Nv) return i == ic ? 1.0 : 0.0; + + // Evaluate nodal polynomial + NumType L = 1.0; + for (SizeType j = 0; j < Nv; j++) L *= (X - Z[j]); + + return L*w[i]/(X - Z[i]); + } + + /* + * Return evaluation of derivative of Lagrange polynomial associated with a + * given vertex at a given coordinate + * + * Currently implemented as a special case of interpolant derivative + * evaluation. There is probably a better way to do this, but I haven't + * gotten around to finding it and implementing it + * + * Parameters + * ---------- + * Nv : number of vertices + * n : order of derivative + * i : index of vertex + * ic : index of vertex coincident with X (-1 if not coincident) + * Z : vertex coordinates + * w : barycentric weights + * X : coordinate at which to evaluate + * c : work array for intermediate coefficients + */ + template + NumType eval_der(const SizeType Nv, const SizeType n, const SizeType i, + const SizeType ic, const NumType *Z, const NumType *w, + const NumType X, NumType *c) { + // Initialize coefficients of interpolant to Kronecker deltas to create + // interpolant equivalent to Lagrange polynomial at vertex + for (SizeType j = 0; j < Nv; j++) { + if (j != i) { c[j] = 0.0; } else { c[j] = 1.0; } + } + + NumType dnl = eval_der_interp(Nv, n, ic, Z, w, X, c); + + return dnl; + } + + /* + * Return evaluation of Lagrange interpolant, which is the sum of the + * products of Lagrange polynomials and provided coefficients, at specified + * coordinates + * + * This implementation uses the modified Lagrange formula (barycentric + * formula of the first kind) from "Barycentric Lagrange Interpolation" + * (Berrut and Trefethen, 2004). + * + * Parameters + * ---------- + * Nv : number of vertices + * i : index of vertex coincident with coordinate (-1 if not coincident) + * Z : vertex coordinates + * w : barycentric vertex weights + * X : coordinate at which to evaluate interpolant + * c : input coefficients (function values at vertices) + */ + template + NumType eval_interp(const SizeType Nv, const SizeType i, const NumType *Z, + const NumType *w, const NumType X, const NumType *c) { + NumType p; + NumType L = 1.0; // nodal polynomial evaluation + + // Evaluate the interpolant + if (i < Nv) { // coincident + return c[i]; + } else { // non-coincident + // Loop over vertices + p = 0.0; + for (SizeType j = 0; j < Nv; j++) { + // Contribution to interpolant evaluation + p += w[j]*c[j]/(X - Z[j]); + + // Contribution to scalar (nodal polynomial evaluation) + L *= (X - Z[j]); + } + + // Apply scaling + p *= L; + } + + return p; + } + + /* + * Return evaluation of derivative of Lagrange interpolant, which is the sum + * of the products of the derivatives of Lagrange polynomials and provided + * coefficients, at specified coordinates + * + * This implementation is based on the formula for the derivative of a + * rational interpolant given in "Some New Aspects of Rational Interpolation" + * (Schneider and Werner, 1986). + * + * Parameters + * ---------- + * Nv : number of vertices + * n : order of derivative + * i : index of vertex coincident with coordinate (-1 if not coincident) + * Z : vertex coordinates + * w : barycentric vertex weights + * X : coordinate at which to eval interpolant + * c : input coefficients (will be modified) + */ + template + NumType eval_der_interp(const SizeType Nv, const SizeType n, const SizeType i, + const NumType *Z, const NumType *w, const NumType X, NumType *c) { + // Interpolant and nodal polynomial evaluation + NumType p = 0.0; // interpolant evaluation + NumType L = 1.0; // nodal polynomial + if (i < Nv) { // coincident + p = c[i]; + } else { // non-coincident + // Loop over vertices + p = 0.0; + for (SizeType j = 0; j < Nv; j++) { + // Contribution to interpolant evaluation + p += w[j]*c[j]/(X - Z[j]); + + // Contribution to scalar (nodal polynomial evaluation) + L *= (X - Z[j]); + } + + // Apply scaling + p *= L; + } + + // Evaluate derivatives, building up to specified order + NumType dkp = p, dnp = 0.0; + NumType M = 1.0; // factorial(k) + if (i < Nv) { // coincident + for (SizeType k = 1; k <= n; k++) { + // Zero the output + dnp = 0.0; + + for (SizeType j = 0; j < Nv; j++) { + // Calculate divided difference and store in intermediate coefficients + NumType sx = 1.0/(Z[i] - Z[j]); + c[j] = sx*(dkp - c[j]); + + // Update output coefficient with contribution from vertex + // TODO optimization: make branchless? Trefethen uses log o exp trick + if (j != i) dnp += w[j]*c[j]; + } + + // Scale the output and copy for use in calculating next order + M *= k; + dnp *= -M/w[i]; + dkp = dnp; + } + } else { // non-coincident + for (SizeType k = 1; k <= n; k++) { + // Zero the output + dnp = 0.0; + + for (SizeType j = 0; j < Nv; j++) { + // Calculate divided difference and store in intermediate coefficients + NumType sx = 1.0/(X - Z[j]); + c[j] = sx*(dkp - c[j]); + + // Update output coefficient with contribution from vertex + dnp += w[j]*c[j]/(X - Z[j]); + } + + // Scale the output and copy for use in calculating next order + M *= k; + dnp *= L*M; + dkp = dnp; + } + } + + return dnp; + } + + // Explicit instantiations of template functions + template SizeType find_coincident_vertex(const SizeType &N, const Real *z, + const Real &x); + template SizeType find_coincident_vertex(const SizeType &N, const Complex *z, + const Complex &x); + + template void compute_barycentric_weights(const SizeType &N, const Real *z, + Real *w); + template void compute_barycentric_weights(const SizeType &N, const Complex *z, + Complex *w); + + template Real eval(const SizeType Nv, const SizeType i, const SizeType ic, + const Real *Z, const Real *w, const Real X); + template Complex eval(const SizeType Nv, const SizeType i, const SizeType ic, + const Complex *Z, const Complex *w, const Complex X); + + template Real eval_der(const SizeType Nv, const SizeType n, const SizeType i, + const SizeType ic, const Real *Z, const Real *w, const Real X, Real *c); + template Complex eval_der(const SizeType Nv, const SizeType n, + const SizeType i, const SizeType ic, const Complex *Z, const Complex *w, + const Complex X, Complex *c); + + template Real eval_interp(const SizeType Nv, const SizeType i, const Real *Z, + const Real *w, const Real X, const Real *c); + template Complex eval_interp(const SizeType Nv, const SizeType i, + const Complex *Z, const Complex *w, const Complex X, const Complex *c); + + template Real eval_der_interp(const SizeType Nv, const SizeType n, + const SizeType i, const Real *Z, const Real *w, const Real X, + Real *c); + template Complex eval_der_interp(const SizeType Nv, const SizeType n, + const SizeType i, const Complex *Z, const Complex *w, const Complex X, + Complex *c); +} diff --git a/elements-kokkos/src/legendre_polynomials.cpp b/elements-kokkos/src/legendre_polynomials.cpp new file mode 100644 index 00000000..3df8b496 --- /dev/null +++ b/elements-kokkos/src/legendre_polynomials.cpp @@ -0,0 +1,95 @@ +#include "legendre_polynomials.h" +#include "jacobi_polynomials.h" + +namespace legendre { + /* + * Return evaluation of Legendre polynomial of specified order at given + * coordinate + * + * Parameters + * ---------- + * n : order of Legendre polynomial + * X : coordinate in reference space [-1, 1] + */ + template + NumType eval(const int n, const NumType X) { + if (n == -1) return 0.0; + if (n == 0) return 1.0; + return (1.0/double(n))*((2.0*double(n) - 1.0)*X*eval(n - 1, X) + - (double(n) - 1.0)*eval(n - 2, X)); + }; + + /* + * Return evaluation of Legendre polynomial of specified order at given + * coordinate + * + * Parameters + * ---------- + * n : order of Legendre polynomial + * k : order of derivative + * X : coordinate in reference space [-1, 1] + */ + template + NumType eval_der(const int n, const int k, const NumType X) { + return jacobi::eval_der(n, k, 0.0, 0.0, X); + }; + + /* + * Return evaluation of Legendre polynomial approximation, which is the sum + * of the products of Legendre polynomials and provided coefficients, at a + * specified coordinate + * + * Parameters + * ---------- + * N : maximum polynomial order + * c : coefficients + * X : coordinate in reference space [-1, 1] + */ + template + NumType eval_approx(const SizeType N, const NumType *c, const NumType X) { + NumType sum = 0.0; + for (SizeType j = 0; j < N; j++) { + sum += c[j]*eval(j, X); + } + + return sum; + } + + /* + * Return evaluation of derivative of Legendre polynomial approximation, + * which is the sum of the products of the derivatives of the Legendre + * polynomials and provided coefficients, at a specified coordinate + * + * Parameters + * ---------- + * N : maximum polynomial order + * c : coefficients + * X : coordinate in reference space [-1, 1] + */ + template + NumType eval_der_approx(const SizeType N, const SizeType k, const NumType *c, + const NumType X) { + NumType sum = 0.0; + for (SizeType j = 0; j < N; j++) { + sum += c[j]*eval_der(j, k, X); + } + + return sum; + } + + // Explicit instatiations of template functions + template Real eval(const int n, const Real X); + template Complex eval(const int n, const Complex X); + + template Real eval_der(const int n, const int k, const Real X); + template Complex eval_der(const int n, const int k, const Complex X); + + template Real eval_approx(const SizeType N, const Real *c, const Real X); + template Complex eval_approx(const SizeType N, const Complex *c, + const Complex X); + + template Real eval_der_approx(const SizeType N, const SizeType k, + const Real *c, const Real X); + template Complex eval_der_approx(const SizeType N, const SizeType k, + const Complex *c, const Complex X); +} diff --git a/elements-kokkos/src/points_and_weights.cpp b/elements-kokkos/src/points_and_weights.cpp new file mode 100644 index 00000000..2130ed42 --- /dev/null +++ b/elements-kokkos/src/points_and_weights.cpp @@ -0,0 +1,1103 @@ +#include "points_and_weights.h" + + +/* + * Fill an array with points equally spaced between end points (inclusive) + * + * Parameters + * ---------- + * N : number of points + * Zl : left end point + * Zr : right end point + * + * Returns + * ------- + * Z : array of equispaced points + */ +template +void equispaced_points(SizeType N, NumType &Zl, NumType &Zr, NumType *Z) { + for (SizeType i = 0; i < N; i++) + Z[i] = Zl + double(i)/double(N - 1)*(Zr - Zl); +} + + +/* + * Fill an array with Chebyshev points of the second kind in the interval + * defined by the specified end points. The symmetry-preserving technique from + * Chebfun (chebtech1/chebpts.m) is used. + * + * Parameters + * ---------- + * N : number of points + * Zl : left end point + * Zr : right end point + * + * Returns + * ------- + * Z : array of Chebyshev points + */ +template +void chebyshev_points(SizeType N, NumType &Zl, NumType &Zr, NumType *Z) { + // Evaluate the points using sine function to preserve symmetry + NumType f = 0.5*M_PI/double(N); + for (SizeType i = 0; i < N; i++) { + int j = (-1*int(N) + 1) + 2*int(i); + Z[i] = sin(f*double(j)); + } + + // Scale the points to fit the domain + for (int i = 0; i < N; i++) + Z[i] = 0.5*(1.0 - Z[i])*Zl + 0.5*(1.0 + Z[i])*Zr; +} + + +// Explicit instantations of template functions +template void equispaced_points(SizeType N, Real &Zl, Real &Zr, Real *Z); +template void equispaced_points(SizeType N, Complex &Zl, Complex &Zr, Complex *Z); + +template void chebyshev_points(SizeType N, Real &Zl, Real &Zr, Real *Z); +template void chebyshev_points(SizeType N, Complex &Zl, Complex &Zr, Complex *Z); + + +/* + * Fill an array with Gauss-Lobatto quadrature points (endpoints are -1 and 1) + * + * Parameters + * ---------- + * lob_points : MATAR CArray to fill with points + * num : number of points in quadrature rule + * + * Returns + * ------- + * lob_points : MATAR CArray to fill with points + */ + +void lobatto_points(MatarRealCArray &lob_points, const int &num) { + switch (num) { + case 1: + lob_points(0) = 0.0; + break; + case 2: + lob_points(0) = -1.0; + lob_points(1) = 1.0; + break; + case 3: + lob_points(0) = -1.0; + lob_points(1) = 0.0; + lob_points(2) = 1.0; + break; + case 4: + lob_points(0) = -1.0; + lob_points(1) = -1.0/5.0*sqrt(5.0); + lob_points(2) = 1.0/5.0*sqrt(5.0); + lob_points(3) = 1.0; + break; + case 5: + lob_points(0) = -1.0; + lob_points(1) = -1.0/7.0*sqrt(21.0); + lob_points(2) = 0.0; + lob_points(3) = 1.0/7.0*sqrt(21.0); + lob_points(4) = 1.0; + break; + case 6: + lob_points(0) = -1.0; + lob_points(1) = -sqrt(1.0/21.0*(7.0 + 2.0*sqrt(7.0))); + lob_points(2) = -sqrt(1.0/21.0*(7.0 - 2.0*sqrt(7.0))); + lob_points(3) = sqrt(1.0/21.0*(7.0 - 2.0*sqrt(7.0))); + lob_points(4) = sqrt(1.0/21.0*(7.0 +2.0*sqrt(7.0))); + lob_points(5) = 1.0; + break; + case 7: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.830223896278566929872032213967E+00; + lob_points(2) = - 0.468848793470714213803771881909E+00; + lob_points(3) = 0.0E+00; + lob_points(4) = 0.468848793470714213803771881909E+00; + lob_points(5) = 0.830223896278566929872032213967E+00; + lob_points(6) = 1.0E+00; + break; + case 8: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.871740148509606615337445761221E+00; + lob_points(2) = - 0.591700181433142302144510731398E+00; + lob_points(3) = - 0.209299217902478868768657260345E+00; + lob_points(4) = 0.209299217902478868768657260345E+00; + lob_points(5) = 0.591700181433142302144510731398E+00; + lob_points(6) = 0.871740148509606615337445761221E+00; + lob_points(7) = 1.0E+00; + break; + case 9: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.899757995411460157312345244418E+00; + lob_points(2) = - 0.677186279510737753445885427091E+00; + lob_points(3) = - 0.363117463826178158710752068709E+00; + lob_points(4) = 0.0E+00; + lob_points(5) = 0.363117463826178158710752068709E+00; + lob_points(6) = 0.677186279510737753445885427091E+00; + lob_points(7) = 0.899757995411460157312345244418E+00; + lob_points(8) = 1.0E+00; + break; + case 10: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.919533908166458813828932660822E+00; + lob_points(2) = - 0.738773865105505075003106174860E+00; + lob_points(3) = - 0.477924949810444495661175092731E+00; + lob_points(4) = - 0.165278957666387024626219765958E+00; + lob_points(5) = 0.165278957666387024626219765958E+00; + lob_points(6) = 0.477924949810444495661175092731E+00; + lob_points(7) = 0.738773865105505075003106174860E+00; + lob_points(8) = 0.919533908166458813828932660822E+00; + lob_points(9) = 1.0E+00; + break; + case 11: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.934001430408059134332274136099E+00; + lob_points(2) = - 0.784483473663144418622417816108E+00; + lob_points(3) = - 0.565235326996205006470963969478E+00; + lob_points(4) = - 0.295758135586939391431911515559E+00; + lob_points(5) = 0.0E+00; + lob_points(6) = 0.295758135586939391431911515559E+00; + lob_points(7) = 0.565235326996205006470963969478E+00; + lob_points(8) = 0.784483473663144418622417816108E+00; + lob_points(9) = 0.934001430408059134332274136099E+00; + lob_points(10) = 1.0E+00; + break; + case 12: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.944899272222882223407580138303E+00; + lob_points(2) = - 0.819279321644006678348641581717E+00; + lob_points(3) = - 0.632876153031869677662404854444E+00; + lob_points(4) = - 0.399530940965348932264349791567E+00; + lob_points(5) = - 0.136552932854927554864061855740E+00; + lob_points(6) = 0.136552932854927554864061855740E+00; + lob_points(7) = 0.399530940965348932264349791567E+00; + lob_points(8) = 0.632876153031869677662404854444E+00; + lob_points(9) = 0.819279321644006678348641581717E+00; + lob_points(10) = 0.944899272222882223407580138303E+00; + lob_points(11) = 1.0E+00; + break; + case 13: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.953309846642163911896905464755E+00; + lob_points(2) = - 0.846347564651872316865925607099E+00; + lob_points(3) = - 0.686188469081757426072759039566E+00; + lob_points(4) = - 0.482909821091336201746937233637E+00; + lob_points(5) = - 0.249286930106239992568673700374E+00; + lob_points(6) = 0.0E+00; + lob_points(7) = 0.249286930106239992568673700374E+00; + lob_points(8) = 0.482909821091336201746937233637E+00; + lob_points(9) = 0.686188469081757426072759039566E+00; + lob_points(10) = 0.846347564651872316865925607099E+00; + lob_points(11) = 0.953309846642163911896905464755E+00; + lob_points(12) = 1.0E+00; + break; + case 14: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.959935045267260901355100162015E+00; + lob_points(2) = - 0.867801053830347251000220202908E+00; + lob_points(3) = - 0.728868599091326140584672400521E+00; + lob_points(4) = - 0.550639402928647055316622705859E+00; + lob_points(5) = - 0.342724013342712845043903403642E+00; + lob_points(6) = - 0.116331868883703867658776709736E+00; + lob_points(7) = 0.116331868883703867658776709736E+00; + lob_points(8) = 0.342724013342712845043903403642E+00; + lob_points(9) = 0.550639402928647055316622705859E+00; + lob_points(10) = 0.728868599091326140584672400521E+00; + lob_points(11) = 0.867801053830347251000220202908E+00; + lob_points(12) = 0.959935045267260901355100162015E+00; + lob_points(13) = 1.0E+00; + break; + case 15: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.965245926503838572795851392070E+00; + lob_points(2) = - 0.885082044222976298825401631482E+00; + lob_points(3) = - 0.763519689951815200704118475976E+00; + lob_points(4) = - 0.606253205469845711123529938637E+00; + lob_points(5) = - 0.420638054713672480921896938739E+00; + lob_points(6) = - 0.215353955363794238225679446273E+00; + lob_points(7) = 0.0E+00; + lob_points(8) = 0.215353955363794238225679446273E+00; + lob_points(9) = 0.420638054713672480921896938739E+00; + lob_points(10) = 0.606253205469845711123529938637E+00; + lob_points(11) = 0.763519689951815200704118475976E+00; + lob_points(12) = 0.885082044222976298825401631482E+00; + lob_points(13) = 0.965245926503838572795851392070E+00; + lob_points(14) = 1.0E+00; + break; + case 16: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.969568046270217932952242738367E+00; + lob_points(2) = - 0.899200533093472092994628261520E+00; + lob_points(3) = - 0.792008291861815063931088270963E+00; + lob_points(4) = - 0.652388702882493089467883219641E+00; + lob_points(5) = - 0.486059421887137611781890785847E+00; + lob_points(6) = - 0.299830468900763208098353454722E+00; + lob_points(7) = - 0.101326273521949447843033005046E+00; + lob_points(8) = 0.101326273521949447843033005046E+00; + lob_points(9) = 0.299830468900763208098353454722E+00; + lob_points(10) = 0.486059421887137611781890785847E+00; + lob_points(11) = 0.652388702882493089467883219641E+00; + lob_points(12) = 0.792008291861815063931088270963E+00; + lob_points(13) = 0.899200533093472092994628261520E+00; + lob_points(14) = 0.969568046270217932952242738367E+00; + lob_points(15) = 1.0E+00; + break; + case 17: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.973132176631418314156979501874E+00; + lob_points(2) = - 0.910879995915573595623802506398E+00; + lob_points(3) = - 0.815696251221770307106750553238E+00; + lob_points(4) = - 0.691028980627684705394919357372E+00; + lob_points(5) = - 0.541385399330101539123733407504E+00; + lob_points(6) = - 0.372174433565477041907234680735E+00; + lob_points(7) = - 0.189511973518317388304263014753E+00; + lob_points(8) = 0.0E+00; + lob_points(9) = 0.189511973518317388304263014753E+00; + lob_points(10) = 0.372174433565477041907234680735E+00; + lob_points(11) = 0.541385399330101539123733407504E+00; + lob_points(12) = 0.691028980627684705394919357372E+00; + lob_points(13) = 0.815696251221770307106750553238E+00; + lob_points(14) = 0.910879995915573595623802506398E+00; + lob_points(15) = 0.973132176631418314156979501874E+00; + lob_points(16) = 1.0E+00; + break; + case 18: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.976105557412198542864518924342E+00; + lob_points(2) = - 0.920649185347533873837854625431E+00; + lob_points(3) = - 0.835593535218090213713646362328E+00; + lob_points(4) = - 0.723679329283242681306210365302E+00; + lob_points(5) = - 0.588504834318661761173535893194E+00; + lob_points(6) = - 0.434415036912123975342287136741E+00; + lob_points(7) = - 0.266362652878280984167665332026E+00; + lob_points(8) = - 0.897490934846521110226450100886E-01; + lob_points(9) = 0.897490934846521110226450100886E-01; + lob_points(10) = 0.266362652878280984167665332026E+00; + lob_points(11) = 0.434415036912123975342287136741E+00; + lob_points(12) = 0.588504834318661761173535893194E+00; + lob_points(13) = 0.723679329283242681306210365302E+00; + lob_points(14) = 0.835593535218090213713646362328E+00; + lob_points(15) = 0.920649185347533873837854625431E+00; + lob_points(16) = 0.976105557412198542864518924342E+00; + lob_points(17) = 1.0E+00; + break; + case 19: + lob_points(0)= - 1.0E+00; + lob_points(1)= - 0.978611766222080095152634063110E+00; + lob_points(2)= - 0.928901528152586243717940258797E+00; + lob_points(3)= - 0.852460577796646093085955970041E+00; + lob_points(4)= - 0.751494202552613014163637489634E+00; + lob_points(5)= - 0.628908137265220497766832306229E+00; + lob_points(6)= - 0.488229285680713502777909637625E+00; + lob_points(7)= - 0.333504847824498610298500103845E+00; + lob_points(8)= - 0.169186023409281571375154153445E+00; + lob_points(9)= 0.0E+00; + lob_points(10) = 0.169186023409281571375154153445E+00; + lob_points(11) = 0.333504847824498610298500103845E+00; + lob_points(12) = 0.488229285680713502777909637625E+00; + lob_points(13) = 0.628908137265220497766832306229E+00; + lob_points(14) = 0.751494202552613014163637489634E+00; + lob_points(15) = 0.852460577796646093085955970041E+00; + lob_points(16) = 0.928901528152586243717940258797E+00; + lob_points(17) = 0.978611766222080095152634063110E+00; + lob_points(18) = 1.0E+00; + break; + case 20: + lob_points(0) = - 1.0E+00; + lob_points(1) = - 0.980743704893914171925446438584E+00; + lob_points(2) = - 0.935934498812665435716181584931E+00; + lob_points(3) = - 0.866877978089950141309847214616E+00; + lob_points(4) = - 0.775368260952055870414317527595E+00; + lob_points(5) = - 0.663776402290311289846403322971E+00; + lob_points(6) = - 0.534992864031886261648135961829E+00; + lob_points(7) = - 0.392353183713909299386474703816E+00; + lob_points(8) = - 0.239551705922986495182401356927E+00; + lob_points(9) = - 0.805459372388218379759445181596E-01; + lob_points(10) = 0.805459372388218379759445181596E-01; + lob_points(11) = 0.239551705922986495182401356927E+00; + lob_points(12) = 0.392353183713909299386474703816E+00; + lob_points(13) = 0.534992864031886261648135961829E+00; + lob_points(14) = 0.663776402290311289846403322971E+00; + lob_points(15) = 0.775368260952055870414317527595E+00; + lob_points(16) = 0.866877978089950141309847214616E+00; + lob_points(17) = 0.935934498812665435716181584931E+00; + lob_points(18) = 0.980743704893914171925446438584E+00; + lob_points(19) = 1.0E+00; + break; + default: + std::ostringstream ss; + ss << "Error: " << num << "-point quadrature rule not implemented."; + throw NotImplemented(ss.str()); + } +} + + +/* + * Fill an array with Gauss-Lobatto quadrature weights + * + * Parameters + * ---------- + * lob_weights : MATAR CArray to fill with weights + * num : number of points in quadrature rule + * + * Returns + * ------- + * lob_weights : MATAR CArray to fill with weights + */ +void lobatto_weights(MatarRealCArray &lob_weights, const int &num) { + switch (num) { + case 1: + lob_weights(0) = 2.0; + break; + case 2: + lob_weights(0) = 1.0; + lob_weights(1) = 1.0; + break; + case 3: + lob_weights(0) = 1.0/3.0; + lob_weights(1) = 4.0/3.0; + lob_weights(2) = 1.0/3.0; + break; + case 4: + lob_weights(0) = 1.0/6.0; + lob_weights(1) = 5.0/6.0; + lob_weights(2) = 5.0/6.0; + lob_weights(3) = 1.0/6.0; + break; + case 5: + lob_weights(0) = 1.0/10.0; + lob_weights(1) = 49.0/90.0; + lob_weights(2) = 32.0/45.0; + lob_weights(3) = 49.0/90.0; + lob_weights(4) = 1.0/10.0; + break; + case 6: + lob_weights(0) = 1.0/15.0; + lob_weights(1) = 1.0/30.0*(14.0 - sqrt(7.0)); + lob_weights(2) = 1.0/30.0*(14.0 + sqrt(7.0)); + lob_weights(3) = 1.0/30.0*(14.0 + sqrt(7.0)); + lob_weights(4) = 1.0/30.0*(14.0 - sqrt(7.0)); + lob_weights(5) = 1.0/15.0; + break; + case 7: + lob_weights(0) = 0.476190476190476190476190476190E-01; + lob_weights(1) = 0.276826047361565948010700406290E+00; + lob_weights(2) = 0.431745381209862623417871022281E+00; + lob_weights(3) = 0.487619047619047619047619047619E+00; + lob_weights(4) = 0.431745381209862623417871022281E+00; + lob_weights(5) = 0.276826047361565948010700406290E+00; + lob_weights(6) = 0.476190476190476190476190476190E-01; + break; + case 8: + lob_weights(0) = 0.357142857142857142857142857143E-01; + lob_weights(1) = 0.210704227143506039382991065776E+00; + lob_weights(2) = 0.341122692483504364764240677108E+00; + lob_weights(3) = 0.412458794658703881567052971402E+00; + lob_weights(4) = 0.412458794658703881567052971402E+00; + lob_weights(5) = 0.341122692483504364764240677108E+00; + lob_weights(6) = 0.210704227143506039382991065776E+00; + lob_weights(7) = 0.357142857142857142857142857143E-01; + break; + case 9: + lob_weights(0) = 0.277777777777777777777777777778E-01; + lob_weights(1) = 0.165495361560805525046339720029E+00; + lob_weights(2) = 0.274538712500161735280705618579E+00; + lob_weights(3) = 0.346428510973046345115131532140E+00; + lob_weights(4) = 0.371519274376417233560090702948E+00; + lob_weights(5) = 0.346428510973046345115131532140E+00; + lob_weights(6) = 0.274538712500161735280705618579E+00; + lob_weights(7) = 0.165495361560805525046339720029E+00; + lob_weights(8) = 0.277777777777777777777777777778E-01; + break; + case 10: + lob_weights(0) = 0.222222222222222222222222222222E-01; + lob_weights(1) = 0.133305990851070111126227170755E+00; + lob_weights(2) = 0.224889342063126452119457821731E+00; + lob_weights(3) = 0.292042683679683757875582257374E+00; + lob_weights(4) = 0.327539761183897456656510527917E+00; + lob_weights(5) = 0.327539761183897456656510527917E+00; + lob_weights(6) = 0.292042683679683757875582257374E+00; + lob_weights(7) = 0.224889342063126452119457821731E+00; + lob_weights(8) = 0.133305990851070111126227170755E+00; + lob_weights(9) = 0.222222222222222222222222222222E-01; + break; + case 11: + lob_weights(0) = 0.181818181818181818181818181818E-01; + lob_weights(1) = 0.109612273266994864461403449580E+00; + lob_weights(2) = 0.187169881780305204108141521899E+00; + lob_weights(3) = 0.248048104264028314040084866422E+00; + lob_weights(4) = 0.286879124779008088679222403332E+00; + lob_weights(5) = 0.300217595455690693785931881170E+00; + lob_weights(6) = 0.286879124779008088679222403332E+00; + lob_weights(7) = 0.248048104264028314040084866422E+00; + lob_weights(8) = 0.187169881780305204108141521899E+00; + lob_weights(9) = 0.109612273266994864461403449580E+00; + lob_weights(10)= 0.181818181818181818181818181818E-01; + break; + case 12: + lob_weights(0) = 0.151515151515151515151515151515E-01; + lob_weights(1) = 0.916845174131961306683425941341E-01; + lob_weights(2) = 0.157974705564370115164671062700E+00; + lob_weights(3) = 0.212508417761021145358302077367E+00; + lob_weights(4) = 0.251275603199201280293244412148E+00; + lob_weights(5) = 0.271405240910696177000288338500E+00; + lob_weights(6) = 0.271405240910696177000288338500E+00; + lob_weights(7) = 0.251275603199201280293244412148E+00; + lob_weights(8) = 0.212508417761021145358302077367E+00; + lob_weights(9) = 0.157974705564370115164671062700E+00; + lob_weights(10) = 0.916845174131961306683425941341E-01; + lob_weights(11) = 0.151515151515151515151515151515E-01; + break; + case 13: + lob_weights(0) = 0.128205128205128205128205128205E-01; + lob_weights(1) = 0.778016867468189277935889883331E-01; + lob_weights(2) = 0.134981926689608349119914762589E+00; + lob_weights(3) = 0.183646865203550092007494258747E+00; + lob_weights(4) = 0.220767793566110086085534008379E+00; + lob_weights(5) = 0.244015790306676356458578148360E+00; + lob_weights(6) = 0.251930849333446736044138641541E+00; + lob_weights(7) = 0.244015790306676356458578148360E+00; + lob_weights(8) = 0.220767793566110086085534008379E+00; + lob_weights(9) = 0.183646865203550092007494258747E+00; + lob_weights(10) = 0.134981926689608349119914762589E+00; + lob_weights(11) = 0.778016867468189277935889883331E-01; + lob_weights(12) = 0.128205128205128205128205128205E-01; + break; + case 14: + lob_weights(0) = 0.109890109890109890109890109890E-01; + lob_weights(1) = 0.668372844976812846340706607461E-01; + lob_weights(2) = 0.116586655898711651540996670655E+00; + lob_weights(3) = 0.160021851762952142412820997988E+00; + lob_weights(4) = 0.194826149373416118640331778376E+00; + lob_weights(5) = 0.219126253009770754871162523954E+00; + lob_weights(6) = 0.231612794468457058889628357293E+00; + lob_weights(7) = 0.231612794468457058889628357293E+00; + lob_weights(8) = 0.219126253009770754871162523954E+00; + lob_weights(9) = 0.194826149373416118640331778376E+00; + lob_weights(10) = 0.160021851762952142412820997988E+00; + lob_weights(11) = 0.116586655898711651540996670655E+00; + lob_weights(12) = 0.668372844976812846340706607461E-01; + lob_weights(13) = 0.109890109890109890109890109890E-01; + break; + case 15: + lob_weights(0) = 0.952380952380952380952380952381E-02; + lob_weights(1) = 0.580298930286012490968805840253E-01; + lob_weights(2) = 0.101660070325718067603666170789E+00; + lob_weights(3) = 0.140511699802428109460446805644E+00; + lob_weights(4) = 0.172789647253600949052077099408E+00; + lob_weights(5) = 0.196987235964613356092500346507E+00; + lob_weights(6) = 0.211973585926820920127430076977E+00; + lob_weights(7) = 0.217048116348815649514950214251E+00; + lob_weights(8) = 0.211973585926820920127430076977E+00; + lob_weights(9) = 0.196987235964613356092500346507E+00; + lob_weights(10) = 0.172789647253600949052077099408E+00; + lob_weights(11) = 0.140511699802428109460446805644E+00; + lob_weights(12) = 0.101660070325718067603666170789E+00; + lob_weights(13) = 0.580298930286012490968805840253E-01; + lob_weights(14) = 0.952380952380952380952380952381E-02; + case 16: + lob_weights(0) = 0.833333333333333333333333333333E-02; + lob_weights(1) = 0.508503610059199054032449195655E-01; + lob_weights(2) = 0.893936973259308009910520801661E-01; + lob_weights(3) = 0.124255382132514098349536332657E+00; + lob_weights(4) = 0.154026980807164280815644940485E+00; + lob_weights(5) = 0.177491913391704125301075669528E+00; + lob_weights(6) = 0.193690023825203584316913598854E+00; + lob_weights(7) = 0.201958308178229871489199125411E+00; + lob_weights(8) = 0.201958308178229871489199125411E+00; + lob_weights(9) = 0.193690023825203584316913598854E+00; + lob_weights(10) = 0.177491913391704125301075669528E+00; + lob_weights(11) = 0.154026980807164280815644940485E+00; + lob_weights(12) = 0.124255382132514098349536332657E+00; + lob_weights(13) = 0.893936973259308009910520801661E-01; + lob_weights(14) = 0.508503610059199054032449195655E-01; + lob_weights(15) = 0.833333333333333333333333333333E-02; + break; + case 17: + lob_weights(0) = 0.735294117647058823529411764706E-02; + lob_weights(1) = 0.449219405432542096474009546232E-01; + lob_weights(2) = 0.791982705036871191902644299528E-01; + lob_weights(3) = 0.110592909007028161375772705220E+00; + lob_weights(4) = 0.137987746201926559056201574954E+00; + lob_weights(5) = 0.160394661997621539516328365865E+00; + lob_weights(6) = 0.177004253515657870436945745363E+00; + lob_weights(7) = 0.187216339677619235892088482861E+00; + lob_weights(8) = 0.190661874753469433299407247028E+00; + lob_weights(9) = 0.187216339677619235892088482861E+00; + lob_weights(10) = 0.177004253515657870436945745363E+00; + lob_weights(11) = 0.160394661997621539516328365865E+00; + lob_weights(12) = 0.137987746201926559056201574954E+00; + lob_weights(13) = 0.110592909007028161375772705220E+00; + lob_weights(14) = 0.791982705036871191902644299528E-01; + lob_weights(15) = 0.449219405432542096474009546232E-01; + lob_weights(16) = 0.735294117647058823529411764706E-02; + break; + case 18: + lob_weights(0) = 0.653594771241830065359477124183E-02; + lob_weights(1) = 0.399706288109140661375991764101E-01; + lob_weights(2) = 0.706371668856336649992229601678E-01; + lob_weights(3) = 0.990162717175028023944236053187E-01; + lob_weights(4) = 0.124210533132967100263396358897E+00; + lob_weights(5) = 0.145411961573802267983003210494E+00; + lob_weights(6) = 0.161939517237602489264326706700E+00; + lob_weights(7) = 0.173262109489456226010614403827E+00; + lob_weights(8) = 0.179015863439703082293818806944E+00; + lob_weights(9) = 0.179015863439703082293818806944E+00; + lob_weights(10) = 0.173262109489456226010614403827E+00; + lob_weights(11) = 0.161939517237602489264326706700E+00; + lob_weights(12) = 0.145411961573802267983003210494E+00; + lob_weights(13) = 0.124210533132967100263396358897E+00; + lob_weights(14) = 0.990162717175028023944236053187E-01; + lob_weights(15) = 0.706371668856336649992229601678E-01; + lob_weights(16) = 0.399706288109140661375991764101E-01; + lob_weights(17) = 0.653594771241830065359477124183E-02; + break; + case 19: + lob_weights(0) = 0.584795321637426900584795321637E-02; + lob_weights(1) = 0.357933651861764771154255690351E-01; + lob_weights(2) = 0.633818917626297368516956904183E-01; + lob_weights(3) = 0.891317570992070844480087905562E-01; + lob_weights(4) = 0.112315341477305044070910015464E+00; + lob_weights(5) = 0.132267280448750776926046733910E+00; + lob_weights(6) = 0.148413942595938885009680643668E+00; + lob_weights(7) = 0.160290924044061241979910968184E+00; + lob_weights(8) = 0.167556584527142867270137277740E+00; + lob_weights(9) = 0.170001919284827234644672715617E+00; + lob_weights(10) = 0.167556584527142867270137277740E+00; + lob_weights(11) = 0.160290924044061241979910968184E+00; + lob_weights(12) = 0.148413942595938885009680643668E+00; + lob_weights(13) = 0.132267280448750776926046733910E+00; + lob_weights(14) = 0.112315341477305044070910015464E+00; + lob_weights(15) = 0.891317570992070844480087905562E-01; + lob_weights(16) = 0.633818917626297368516956904183E-01; + lob_weights(17) = 0.357933651861764771154255690351E-01; + lob_weights(18) = 0.584795321637426900584795321637E-02; + break; + case 20: + lob_weights(0) = 0.526315789473684210526315789474E-02; + lob_weights(1) = 0.322371231884889414916050281173E-01; + lob_weights(2) = 0.571818021275668260047536271732E-01; + lob_weights(3) = 0.806317639961196031447768461137E-01; + lob_weights(4) = 0.101991499699450815683781205733E+00; + lob_weights(5) = 0.120709227628674725099429705002E+00; + lob_weights(6) = 0.136300482358724184489780792989E+00; + lob_weights(7) = 0.148361554070916825814713013734E+00; + lob_weights(8) = 0.156580102647475487158169896794E+00; + lob_weights(9) = 0.160743286387845749007726726449E+00; + lob_weights(10) = 0.160743286387845749007726726449E+00; + lob_weights(11) = 0.156580102647475487158169896794E+00; + lob_weights(12) = 0.148361554070916825814713013734E+00; + lob_weights(13) = 0.136300482358724184489780792989E+00; + lob_weights(14) = 0.120709227628674725099429705002E+00; + lob_weights(15) = 0.101991499699450815683781205733E+00; + lob_weights(16) = 0.806317639961196031447768461137E-01; + lob_weights(17) = 0.571818021275668260047536271732E-01; + lob_weights(18) = 0.322371231884889414916050281173E-01; + lob_weights(19) = 0.526315789473684210526315789474E-02; + break; + default: + std::ostringstream ss; + ss << "Error: " << num << "-point quadrature rule not implemented."; + throw NotImplemented(ss.str()); + } +} + + +/* + * Fill an array with Gauss-Legendre quadrature points (endpoints are -1 and 1) + * + * Parameters + * ---------- + * leg_points : MATAR CArray to fill with points + * num : number of points in quadrature rule + * + * Returns + * ------- + * leg_points : MATAR CArray to fill with points + */ +void legendre_points(CArray &leg_points, const int &num) { + switch (num) { + case 1: + leg_points(0) = 0.0; + break; + case 2: + leg_points(0) = -0.577350269189625764509148780501; + leg_points(1) = 0.577350269189625764509148780501; + break; + case 3: + leg_points(0) = -0.774596669241483377035853079956; + leg_points(1) = 0.0; + leg_points(2) = 0.774596669241483377035853079956; + break; + case 4: + leg_points(0) = -0.861136311594052575223946488892; + leg_points(1) = -0.339981043584856264802665759103; + leg_points(2) = 0.339981043584856264802665759103; + leg_points(3) = 0.861136311594052575223946488892; + break; + case 5: + leg_points(0) = -0.906179845938663992797626878299; + leg_points(1) = -0.538469310105683091036314420700; + leg_points(2) = 0.0; + leg_points(3) = 0.538469310105683091036314420700; + leg_points(4) = 0.906179845938663992797626878299; + break; + case 6: + leg_points(0) = -0.932469514203152027812301554493; + leg_points(1) = -0.661209386466264513661399595019; + leg_points(2) = -0.238619186083196908630501721680; + leg_points(3) = 0.238619186083196908630501721680; + leg_points(4) = 0.661209386466264513661399595019; + leg_points(5) = 0.932469514203152027812301554493; + break; + case 7: + leg_points(0) = -0.949107912342758524526189684047; + leg_points(1) = -0.741531185599394439863864773280; + leg_points(2) = -0.405845151377397166906606412076; + leg_points(3) = 0.0E+00; + leg_points(4) = 0.405845151377397166906606412076; + leg_points(5) = 0.741531185599394439863864773280; + leg_points(6) = 0.949107912342758524526189684047; + break; + case 8: + leg_points(0) = -0.960289856497536231683560868569; + leg_points(1) = -0.796666477413626739591553936475; + leg_points(2) = -0.525532409916328985817739049189; + leg_points(3) = -0.183434642495649804939476142360; + leg_points(4) = 0.183434642495649804939476142360; + leg_points(5) = 0.525532409916328985817739049189; + leg_points(6) = 0.796666477413626739591553936475; + leg_points(7) = 0.960289856497536231683560868569; + break; + case 9: + leg_points(0) = -0.968160239507626089835576202903; + leg_points(1) = -0.836031107326635794299429788069; + leg_points(2) = -0.613371432700590397308702039341; + leg_points(3) = -0.324253423403808929038538014643; + leg_points(4) = 0.0E+00; + leg_points(5) = 0.324253423403808929038538014643; + leg_points(6) = 0.613371432700590397308702039341; + leg_points(7) = 0.836031107326635794299429788069; + leg_points(8) = 0.968160239507626089835576202903; + break; + case 10: + leg_points(0) = -0.9739065285171717200779640120844; + leg_points(1) = -0.8650633666889845107320966884234; + leg_points(2) = -0.6794095682990244062343273651148; + leg_points(3) = -0.4333953941292471907992659431657; + leg_points(4) = -0.1488743389816312108848260011297; + leg_points(5) = 0.1488743389816312108848260011297; + leg_points(6) = 0.4333953941292471907992659431657; + leg_points(7) = 0.6794095682990244062343273651148; + leg_points(8) = 0.8650633666889845107320966884234; + leg_points(9) = 0.9739065285171717200779640120844; + break; + case 11: + leg_points(0) = -0.9782286581460569928039380011228; + leg_points(1) = -0.8870625997680952990751577693039; + leg_points(2) = -0.7301520055740493240934162520311; + leg_points(3) = -0.5190961292068118159257256694586; + leg_points(4) = -0.2695431559523449723315319854008; + leg_points(5) = 0.0E+00; + leg_points(6) = 0.2695431559523449723315319854008; + leg_points(7) = 0.5190961292068118159257256694586; + leg_points(8) = 0.7301520055740493240934162520311; + leg_points(9) = 0.8870625997680952990751577693039; + leg_points(10) = 0.9782286581460569928039380011228; + break; + case 12: + leg_points(0) = -0.9815606342467192506905490901492; + leg_points(1) = -0.9041172563704748566784658661190; + leg_points(2) = -0.7699026741943046870368938332128; + leg_points(3) = -0.5873179542866174472967024189405; + leg_points(4) = -0.3678314989981801937526915366437; + leg_points(5) = -0.1252334085114689154724413694638; + leg_points(6) = 0.1252334085114689154724413694638; + leg_points(7) = 0.3678314989981801937526915366437; + leg_points(8) = 0.5873179542866174472967024189405; + leg_points(9) = 0.7699026741943046870368938332128; + leg_points(10) = 0.9041172563704748566784658661190; + leg_points(11) = 0.9815606342467192506905490901492; + break; + case 13: + leg_points(0) = -0.98418305471858814947282944880710; + leg_points(1) = -0.91759839922297796520654783650071; + leg_points(2) = -0.80157809073330991279420648958285; + leg_points(3) = -0.64234933944034022064398460699551; + leg_points(4) = -0.44849275103644685287791285212763; + leg_points(5) = -0.23045831595513479406552812109798; + leg_points(6) = 0.0E+00; + leg_points(7) = 0.23045831595513479406552812109798; + leg_points(8) = 0.44849275103644685287791285212763; + leg_points(9) = 0.64234933944034022064398460699551; + leg_points(10) = 0.80157809073330991279420648958285; + leg_points(11) = 0.91759839922297796520654783650071; + leg_points(12) = 0.98418305471858814947282944880710; + break; + case 14: + leg_points(0) = -0.986283808696812338841597266704052; + leg_points(1) = -0.928434883663573517336391139377874; + leg_points(2) = -0.827201315069764993189794742650394; + leg_points(3) = -0.687292904811685470148019803019334; + leg_points(4) = -0.515248636358154091965290718551188; + leg_points(5) = -0.319112368927889760435671824168475; + leg_points(6) = -0.108054948707343662066244650219834; + leg_points(7) = 0.108054948707343662066244650219834; + leg_points(8) = 0.319112368927889760435671824168475; + leg_points(9) = 0.515248636358154091965290718551188; + leg_points(10) = 0.687292904811685470148019803019334; + leg_points(11) = 0.827201315069764993189794742650394; + leg_points(12) = 0.928434883663573517336391139377874; + leg_points(13) = 0.986283808696812338841597266704052; + break; + case 15: + leg_points(0) = -0.987992518020485428489565718586612; + leg_points(1) = -0.937273392400705904307758947710209; + leg_points(2) = -0.848206583410427216200648320774216; + leg_points(3) = -0.724417731360170047416186054613938; + leg_points(4) = -0.570972172608538847537226737253910; + leg_points(5) = -0.394151347077563369897207370981045; + leg_points(6) = -0.201194093997434522300628303394596; + leg_points(7) = 0.0E+00; + leg_points(8) = 0.201194093997434522300628303394596; + leg_points(9) = 0.394151347077563369897207370981045; + leg_points(10) = 0.570972172608538847537226737253910; + leg_points(11) = 0.724417731360170047416186054613938; + leg_points(12) = 0.848206583410427216200648320774216; + leg_points(13) = 0.937273392400705904307758947710209; + leg_points(14) = 0.987992518020485428489565718586612; + break; + case 16: + leg_points(0) = -0.989400934991649932596154173450332; + leg_points(1) = -0.944575023073232576077988415534608; + leg_points(2) = -0.865631202387831743880467897712393; + leg_points(3) = -0.755404408355003033895101194847442; + leg_points(4) = -0.617876244402643748446671764048791; + leg_points(5) = -0.458016777657227386342419442983577; + leg_points(6) = -0.281603550779258913230460501460496; + leg_points(7) = -0.095012509837637440185319335424958; + leg_points(8) = 0.095012509837637440185319335424958; + leg_points(9) = 0.281603550779258913230460501460496; + leg_points(10) = 0.458016777657227386342419442983577; + leg_points(11) = 0.617876244402643748446671764048791; + leg_points(12) = 0.755404408355003033895101194847442; + leg_points(13) = 0.865631202387831743880467897712393; + leg_points(14) = 0.944575023073232576077988415534608; + leg_points(15) = 0.989400934991649932596154173450332; + break; + case 17: + leg_points(0) = -0.990575475314417335675434019940665; + leg_points(1) = -0.950675521768767761222716957895803; + leg_points(2) = -0.880239153726985902122955694488155; + leg_points(3) = -0.781514003896801406925230055520476; + leg_points(4) = -0.657671159216690765850302216643002; + leg_points(5) = -0.512690537086476967886246568629551; + leg_points(6) = -0.351231763453876315297185517095346; + leg_points(7) = -0.178484181495847855850677493654065; + leg_points(8) = 0.0E+00; + leg_points(9) = 0.178484181495847855850677493654065; + leg_points(10) = 0.351231763453876315297185517095346; + leg_points(11) = 0.512690537086476967886246568629551; + leg_points(12) = 0.657671159216690765850302216643002; + leg_points(13) = 0.781514003896801406925230055520476; + leg_points(14) = 0.880239153726985902122955694488155; + leg_points(15) = 0.950675521768767761222716957895803; + leg_points(16) = 0.990575475314417335675434019940665; + break; + case 18: + leg_points(0) = -0.991565168420930946730016004706150; + leg_points(1) = -0.955823949571397755181195892929776; + leg_points(2) = -0.892602466497555739206060591127145; + leg_points(3) = -0.803704958972523115682417455014590; + leg_points(4) = -0.691687043060353207874891081288848; + leg_points(5) = -0.559770831073947534607871548525329; + leg_points(6) = -0.411751161462842646035931793833051; + leg_points(7) = -0.251886225691505509588972854877911; + leg_points(8) = -0.084775013041735301242261852935783; + leg_points(9) = 0.084775013041735301242261852935783; + leg_points(10) = 0.251886225691505509588972854877911; + leg_points(11) = 0.411751161462842646035931793833051; + leg_points(12) = 0.559770831073947534607871548525329; + leg_points(13) = 0.691687043060353207874891081288848; + leg_points(14) = 0.803704958972523115682417455014590; + leg_points(15) = 0.892602466497555739206060591127145; + leg_points(16) = 0.955823949571397755181195892929776; + leg_points(17) = 0.991565168420930946730016004706150; + break; + case 19: + leg_points(0) = -0.992406843843584403189017670253260; + leg_points(1) = -0.960208152134830030852778840687651; + leg_points(2) = -0.903155903614817901642660928532312; + leg_points(3) = -0.822714656537142824978922486712713; + leg_points(4) = -0.720966177335229378617095860823781; + leg_points(5) = -0.600545304661681023469638164946239; + leg_points(6) = -0.464570741375960945717267148104102; + leg_points(7) = -0.316564099963629831990117328849844; + leg_points(8) = -0.160358645640225375868096115740743; + leg_points(9) = 0.0E+00; + leg_points(10) = 0.160358645640225375868096115740743; + leg_points(11) = 0.316564099963629831990117328849844; + leg_points(12) = 0.464570741375960945717267148104102; + leg_points(13) = 0.600545304661681023469638164946239; + leg_points(14) = 0.720966177335229378617095860823781; + leg_points(15) = 0.822714656537142824978922486712713; + leg_points(16) = 0.903155903614817901642660928532312; + leg_points(17) = 0.960208152134830030852778840687651; + leg_points(18) = 0.992406843843584403189017670253260; + break; + default: + std::ostringstream ss; + ss << "Error: " << num << "-point quadrature rule not implemented."; + throw NotImplemented(ss.str()); + } +} + + +/* + * Fill an array with Gauss-Legendre quadrature weights + * + * Parameters + * ---------- + * leg_weights : MATAR CArray to fill with weights + * num : number of weights in quadrature rule + * + * Returns + * ------- + * leg_weights : MATAR CArray to fill with weights + */ +void legendre_weights_1D(CArray &leg_weights_1D, const int &num) { + switch (num) { + case 1: + leg_weights_1D(0) = 2.0; + break; + case 2: + leg_weights_1D(0) = 1.0; + leg_weights_1D(1) = 1.0; + break; + case 3: + leg_weights_1D(0) = 0.555555555555555555555555555555555; + leg_weights_1D(1) = 0.888888888888888888888888888888888; + leg_weights_1D(2) = 0.555555555555555555555555555555555; + break; + case 4: + leg_weights_1D(0) = 0.347854845137453857373063949221999; + leg_weights_1D(1) = 0.652145154862546142626936050778000; + leg_weights_1D(2) = 0.652145154862546142626936050778000; + leg_weights_1D(3) = 0.347854845137453857373063949221999; + break; + case 5: + leg_weights_1D(0) = 0.236926885056189087514264040719917; + leg_weights_1D(1) = 0.478628670499366468041291514835638; + leg_weights_1D(2) = 0.568888888888888888888888888888888; + leg_weights_1D(3) = 0.478628670499366468041291514835638; + leg_weights_1D(4) = 0.236926885056189087514264040719917; + break; + case 6: + leg_weights_1D(0) = 0.171324492379170345040296142172732; + leg_weights_1D(1) = 0.360761573048138607569833513837716; + leg_weights_1D(2) = 0.467913934572691047389870343989550; + leg_weights_1D(3) = 0.467913934572691047389870343989550; + leg_weights_1D(4) = 0.360761573048138607569833513837716; + leg_weights_1D(5) = 0.171324492379170345040296142172732; + break; + case 7: + leg_weights_1D(0) = 0.129484966168869693270611432679082; + leg_weights_1D(1) = 0.279705391489276667901467771423779; + leg_weights_1D(2) = 0.381830050505118944950369775488975; + leg_weights_1D(3) = 0.417959183673469387755102040816326; + leg_weights_1D(4) = 0.381830050505118944950369775488975; + leg_weights_1D(5) = 0.279705391489276667901467771423779; + leg_weights_1D(6) = 0.129484966168869693270611432679082; + break; + case 8: + leg_weights_1D(0) = 0.101228536290376259152531354309962; + leg_weights_1D(1) = 0.222381034453374470544355994426240; + leg_weights_1D(2) = 0.313706645877887287337962201986601; + leg_weights_1D(3) = 0.362683783378361982965150449277195; + leg_weights_1D(4) = 0.362683783378361982965150449277195; + leg_weights_1D(5) = 0.313706645877887287337962201986601; + leg_weights_1D(6) = 0.222381034453374470544355994426240; + leg_weights_1D(7) = 0.101228536290376259152531354309962; + break; + case 9: + leg_weights_1D(0) = 0.081274388361574411971892158110523; + leg_weights_1D(1) = 0.180648160694857404058472031242912; + leg_weights_1D(2) = 0.260610696402935462318742869418632; + leg_weights_1D(3) = 0.312347077040002840068630406584443; + leg_weights_1D(4) = 0.330239355001259763164525069286974; + leg_weights_1D(5) = 0.312347077040002840068630406584443; + leg_weights_1D(6) = 0.260610696402935462318742869418632; + leg_weights_1D(7) = 0.180648160694857404058472031242912; + leg_weights_1D(8) = 0.081274388361574411971892158110523; + break; + case 10: + leg_weights_1D(0) = 0.066671344308688137593568809893331; + leg_weights_1D(1) = 0.149451349150580593145776339657697; + leg_weights_1D(2) = 0.219086362515982043995534934228163; + leg_weights_1D(3) = 0.269266719309996355091226921569469; + leg_weights_1D(4) = 0.295524224714752870173892994651338; + leg_weights_1D(5) = 0.295524224714752870173892994651338; + leg_weights_1D(6) = 0.269266719309996355091226921569469; + leg_weights_1D(7) = 0.219086362515982043995534934228163; + leg_weights_1D(8) = 0.149451349150580593145776339657697; + leg_weights_1D(9) = 0.066671344308688137593568809893331; + break; + case 11: + leg_weights_1D(0) = 0.055668567116173666482753720442548; + leg_weights_1D(1) = 0.125580369464904624634694299223940; + leg_weights_1D(2) = 0.186290210927734251426097641431655; + leg_weights_1D(3) = 0.233193764591990479918523704843175; + leg_weights_1D(4) = 0.262804544510246662180688869890509; + leg_weights_1D(5) = 0.272925086777900630714483528336342; + leg_weights_1D(6) = 0.262804544510246662180688869890509; + leg_weights_1D(7) = 0.233193764591990479918523704843175; + leg_weights_1D(8) = 0.186290210927734251426097641431655; + leg_weights_1D(9) = 0.125580369464904624634694299223940; + leg_weights_1D(10)= 0.055668567116173666482753720442548; + break; + case 12: + leg_weights_1D(0) = 0.04717533638651182719461596148501; + leg_weights_1D(1) = 0.10693932599531843096025471819399; + leg_weights_1D(2) = 0.16007832854334622633465252954335; + leg_weights_1D(3) = 0.20316742672306592174906445580979; + leg_weights_1D(4) = 0.23349253653835480876084989892487; + leg_weights_1D(5) = 0.24914704581340278500056243604295; + leg_weights_1D(6) = 0.24914704581340278500056243604295; + leg_weights_1D(7) = 0.23349253653835480876084989892487; + leg_weights_1D(8) = 0.20316742672306592174906445580979; + leg_weights_1D(9) = 0.16007832854334622633465252954335; + leg_weights_1D(10) = 0.10693932599531843096025471819399; + leg_weights_1D(11) = 0.04717533638651182719461596148501; + break; + case 13: + leg_weights_1D(0) = 0.04048400476531587952002159220098; + leg_weights_1D(1) = 0.09212149983772844791442177595379; + leg_weights_1D(2) = 0.13887351021978723846360177686887; + leg_weights_1D(3) = 0.17814598076194573828004669199609; + leg_weights_1D(4) = 0.20781604753688850231252321930605; + leg_weights_1D(5) = 0.22628318026289723841209018603977; + leg_weights_1D(6) = 0.23255155323087391019458951526883; + leg_weights_1D(7) = 0.22628318026289723841209018603977; + leg_weights_1D(8) = 0.20781604753688850231252321930605; + leg_weights_1D(9) = 0.17814598076194573828004669199609; + leg_weights_1D(10) = 0.13887351021978723846360177686887; + leg_weights_1D(11) = 0.09212149983772844791442177595379; + leg_weights_1D(12) = 0.04048400476531587952002159220098; + break; + case 14: + leg_weights_1D(0) = 0.03511946033175186303183287613819; + leg_weights_1D(1) = 0.08015808715976020980563327706285; + leg_weights_1D(2) = 0.12151857068790318468941480907247; + leg_weights_1D(3) = 0.15720316715819353456960193862384; + leg_weights_1D(4) = 0.18553839747793781374171659012515; + leg_weights_1D(5) = 0.20519846372129560396592406566121; + leg_weights_1D(6) = 0.21526385346315779019587644331626; + leg_weights_1D(7) = 0.21526385346315779019587644331626; + leg_weights_1D(8) = 0.20519846372129560396592406566121; + leg_weights_1D(9) = 0.18553839747793781374171659012515; + leg_weights_1D(10) = 0.15720316715819353456960193862384; + leg_weights_1D(11) = 0.12151857068790318468941480907247; + leg_weights_1D(12) = 0.08015808715976020980563327706285; + leg_weights_1D(13) = 0.03511946033175186303183287613819; + break; + case 15: + leg_weights_1D(0) = 0.03075324199611726835462839357720; + leg_weights_1D(1) = 0.07036604748810812470926741645066; + leg_weights_1D(2) = 0.10715922046717193501186954668586; + leg_weights_1D(3) = 0.13957067792615431444780479451102; + leg_weights_1D(4) = 0.16626920581699393355320086048120; + leg_weights_1D(5) = 0.18616100001556221102680056186642; + leg_weights_1D(6) = 0.19843148532711157645611832644383; + leg_weights_1D(7) = 0.20257824192556127288062019996751; + leg_weights_1D(8) = 0.19843148532711157645611832644383; + leg_weights_1D(9) = 0.18616100001556221102680056186642; + leg_weights_1D(10) = 0.16626920581699393355320086048120; + leg_weights_1D(11) = 0.13957067792615431444780479451102; + leg_weights_1D(12) = 0.10715922046717193501186954668586; + leg_weights_1D(13) = 0.07036604748810812470926741645066; + leg_weights_1D(14) = 0.03075324199611726835462839357720; + break; + case 16: + leg_weights_1D(0) = 0.02715245941175409485178057245601; + leg_weights_1D(1) = 0.06225352393864789286284383699437; + leg_weights_1D(2) = 0.09515851168249278480992510760224; + leg_weights_1D(3) = 0.12462897125553387205247628219201; + leg_weights_1D(4) = 0.14959598881657673208150173054747; + leg_weights_1D(5) = 0.16915651939500253818931207903035; + leg_weights_1D(6) = 0.18260341504492358886676366796921; + leg_weights_1D(7) = 0.18945061045506849628539672320828; + leg_weights_1D(8) = 0.18945061045506849628539672320828; + leg_weights_1D(9) = 0.18260341504492358886676366796921; + leg_weights_1D(10) = 0.16915651939500253818931207903035; + leg_weights_1D(11) = 0.14959598881657673208150173054747; + leg_weights_1D(12) = 0.12462897125553387205247628219201; + leg_weights_1D(13) = 0.09515851168249278480992510760224; + leg_weights_1D(14) = 0.06225352393864789286284383699437; + leg_weights_1D(15) = 0.02715245941175409485178057245601; + break; + case 17: + leg_weights_1D(0) = 0.02414830286854793196011002628756; + leg_weights_1D(1) = 0.05545952937398720112944016535824; + leg_weights_1D(2) = 0.08503614831717918088353537019106; + leg_weights_1D(3) = 0.11188384719340397109478838562635; + leg_weights_1D(4) = 0.13513636846852547328631998170235; + leg_weights_1D(5) = 0.15404576107681028808143159480195; + leg_weights_1D(6) = 0.16800410215645004450997066378832; + leg_weights_1D(7) = 0.17656270536699264632527099011319; + leg_weights_1D(8) = 0.17944647035620652545826564426188; + leg_weights_1D(9) = 0.17656270536699264632527099011319; + leg_weights_1D(10) = 0.16800410215645004450997066378832; + leg_weights_1D(11) = 0.15404576107681028808143159480195; + leg_weights_1D(12) = 0.13513636846852547328631998170235; + leg_weights_1D(13) = 0.11188384719340397109478838562635; + leg_weights_1D(14) = 0.08503614831717918088353537019106; + leg_weights_1D(15) = 0.05545952937398720112944016535824; + leg_weights_1D(16) = 0.02414830286854793196011002628756; + break; + case 18: + leg_weights_1D(0) = 0.02161601352648331031334271026645; + leg_weights_1D(1) = 0.04971454889496979645333494620263; + leg_weights_1D(2) = 0.07642573025488905652912967761663; + leg_weights_1D(3) = 0.10094204410628716556281398492483; + leg_weights_1D(4) = 0.12255520671147846018451912680020; + leg_weights_1D(5) = 0.14064291467065065120473130375194; + leg_weights_1D(6) = 0.15468467512626524492541800383637; + leg_weights_1D(7) = 0.16427648374583272298605377646592; + leg_weights_1D(8) = 0.16914238296314359184065647013498; + leg_weights_1D(9) = 0.16914238296314359184065647013498; + leg_weights_1D(10) = 0.16427648374583272298605377646592; + leg_weights_1D(11) = 0.15468467512626524492541800383637; + leg_weights_1D(12) = 0.14064291467065065120473130375194; + leg_weights_1D(13) = 0.12255520671147846018451912680020; + leg_weights_1D(14) = 0.10094204410628716556281398492483; + leg_weights_1D(15) = 0.07642573025488905652912967761663; + leg_weights_1D(16) = 0.04971454889496979645333494620263; + leg_weights_1D(17) = 0.02161601352648331031334271026645; + break; + case 19: + leg_weights_1D(0) = 0.01946178822972647703631204146443; + leg_weights_1D(1) = 0.04481422676569960033283815740199; + leg_weights_1D(2) = 0.06904454273764122658070825800601; + leg_weights_1D(3) = 0.09149002162244999946446209412383; + leg_weights_1D(4) = 0.11156664554733399471602390168176; + leg_weights_1D(5) = 0.12875396253933622767551578485687; + leg_weights_1D(6) = 0.14260670217360661177574610944190; + leg_weights_1D(7) = 0.15276604206585966677885540089766; + leg_weights_1D(8) = 0.15896884339395434764995643946504; + leg_weights_1D(9) = 0.16105444984878369597916362532091; + leg_weights_1D(10) = 0.15896884339395434764995643946504; + leg_weights_1D(11) = 0.15276604206585966677885540089766; + leg_weights_1D(12) = 0.14260670217360661177574610944190; + leg_weights_1D(13) = 0.12875396253933622767551578485687; + leg_weights_1D(14) = 0.11156664554733399471602390168176; + leg_weights_1D(15) = 0.09149002162244999946446209412383; + leg_weights_1D(16) = 0.06904454273764122658070825800601; + leg_weights_1D(17) = 0.04481422676569960033283815740199; + leg_weights_1D(18) = 0.01946178822972647703631204146443; + break; + default: + std::ostringstream ss; + ss << "Error: " << num << "-point quadrature rule not implemented."; + throw NotImplemented(ss.str()); + } +} From 0c7648aaf9cb85cbc0ae67ce2bea16b551a8103f Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Wed, 14 Sep 2022 17:15:46 -0500 Subject: [PATCH 13/20] Reverting MATAR-Kokkoification of elements/ Focus MATAR-Kokkoification in elements-kokkos/ --- elements/CMakeLists.txt | 55 +- elements/elements.cpp | 142 +-- elements/elements.h | 1398 ++++++++++++++++++++++-- elements/elements_2d.h | 387 ------- elements/elements_3d.h | 464 -------- elements/elements_4d.h | 184 ---- elements/elements_jacobians.h | 90 -- elements/elements_points_and_weights.h | 137 --- elements/elements_ref_element.h | 232 ---- 9 files changed, 1395 insertions(+), 1694 deletions(-) delete mode 100644 elements/elements_2d.h delete mode 100644 elements/elements_3d.h delete mode 100644 elements/elements_4d.h delete mode 100644 elements/elements_jacobians.h delete mode 100644 elements/elements_points_and_weights.h delete mode 100644 elements/elements_ref_element.h diff --git a/elements/CMakeLists.txt b/elements/CMakeLists.txt index c7a21251..2e9026f5 100644 --- a/elements/CMakeLists.txt +++ b/elements/CMakeLists.txt @@ -1,46 +1,15 @@ add_library( elements - elements.cpp - lagrange_polynomials.cpp - lagrange_element.cpp - legendre_polynomials.cpp - legendre_element.cpp - jacobi_polynomials.cpp - gauss_jacobi_quadrature.cpp - point_distributions.cpp + elements.cpp + lagrange_polynomials.cpp + lagrange_element.cpp + legendre_polynomials.cpp + legendre_element.cpp + jacobi_polynomials.cpp + gauss_jacobi_quadrature.cpp + point_distributions.cpp +) +target_link_libraries( + elements + common ) - -if (MATAR_WITH_KOKKOS) - target_compile_definitions( - elements - PUBLIC - MATAR_WITH_KOKKOS - HAVE_KOKKOS=1 - HAVE_OPENMP=1 - ) - - if (CUDA) - target_compile_definitions(elements PUBLIC -DHAVE_CUDA=1) - elseif (HIP) - target_compile_definitions(elements PUBLIC -DHAVE_HIP=1) - elseif (OPENMP) - target_compile_definitions(elements PUBLIC -DHAVE_OPENMP=1) - elseif (THREADS) - target_compile_definitions(elements PUBLIC -DHAVE_THREADS=1) - else() - message(FATAL_ERROR "Please specify whether you are using CUDA, HIP, OPENMP, etc.") - endif() - - target_link_libraries( - elements - common - matar - Kokkos::kokkos - ) -else() - target_link_libraries( - elements - common - matar - ) -endif() diff --git a/elements/elements.cpp b/elements/elements.cpp index 6e596d65..ec546b01 100644 --- a/elements/elements.cpp +++ b/elements/elements.cpp @@ -123,7 +123,9 @@ patch 6; [1,3,7,5] * in place. The integer num is the numer of points being defined in 1D. *****************************************************************************************/ -void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num){ +void lobatto_nodes_1D( + CArray &lob_nodes_1D, + const int &num){ if (num == 1){ lob_nodes_1D(0) = 0.0; } @@ -395,10 +397,9 @@ void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num){ * defined in 1D. *****************************************************************************************/ -/// @param lob_weights_1D Lobatto weights -/// @param num Interpolation order -void lobatto_weights_1D( MatarRealCArray &lob_weights_1D, - const int &num) { +void lobatto_weights_1D( + CArray &lob_weights_1D, // Lobbatto weights + const int &num){ // Interpolation order if (num == 1){ lob_weights_1D(0) = 2.0; } @@ -663,7 +664,8 @@ void lobatto_weights_1D( MatarRealCArray &lob_weights_1D, } // end if } // end of lobatto_weights_1D function -void legendre_nodes_1D(CArray &leg_nodes_1D, +void legendre_nodes_1D( + CArray &leg_nodes_1D, const int &num){ if (num == 1){ @@ -1163,12 +1165,11 @@ void legendre_weights_1D( * polynomial order of the desired element. Note: This function currently only supports up * to third order elements. *****************************************************************************************/ -/// @param len_weights_1D Partitioned Lobotto weights -/// @param lob_weights_1D Lobotto weights -void length_weights( MatarRealCArray &len_weights_1D, - MatarRealCArray &lob_weights_1D, - MatarRealCArray &lob_nodes_1D, - const int &p_order) { +void length_weights( + CArray &len_weights_1D, // partitioned Lobbatto weights + CArray &lob_weights_1D, // Lobbatto weights + CArray &lob_nodes_1D, + const int &p_order){ real_t alpha1 = (lob_nodes_1D(1) - lob_nodes_1D(0) - lob_weights_1D(0)) /lob_weights_1D(1); @@ -1202,15 +1203,15 @@ void length_weights( MatarRealCArray &len_weights_1D, } -/******************************************************************** -* sub_weights partitions quadrature weights to the corners -* corresponding the 1D nodal positions defined on [-1,1] using a -* distance weighted partition. -*********************************************************************/ -void sub_weights( MatarRealCArray &sub_weights_1D, // Labbatto weights - MatarRealCArray &lob_weights_1D, // Labbatto weights - MatarRealCArray &lob_nodes_1D, - const int &p_order ) { +/**************************************************************************************//** +* sub_weights partitions quadrature weights to the corners corresponding the 1D nodal +* positions defined on [-1,1] using a distance weighted partition. +*****************************************************************************************/ +void sub_weights( + CArray &sub_weights_1D, // Labbatto weights + CArray &lob_weights_1D, // Labbatto weights + CArray &lob_nodes_1D, + const int &p_order){ real_t alpha1 = (lob_nodes_1D(1) - lob_nodes_1D(0) - lob_weights_1D(0)) /lob_weights_1D(1); @@ -1327,10 +1328,10 @@ void mat_inverse( * partitioned weights and initializes everyting based of the desired polynomial order *****************************************************************************************/ void set_nodes_wgts( - MatarRealCArray &lob_nodes_1D, - MatarRealCArray &lob_weights_1D, - MatarRealCArray &len_weights_1D, - MatarRealCArray &sub_weights_1D, + CArray &lob_nodes_1D, + CArray &lob_weights_1D, + CArray &len_weights_1D, + CArray &sub_weights_1D, const int p_order){ int num_g_pts_1d = 2 * p_order + 1; @@ -1349,8 +1350,7 @@ void set_nodes_wgts( } -/**************************************************************************************/ -/** +/**************************************************************************************//** * set_unit_normals takes in the CArray defined to hold the unit normals of the corners * in a cell in reference space and initializes them. *****************************************************************************************/ @@ -2394,10 +2394,10 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ ref_inside_nodes_in_elem_ = CArray (num_ref_inside_nodes_in_elem_); // --- build gauss nodal positions and weights --- - auto lob_nodes_1D = MatarRealCArray(num_ref_nodes_1D_); + auto lob_nodes_1D = CArray (num_ref_nodes_1D_); lobatto_nodes_1D(lob_nodes_1D, num_ref_nodes_1D_); - auto lob_weights_1D = MatarRealCArray(num_ref_nodes_1D_); + auto lob_weights_1D = CArray (num_ref_nodes_1D_); lobatto_weights_1D(lob_weights_1D, num_ref_nodes_1D_); for(int k = 0; k < num_ref_nodes_1D_; k++){ @@ -2637,14 +2637,14 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // --- evaluate the basis at the nodal positions for(int node_rlid = 0; node_rlid < num_ref_nodes_in_elem_; node_rlid++){ - auto point = MatarRealCArray(3); + auto point = CArray (3); // Get the nodal coordinates for(int dim = 0; dim < 3; dim++){ point(dim) = ref_node_positions_(node_rlid, dim); } - auto node_basis = MatarRealCArray(num_ref_verts_in_elem_); + auto node_basis = CArray (num_ref_verts_in_elem_); elem.basis(node_basis, point); @@ -2658,15 +2658,15 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // --- evaluate grad_basis functions at the ref nodes --- - auto partial_xi = MatarRealCArray(num_ref_nodes_in_elem_); - auto partial_eta = MatarRealCArray(num_ref_nodes_in_elem_); - auto partial_mu = MatarRealCArray(num_ref_nodes_in_elem_); + auto partial_xi = CArray (num_ref_nodes_in_elem_); + auto partial_eta = CArray (num_ref_nodes_in_elem_); + auto partial_mu = CArray (num_ref_nodes_in_elem_); for(int node_lid = 0; node_lid < num_ref_nodes_in_elem_; node_lid++){ - auto point = MatarRealCArray(3); + auto point = CArray (3); // Get the nodal coordinates for(int dim = 0; dim < 3; dim++){ @@ -2906,7 +2906,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ - auto point = MatarRealCArray(3); + auto point = CArray (3); // Get the patch coordinates for(int dim = 0; dim < 3; dim++){ @@ -2914,7 +2914,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // the basis function values at the patch for each vertex - auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); + auto patch_basis = CArray (num_ref_verts_in_elem_); // calculate the patch basis function values at the point, for each vertex elem.basis(patch_basis, point); @@ -2934,7 +2934,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // loop over the patches for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++){ - auto point = MatarRealCArray(3); + auto point = CArray (3); // Get the patch coordinates for(int dim = 0; dim < 3; dim++){ @@ -2967,7 +2967,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ - auto point = MatarRealCArray(3); + auto point = CArray (3); // Get the patch coordinates for(int dim = 0; dim < 3; dim++){ @@ -2975,7 +2975,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ } // the basis function values at the patch for each vertex - auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); + auto cell_basis = CArray (num_ref_verts_in_elem_); // calculate the cell basis function values at the point, for each vertex elem.basis(cell_basis, point); @@ -2994,7 +2994,7 @@ void ref_element::init(int p_order, int num_dim, HexN &elem){ // loop over the patches for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++){ - auto point = MatarRealCArray(3); + auto point = CArray (3); // Get the cell coordinates for(int dim = 0; dim < 3; dim++){ @@ -5380,8 +5380,8 @@ representative linear element for visualization num_nodes_1d_ = 2; num_nodes_ = pow(num_nodes_1d_, 3); - HexN_Nodes_1d_ = MatarRealCArray (num_nodes_); - HexN_Nodes_ = MatarRealCArray (num_nodes_, 3); + HexN_Nodes_1d_ = CArray (num_nodes_); + HexN_Nodes_ = CArray (num_nodes_, 3); // Vertices @@ -5389,11 +5389,11 @@ representative linear element for visualization num_verts_ = pow(num_verts_1d_, 3); num_basis_ = pow(num_verts_1d_, 3); - HexN_Verts_1d_ = MatarRealCArray (num_verts_); - HexN_Verts_ = MatarRealCArray (num_verts_, 3); + HexN_Verts_1d_ = CArray (num_verts_); + HexN_Verts_ = CArray (num_verts_, 3); - Vert_Node_map_ = MatarUIntCArray (num_verts_); + Vert_Node_map_ = CArray (num_verts_); order_ = elem_order+1; @@ -5407,8 +5407,8 @@ representative linear element for visualization num_nodes_1d_ = 2 * elem_order + 1; num_nodes_ = pow(num_nodes_1d_, 3); - HexN_Nodes_1d_ = MatarRealCArray (num_nodes_); - HexN_Nodes_ = MatarRealCArray (num_nodes_, 3); + HexN_Nodes_1d_ = CArray (num_nodes_); + HexN_Nodes_ = CArray (num_nodes_, 3); // Vertices @@ -5416,11 +5416,11 @@ representative linear element for visualization num_verts_ = pow(num_verts_1d_, 3); num_basis_ = pow(num_verts_1d_, 3); - HexN_Verts_1d_ = MatarRealCArray (num_verts_); - HexN_Verts_ = MatarRealCArray (num_verts_, 3); + HexN_Verts_1d_ = CArray (num_verts_); + HexN_Verts_ = CArray (num_verts_, 3); - Vert_Node_map_ = MatarUIntCArray (num_verts_); + Vert_Node_map_ = CArray (num_verts_); order_ = elem_order; @@ -5502,11 +5502,11 @@ representative linear element for visualization return i + j*num_verts_1d_ + k*num_verts_1d_*num_verts_1d_; }; - void HexN::basis(MatarRealCArray &basis, MatarRealCArray &point) + void HexN::basis(CArray &basis, CArray &point) { - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); + auto val_1d = CArray (num_verts_1d_); + auto val_3d = CArray (num_verts_1d_, 3); // Calculate 1D basis for the X coordinate of the point lagrange_basis_1D(val_1d, point(0)); @@ -5549,15 +5549,15 @@ representative linear element for visualization }; - void HexN::partial_xi_basis(MatarRealCArray &partial_xi, MatarRealCArray &point) + void HexN::partial_xi_basis(CArray &partial_xi, CArray &point) { - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); + auto val_1d = CArray (num_verts_1d_); + auto val_3d = CArray (num_verts_1d_, 3); - auto Dval_1d = MatarRealCArray (num_verts_1d_); - auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); + auto Dval_1d = CArray (num_verts_1d_); + auto Dval_3d = CArray (num_verts_1d_, 3); // Calculate 1D partial w.r.t. xi for the X coordinate of the point lagrange_derivative_1D(Dval_1d, point(0)); @@ -5609,14 +5609,14 @@ representative linear element for visualization }; - void HexN::partial_eta_basis(MatarRealCArray &partial_eta, MatarRealCArray &point) + void HexN::partial_eta_basis(CArray &partial_eta, CArray &point) { - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); + auto val_1d = CArray (num_verts_1d_); + auto val_3d = CArray (num_verts_1d_, 3); - auto Dval_1d = MatarRealCArray (num_verts_1d_); - auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); + auto Dval_1d = CArray (num_verts_1d_); + auto Dval_3d = CArray (num_verts_1d_, 3); // Calculate 1D basis for the Y coordinate of the point lagrange_basis_1D(val_1d, point(0)); @@ -5667,14 +5667,14 @@ representative linear element for visualization }; - void HexN::partial_mu_basis(MatarRealCArray &partial_mu, MatarRealCArray &point){ + void HexN::partial_mu_basis(CArray &partial_mu, CArray &point){ - auto val_1d = MatarRealCArray (num_verts_1d_); - auto val_3d = MatarRealCArray (num_verts_1d_, 3); + auto val_1d = CArray (num_verts_1d_); + auto val_3d = CArray (num_verts_1d_, 3); - auto Dval_1d = MatarRealCArray (num_verts_1d_); - auto Dval_3d = MatarRealCArray (num_verts_1d_, 3); + auto Dval_1d = CArray (num_verts_1d_); + auto Dval_3d = CArray (num_verts_1d_, 3); // Calculate 1D basis for the X coordinate of the point lagrange_basis_1D(val_1d, point(0)); @@ -5727,7 +5727,7 @@ representative linear element for visualization void HexN::lagrange_basis_1D( - MatarRealCArray &interp, // interpolant from each basis + CArray &interp, // interpolant from each basis const real_t &x_point){ // point of interest in element @@ -5761,7 +5761,7 @@ representative linear element for visualization } // end of Legrange_1D function void HexN::lagrange_derivative_1D( - MatarRealCArray &derivative, // derivative + CArray &derivative, // derivative const real_t &x_point){ // point of interest in element for(int vert_i = 0; vert_i < num_verts_1d_; vert_i++){ // looping over the nodes diff --git a/elements/elements.h b/elements/elements.h index 0d7feac3..a1e10ec2 100644 --- a/elements/elements.h +++ b/elements/elements.h @@ -1,3 +1,5 @@ +#ifndef ELEMENTS_H +#define ELEMENTS_H /***************************************************************************** © 2020. Triad National Security, LLC. All rights reserved. This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos @@ -38,45 +40,61 @@ OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. **********************************************************************************************/ -#ifndef ELEMENTS_H -#define ELEMENTS_H -// C/C++ standard library includes + + #include #include #include #include - -// MATAR includes +#include "utilities.h" #include "matar.h" +using namespace utils; -// Switch between MATAR Kokkos/non-Kokkos data structures, depending on -// availability of Kokkos -#ifdef MATAR_WITH_KOKKOS -typedef CArrayKokkos MatarRealCArray; -typedef CArrayKokkos MatarUIntCArray; -#else -typedef CArray MatarRealCArray; -typedef CArray MatarUIntCArray; -#endif // MATAR_WITH_KOKKOS -// ELEMENTS includes -#include "utilities.h" -using namespace utils; -#include "elements_jacobians.h" -#include "elements_points_and_weights.h" -#include "elements_2d.h" -#include "elements_3d.h" -#include "elements_4d.h" -#include "elements_ref_element.h" +namespace elements { + + //============================================================================== + // Function Declaration + //============================================================================== -namespace elements { + // Used by Lobatto 1D/2D to set Lobatto quadrature points + + void lobatto_nodes_1D( + CArray &lob_nodes_1D, + const int &num); + + void lobatto_weights_1D( + CArray &lob_weights_1D, // Labbatto weights + const int &num); + + + void legendre_nodes_1D( + CArray &leg_nodes_1D, + const int &num); + + void legendre_weights_1D( + CArray &leg_weights_1D, // Legendre weights + const int &num); + + + void length_weights( + CArray &len_weights_1D, // Labbatto weights + CArray &lab_weights_1D, // Labbatto weights + CArray &lab_nodes_1D, + const int &order); + + void sub_weights( + CArray &sub_weights_1D, // Labbatto weights + CArray &lab_weights_1D, // Labbatto weights + CArray &lab_nodes_1D, + const int &order); void mat_inverse( ViewCArray &mat_inv, @@ -91,6 +109,13 @@ namespace elements { // CArray &trans, // CArray &mat); + void set_nodes_wgts( + CArray &lab_nodes_1D, + CArray &lab_weights_1D, + CArray &len_weights_1D, + CArray &sub_weights_1D, + int p_order); + // void sub_cells( // CArray &lab_nodes_1D, // int &p_order, @@ -100,74 +125,1275 @@ namespace elements { void set_unit_normals(CArray &unit_normals); - /* Add enumerated list of element types to choose from */ - namespace elem_types - { + // Used by Gauss2/3D to set quadrature points + void line_gauss_info( + real_t &x, + real_t &w, + int &m, + int &p); + + // Used by Lovatto 1D/2D to set Lobatto quadrature points + void line_lobatto_info( + real_t &x, + real_t &w, + int &m, + int &p); + + // setting gauss quadrature points for 2D elements + void gauss_2d( + ViewCArray &these_g_pts, // gauss points + ViewCArray &these_weights, // gauss weights + ViewCArray &tot_g_weight, // 2D product of gauss weights + int &quad_order); // quadrature order (n) + + // setting gauss quadrature points for 2D elements + void gauss_3d( + ViewCArray &these_g_pts, // gauss points + ViewCArray &these_weights, // gauss weights + ViewCArray &tot_g_weight, // 3D product of gauss weights + int &quad_order); // quadrature order (n) + + // setting gauss quadrature points for 4D elements + void gauss_4d( + ViewCArray &these_g_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order, // quadrature order (n) + const int &dim); + + // setting Gauss-Lobatto quadrature points for 2D elements + void lobatto_2d( + ViewCArray &these_L_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order); // quadrature order (n) + + // setting Gauss-Lobatto quadrature points for 3D elements + void lobatto_3d( + ViewCArray &these_L_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order); + + // setting gauss quadrature points for 4D elements + void lobatto_4d( + ViewCArray &these_L_pts, // gauss points + ViewCArray &these_weights, // gauss weights + int &quad_order, // quadrature order (n) + const int &dim); + + //defining the jacobian for 2D elements + void jacobian_2d( + ViewCArray &J_matrix, + real_t &det_J, + const ViewCArray &vertices, + const ViewCArray &this_partial, + const int &num_nodes); + + //defining the jacobian for 3D elements + void jacobian_3d( + ViewCArray &J_matrix, + real_t &det_J, + const ViewCArray &vertices, + const ViewCArray &this_partial, + const int &num_nodes); + + //defining the jacobian for 4D elements + void jacobian_4d( + ViewCArray &J_matrix, + real_t &det_J, + const ViewCArray &vertices, + const ViewCArray &this_partial, + const int &num_nodes, + const int &dim); + + //defining the inverse jacobian for 2D element + void jacobian_inverse_2d( + ViewCArray &J_inverse, + const ViewCArray &jacobian); + + //defining the inverse jacobian for 2D element + void jacobian_inverse_3d( + ViewCArray &J_inverse_matrix, + const ViewCArray &jacobian); + + // defining the inverse of the Jacobian for 4D elements + void jacobian_inverse_4d( + ViewCArray &J_inverse_matrix, + const ViewCArray &jacobian, + const real_t &det_J); + + // creates nodal positions with Chebyshev spacing + void chebyshev_nodes_1D( + ViewCArray &cheb_nodes_1D, // Chebyshev nodes + const int &order); // Interpolation order + + + + + class Element2D { + + protected: + const static int num_dim_ = 2; + + public: + + virtual int num_verts() = 0; + virtual int num_nodes() = 0; + virtual int num_basis() = 0; + + //list of local ids to basis functions needed to interpolate throughout a given element surface + RaggedRightArray surface_to_dof_lid; + int nsurfaces; + + // calculate a physical position in an element for a given xi,eta + virtual void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices) = 0; + + // calculate the value for the basis at each node for a given xi,eta + virtual void basis( + ViewCArray &basis, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Xi + virtual void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point) = 0; + + + // Partial derivative of shape functions with respect to Xi + virtual void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point) = 0; + + // Map from vertex to node + virtual int vert_node_map( const int vert_lid) = 0; + + }; // end of 2D element class + + class Element3D { + + protected: + const static int num_dim_ = 3; + + public: + + virtual int num_verts() = 0; + virtual int num_nodes() = 0; + virtual int num_basis() = 0; + + //list of local ids to basis functions needed to interpolate throughout a given element surface + RaggedRightArray surface_to_dof_lid; + int nsurfaces; + + // calculate a physical position in an element for a given xi,eta,mu + virtual void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices) = 0; + + // calculate the value for the basis at each node for a given xi,eta, mu + virtual void basis( + ViewCArray &basis, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Xi at Xi_point + virtual void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Eta + virtual void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Mu + virtual void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point) = 0; + + // Map from vertex to node + virtual inline int vert_node_map(const int vert_lid) = 0; + + // Reference vertices location + virtual real_t& ref_locs(const int vert_lid, const int dim) = 0; + + }; // end of 3D parent class + + class Element4D { + + public: + + //list of local ids to basis functions needed to interpolate throughout a given element surface + CArray surface_to_dof_lid; + + // calculate a physical position in an element for a given xi,eta,mu,tau + virtual void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices) = 0; + + // calculate the value for the basis at each node for a given xi,eta,mu,tau + virtual void basis( + ViewCArray &basis, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Xi at Xi_point + virtual void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Eta + virtual void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Mu + virtual void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point) = 0; + + // Partial derivative of shape functions with respect to Tau + virtual void partial_tau_basis( + ViewCArray &partial_tau, + const ViewCArray &xi_point) = 0; + + + }; // end of 3D parent class + + + + + /* + .-------------------------------. + | .----------------------------. | + | | _____ ________ | | + | | / ___ `. |_ ___ `. | | + | | |_/___) | | | `. \ | | + | | .'____.' | | | | | | + | | / /____ _| |___.' / | | + | | |_______| |________.' | | + | | | | + | '----------------------------' | + '-------------------------------' + */ + /* + =========================== + 2D Quad 4 Elements + =========================== + + + The finite element local point numbering for a 4 node quadralateral is + as follows + + Eta + ^ + | + 3------+-----2 + | | | + | | | + | | | + | ------+------> Xi + | | + | | + 0------------1 + */ + + + + + class Quad4: public Element2D { + + protected: + + static const int num_verts_ = 4; + static const int num_nodes_ = 4; + static const int num_basis_ = 4; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Quad4(); + ~Quad4(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map( const int vert_lid); + + }; // end of quad_4_2D class + + + /* + =========================== + 2D Quad 8 Elements + =========================== + + + The finite element local point numbering for a 8 node Hexahedral is + as follows + + Eta + ^ + | + 3-------6------2 + | | | + | | | + | | | + | | | + 7 +------5-----> Xi + | | + | | + | | + 0------4-------1 + */ + + class Quad8: public Element2D { + + protected: + + static const int num_verts_ = 8; + static const int num_nodes_ = 8; + static const int num_basis_ = 8; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Quad8(); + ~Quad8(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map( const int vert_lid); + + }; // end of quad_8_2D class + + /* + =========================== + 2D Quad 12 Elements + =========================== + + + The finite element local point numbering for a 8 node Hexahedral is + as follows (NEED TO DEFINE) + + Eta + ^ + | + 3---7------6---2 + | | | + | | | + 11 | 10 + | | | + | +------|-----> Xi + | | + 8 9 + | | + 0----4-----5---1 + + */ + + class Quad12: public Element2D { + + protected: + + static const int num_verts_ = 12; + static const int num_nodes_ = 12; + static const int num_basis_ = 12; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Quad12(); + ~Quad12(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map( const int vert_lid); + + }; // end of quad_8_2D class + + /* + ========================== + Arbitrary Order Elements + ========================== + + __ _ _ _ + / __ \ | | \ | | + | | | |_ _ __ _ __| | \| | + | | | | | | |/ _` |/ _` | . ` | + | |__| | |_| | (_| | (_| | |\ | + \___\_\\__,_|\__,_|\__,_|_| \_| + + Representative linear element for visualization + + Eta (j) + ^ + | + 3--------------2 + | | | + | | | + | | | + | | | + | +------|-----> Xi (i) + | | + | | + | | + 0--------------1 + */ + + + class QuadN{ + public: + + const static int num_dim = 2; + + int num_basis; + int num_verts; + + // calculates the basis values and derivatives in 1D + // used in the basis_partials functiosn to build the 3D element + void lagrange_1D( + ViewCArray &interp, // interpolant + ViewCArray &Dinterp, // derivative of function + const real_t &x_point, // point of interest in element + const ViewCArray &xi_point, // nodal positions in 1D, normally chebyshev + const int &orderN); // order of element + + void corners ( + ViewCArray &lag_nodes, // Nodes of Lagrange elements + ViewCArray &lag_corner, // corner nodes of QuadN element + const int &orderN); // Element order + + void physical_position ( + ViewCArray &x_point, // location in real space + const ViewCArray &lag_nodes, // Nodes of Lagrange elements + const ViewCArray &lag_basis_2d, // 2D basis values + const int &orderN); // order of the element + + void basis_partials ( + ViewCArray &lag_nodes, // Nodes of Lagrange elements (to be filled in) + ViewCArray &nodes_1d, // Nodal spacing in 1D, any spacing is accepted + ViewCArray &val_1d, // Interpolant Value in 1D + ViewCArray &DVal_1d, // Derivateive of basis in 1D + ViewCArray &val_2d, // for holding the interpolant in each direction + ViewCArray &DVal_2d, // for holding the derivatives in each direction + ViewCArray &lag_basis_2d, // 2D basis values + ViewCArray &lag_partial, // Partial of basis + const ViewCArray &xi_point, // point of interest + const int &orderN); // Element order + }; + + + + /* + .-------------------------------. + | .----------------------------. | + | | ______ ________ | | + | | / ____ `. |_ ___ `. | | + | | `' __) | | | `. \ | | + | | _ |__ '. | | | | | | + | | | \____) | _| |___.' / | | + | | \______.' |________.' | | + | | | | + | '----------------------------' | + '------------------------------' + */ + + /* + ========================== + Hex 8 + ========================== + + The finite element local vertex numbering for a 8 node Hexahedral is + as follows + + Mu (k) + | Eta (j) + | / + | / + 6---+----7 + /| | /| + / | | / | + 4--------5 | + | | -|--+---> Xi (i) + | | | | + | 2-----|--3 + | / | / + |/ |/ + 0----*----1 + +*/ + +class Hex8: public Element3D { + + protected: + + static const int num_verts_ = 8; + static const int num_nodes_ = 8; + static const int num_basis_ = 8; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Hex8(); + ~Hex8(); + + int num_verts(); + int num_nodes(); + int num_basis(); - enum elem_type - { - // 2D element types - Quad4 = 0, // 4 node serendipity quadrilateral element - Quad8 = 1, // 8 node serendipity quadrilateral element - Quad12 = 2, // 12 node serendipity quadrilateral element - QuadN = 3, // N node lagrangian quadrilateral element + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // with repsect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Map from vertex to node + inline int vert_node_map(const int vert_lid); + + real_t& ref_locs(const int vert_lid, const int dim); + + }; // end of hex 8 class + + + /* + ========================== + Hex 20 + ========================== + + The finite element local point numbering for a 20 node Hexahedral is + as follows + + Mu (k) + | Eta (j) + | / + | / + 7----14----6 + /| /| + 15 | 13 | + / 19 / 18 + 4----12----5 | + | | | | --> Xi (i) + | | | | + | 3---10-|---2 + 16 / 17 / + | 11 | 9 + |/ |/ + 0-----8----1 + */ + + class Hex20: public Element3D { + protected: + + static const int num_verts_ = 20; + static const int num_nodes_ = 20; + static const int num_basis_ = 20; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Hex20(); + ~Hex20(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // with repsect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Map from vertex to node + inline int vert_node_map(const int vert_lid); + + real_t& ref_locs(const int vert_lid, const int dim); + + }; // end of hex20 class + + /* + ========================== + Hex 32 + ========================== + + The finite element local point numbering for a 32 node Hexahedral is + shown below + + + Mu (k) + ^ Eta (j) + | / + | / + / + 7----23------22----6 + /| /| + 15 | 14 | + / | / | + 12 31 13 30 + / | / | + 4-----20-----21----5 | + | | | | ----> Xi (i) + | 27 | 26 + | | | | + 28 | 29 | + | 3----19------|18---2 + | / | / + | 11 | 10 + 24 / 25 / + | 8 | 9 + |/ |/ + 0----16------17----1 + */ + + class Hex32: public Element3D { + + protected: + + static const int num_verts_ = 32; + static const int num_nodes_ = 32; + static const int num_basis_ = 32; + + static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} + static const int vert_to_node[num_verts_]; + + public: + + Hex32(); + ~Hex32(); + + int num_verts(); + int num_nodes(); + int num_basis(); + + // calculate a physical position in an element for a given xi,eta + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + + // calculate the value for the basis at each node for a given xi,eta + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // with repsect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Map from vertex to node + int vert_node_map(const int vert_lid); + + real_t& ref_locs(const int vert_lid, const int dim); + + }; // end of hex32 class + + + /* + ========================== + Arbitrary Order Elements + ========================== + _ _ _ _ + | | | | _____ _| \ | | + | |_| |/ _ \ \/ / \| | + | _ | __/> <| |\ | + |_| |_|\___/_/\_\_| \_| + + Representative linear element for visualization + + k + | j + | / + | / + 6---+----7 + /| | /| + / | | / | + 4--------5 | + | | -|--+---> i + | | | | + | 2-----|--3 + | / | / + |/ |/ + 0--------1 + */ + + class HexN{ + + protected: + + const static int num_dim_ = 3; + + // Nodes + int num_nodes_1d_; + int num_nodes_; + + CArray HexN_Nodes_1d_; + CArray HexN_Nodes_; + + // Vertices + int num_verts_1d_; + int num_verts_; + int num_basis_; + + CArray HexN_Verts_1d_; + CArray HexN_Verts_; + + CArray Vert_Node_map_; + + int order_; + + + public: + + void setup_HexN(int elem_order); + + int num_verts(); + int num_nodes(); + int num_basis(); + int node_rid(int i, int j, int k) const; + int vert_rid(int i, int j, int k) const; + + // Return the noda coordinates in reference space + real_t &node_coords(int node_rlid, int dim); + + + int vert_node_map(int vert_rid) const; + + // Evaluate the basis at a given point + void basis( + CArray &basis, + CArray &point); + + void build_nodal_gradient( + CArray &gradient); + + // calculate the partial of the basis w.r.t xi at a given point + void partial_xi_basis( + CArray &partial_xi, + CArray &point); + + // calculate the partial of the basis w.r.t eta at a given point + void partial_eta_basis( + CArray &partial_eta, + CArray &point); + + // calculate the partial of the basis w.r.t mu at a given point + void partial_mu_basis( + CArray &partial_mu, + CArray &point); + + void lagrange_basis_1D( + CArray &interp, // interpolant + const real_t &x_point); // point of interest in element - // 3D element types - Hex8 = 4, // 8 node lagrangian hexahedral element - Hex20 = 5, // 20 node serendipity hexahedral element - Hex32 = 6, // 32 node serendipity hexahedral element - HexN = 7 // N node lagrangian hexahedral element + void lagrange_derivative_1D( + CArray &partials, //derivative + const real_t &x_point); // point of interest in element + + void create_lobatto_nodes(int element_order); + + }; + + + + /* + ========================== + 4D Tesseract element + ========================== + + The finite element local point numbering for a 16 node Tesseract is + based on the 3D Hex8 Ensight element + + + _.15--------------------------------------14 + _.+< |\ . >-"/ | + _ .+> | \ .>"" ./ | + .>"" | \ ."" / | + 12----------------------+------------------13 ./ | + | )<= | \ / | _/"" | + | )\+ | \ / /"| | + | (\= | _. 7---------+--6 | | + | \> .|+< | / . "| | | + | '4--+------+------5' | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | | | | | | + | | | _ .3------+-----2_ | | + | | | " / | /' '| \= _ | + | 0--+---+---------1*" | '\ | + | ./' | " \ | ""\ | + | / |/ \ | '". | + | / 11----------------+-----+---------------10 + | ./ .+<"" ) | .( + 8------------------------------------------9' + + j + ^ k + | / + | / + | / + |/ + +---------->i + + i = Xi + j = Eta + k = Mu + t = Tau + + */ + + class Tess16: public Element4D { + public: + const static int num_verts = 16; + const static int num_dim = 4; + const static int num_basis = 16; + + protected: + static real_t ref_vert[num_verts*num_dim]; // listed as {Xi, Eta, Mu, Tau} + + + public: + + // calculate a physical position in an element for a given xi,eta,mu + void physical_position( + ViewCArray &x_point, + const ViewCArray &xi_point, + const ViewCArray &vertices); + + // calculate the value for the basis at each node for a given xi,eta,mu,tau + void basis( + ViewCArray &basis, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Xi at Xi_point + void partial_xi_basis( + ViewCArray &partial_xi, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Eta + void partial_eta_basis( + ViewCArray &partial_eta, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Mu + void partial_mu_basis( + ViewCArray &partial_mu, + const ViewCArray &xi_point); + + // Partial derivative of shape functions with respect to Tau + void partial_tau_basis( + ViewCArray &partial_tau, + const ViewCArray &xi_point); + }; // End of Tess16 Element Class + +/* Add enumerated list of element types to choose from */ + +namespace elem_types +{ + + enum elem_type + { + // 2D element types + Quad4 = 0, // 4 node serendipity quadrilateral element + Quad8 = 1, // 8 node serendipity quadrilateral element + Quad12 = 2, // 12 node serendipity quadrilateral element + QuadN = 3, // N node lagrangian quadrilateral element - // add tesseract element - - }; - - //Nodes per each element type - //CArray Nodes_Per_Element_Type(8); - //Quad4 - //Nodes_Per_Element_Type(0) = 4; - //Quad8 - //Nodes_Per_Element_Type(1) = 8; - //Quad12 - //Nodes_Per_Element_Type(2) = 12; - //QuadN has to be set on a casewise base - //Nodes_Per_Element_Type(3) = 0; - //Hex8 - //Nodes_Per_Element_Type(4) = 8; - //Hex20 - //Nodes_Per_Element_Type(5) = 20; - //Hex32 - //Nodes_Per_Element_Type(6) = 32; - //HexN set on a casewise basis - //Nodes_Per_Element_Type(7) = 0; - - } // end of elem_type namespace - - - // Choose the type of element to use for the calculation - struct elem_type_t { - // element type - elem_types::elem_type type; + // 3D element types + Hex8 = 4, // 8 node lagrangian hexahedral element + Hex20 = 5, // 20 node serendipity hexahedral element + Hex32 = 6, // 32 node serendipity hexahedral element + HexN = 7 // N node lagrangian hexahedral element + + // add tesseract element + }; - class element_selector{ - public: - //2D element objects - Quad4 Quad4_Object; - Quad8 Quad8_Object; - Quad12 Quad12_Object; - QuadN QuadN_Object; - - //3D element objects - Hex8 Hex8_Object; - Hex20 Hex20_Object; - Hex32 Hex32_Object; - HexN HexN_Object; - - void choose_3Delem_type(elem_types::elem_type element_type, Element3D *&elem); - void choose_2Delem_type(elem_types::elem_type element_type, Element2D *&elem2D); + //Nodes per each element type + //CArray Nodes_Per_Element_Type(8); + //Quad4 + //Nodes_Per_Element_Type(0) = 4; + //Quad8 + //Nodes_Per_Element_Type(1) = 8; + //Quad12 + //Nodes_Per_Element_Type(2) = 12; + //QuadN has to be set on a casewise base + //Nodes_Per_Element_Type(3) = 0; + //Hex8 + //Nodes_Per_Element_Type(4) = 8; + //Hex20 + //Nodes_Per_Element_Type(5) = 20; + //Hex32 + //Nodes_Per_Element_Type(6) = 32; + //HexN set on a casewise basis + //Nodes_Per_Element_Type(7) = 0; + +} // end of elem_type namespace + + +// Choose the type of element to use for the calculation +struct elem_type_t { + // element type + elem_types::elem_type type; +}; + +class element_selector{ + public: + //2D element objects + Quad4 Quad4_Object; + Quad8 Quad8_Object; + Quad12 Quad12_Object; + QuadN QuadN_Object; + + //3D element objects + Hex8 Hex8_Object; + Hex20 Hex20_Object; + Hex32 Hex32_Object; + HexN HexN_Object; + + void choose_3Delem_type(elem_types::elem_type element_type, Element3D *&elem); + void choose_2Delem_type(elem_types::elem_type element_type, Element2D *&elem2D); +}; + + + +// Reference Element Informations +class ref_element{ +private: + + // this assumes i,j,k structured indexing of nodes + const int node_rlid_in_patch_in_cell_[24] = { + // patches in xi-dir + 0,2,6,4, + 1,3,7,5, + // patches in eta-dir + 0,4,5,1, + 2,6,7,3, + // patches in mu-dir + 0,1,3,2, + 4,5,7,6 }; + + // return the local ref id for the same patch in the cell-patch neighbor + const int patch_rlid_cell_neighbor_[6] = { + 1, // xi left side of my cell + 0, // xi right side of my cell + 3, // eta front side of my cell + 2, // eta bact side of my cell + 5, // mu bottom side of my cell + 4 // mu top side of my cell + }; + + // return the reference coordinate unit normal of the sides in a cell + const real_t cell_side_unit_normals_[18] = { + -1, 0, 0, // xi left side of my cell + 1, 0, 0, // xi right side of my cell + 0,-1, 0, // eta minus side of my cell + 0, 1, 0, // eta plus side of my cell + 0, 0,-1, // mu minus side of my cell + 0, 0, 1 // mu plus side of my cell + }; + + int num_dim_; + + int num_ref_nodes_1D_; + int num_ref_cells_1D_; + int num_ref_corners_1D_; + + int num_ref_surface_nodes_in_elem_; + int num_ref_inside_nodes_in_elem_; + + // Zones + int num_zones_1d_; + int num_zones_in_elem_; + + // cells + int num_ref_cells_in_elem_; + + CArray cells_in_zone_list_; + + // nodes + int num_ref_nodes_in_elem_; + int num_ref_nodes_in_cell_; + + CArray ref_nodes_in_cell_; + CArray ref_surface_nodes_in_elem_; + CArray ref_inside_nodes_in_elem_; + + CArray ref_node_positions_; + CArray ref_node_g_weights_; + + CArray cell_nodes_in_elem_list_; + + // Vertices + int num_ref_verts_1d_; + int num_ref_verts_in_elem_; + + // corners + int num_ref_corners_in_cell_; + int num_ref_corners_in_elem_; + + CArray ref_corners_in_cell_; + + CArray ref_corner_surf_normals_; + CArray ref_corner_g_weights_; + CArray ref_corner_surf_g_weights_; + + // patches and sides + int num_patches_in_elem_; + int num_sides_in_elem_; + + CArray ref_cell_positions_; + CArray ref_cell_g_weights_; + CArray ref_patch_positions_; + CArray ref_patch_g_weights_; + + CArray ref_patches_in_cell_list_; + + CArray ref_patch_basis_; + CArray ref_patch_gradient_; // grad basis at patch + + CArray ref_cell_basis_; + CArray ref_cell_gradient_; // grad basis at cell + + // Num basis functions + int num_basis_; + + // Basis evaluation at nodes + CArray ref_nodal_basis_; + + // Pointer to HexN object + HexN *elem_ptr; + +public: + + // Gradient of basis + CArray ref_nodal_gradient_; + //real_t * ref_nodal_gradient_; + + // Function Declarations + + // Default constructor + ref_element() : elem_ptr(nullptr) {}; + + // Initialize reference element information + void init(int poly_order, int num_dim, HexN &elem); + + int num_dim() const; + + int num_basis() const; + + int num_ref_nodes() const; + + int num_ref_cells_in_elem() const; + int num_ref_corners_in_cell() const; + + // local i,j,k indexing + int node_rid(int i, int j, int k) const; + int cell_rid(int i, int j, int k) const; + int corner_rid(int i, int j, int k) const; + + int ref_corners_in_cell(int cell_rid, int corner_rlid) const; + int ref_nodes_in_cell(int cell_rid, int node_rlid) const; + + int ref_surface_nodes_in_elem(int node_rlid) const; + int ref_inside_nodes_in_elem(int node_rlid) const; + int num_ref_surface_nodes_in_elem() const; + int num_ref_inside_nodes_in_elem() const; + + real_t ref_node_positions(int node_rid, int dim) const; + + real_t ref_corner_surface_normals(int corner_rid, int surf_rlid, int dim) const; + + real_t ref_corner_g_surface_weights(int corner_rid, int surf_rlid) const; + + real_t ref_node_g_weights(int node_rid) const; + + real_t ref_corner_g_weights(int corner_rid) const; + + real_t &ref_nodal_gradient(int node_rid, int basis_id, int dim) const; + + real_t &ref_nodal_basis(int node_rid, int basis_id) const; + + int& cell_lid_in_zone(int zone_lid, int cell_lid) const; + + real_t ref_cell_positions(int cell_rid, int dim) const; + real_t ref_cell_g_weights(int cell_rid) const; + real_t ref_cell_basis(int cell_rid, int basis_id) const; + real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; + + real_t cell_side_unit_normals(int side_rlid, int dim) const; + + int& cell_nodes_in_elem(int cell_lid, int node_lid) const; + + int node_in_patch_in_cell(int patch_lid, int node_lid) const; + + int patch_rlid_in_cell_neighbor(int patch_rlid) const; + + int ref_patches_in_cell(int cell_lid, int patch_rlid) const; + + real_t ref_patch_positions(int patch_rid, int dim) const; + real_t ref_patch_g_weights(int patch_rid) const; + real_t ref_patch_basis(int patch_rid, int basis_id) const; + real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; + + int vert_node_map(int vert_lid); + + // Deconstructor + ~ref_element(); + +}; + } // end namespace elements -#endif // ELEMENTS_H +#endif //ELEMENTS_H diff --git a/elements/elements_2d.h b/elements/elements_2d.h deleted file mode 100644 index 4fbee2f6..00000000 --- a/elements/elements_2d.h +++ /dev/null @@ -1,387 +0,0 @@ -/***************************************************************************** -© 2020. Triad National Security, LLC. All rights reserved. -This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos -National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. -Department of Energy/National Nuclear Security Administration. All rights in the program are -reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear -Security Administration. The Government is granted for itself and others acting on its behalf a -nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare -derivative works, distribute copies to the public, perform publicly and display publicly, and -to permit others to do so. - - -This program is open source under the BSD-3 License. -Redistribution and use in source and binary forms, with or without modification, are permitted -provided that the following conditions are met: - - 1. Redistributions of source code must retain the above copyright notice, this list of - conditions and the following disclaimer. - - 2. Redistributions in binary form must reproduce the above copyright notice, this list of - conditions and the following disclaimer in the documentation and/or other materials - provided with the distribution. - - 3. Neither the name of the copyright holder nor the names of its contributors may be used - to endorse or promote products derived from this software without specific prior - written permission. - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS -IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR -CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; -OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, -WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR -OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF -ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - -**********************************************************************************************/ -#ifndef ELEMENTS_2D_H -#define ELEMENTS_2D_H - -namespace elements { - - /* - .-------------------------------. - | .----------------------------. | - | | _____ ________ | | - | | / ___ `. |_ ___ `. | | - | | |_/___) | | | `. \ | | - | | .'____.' | | | | | | - | | / /____ _| |___.' / | | - | | |_______| |________.' | | - | | | | - | '----------------------------' | - '-------------------------------' - */ - class Element2D { - - protected: - const static int num_dim_ = 2; - - public: - - virtual int num_verts() = 0; - virtual int num_nodes() = 0; - virtual int num_basis() = 0; - - //list of local ids to basis functions needed to interpolate throughout a given element surface - RaggedRightArray surface_to_dof_lid; - int nsurfaces; - - // calculate a physical position in an element for a given xi,eta - virtual void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices) = 0; - - // calculate the value for the basis at each node for a given xi,eta - virtual void basis( - ViewCArray &basis, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Xi - virtual void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point) = 0; - - - // Partial derivative of shape functions with respect to Xi - virtual void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point) = 0; - - // Map from vertex to node - virtual int vert_node_map( const int vert_lid) = 0; - - }; - - - /* - =========================== - 2D Quad 4 Elements - =========================== - - - The finite element local point numbering for a 4 node quadralateral is - as follows - - Eta - ^ - | - 3------+-----2 - | | | - | | | - | | | - | ------+------> Xi - | | - | | - 0------------1 - */ - class Quad4: public Element2D { - - protected: - - static const int num_verts_ = 4; - static const int num_nodes_ = 4; - static const int num_basis_ = 4; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Quad4(); - ~Quad4(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map( const int vert_lid); - - }; // end of quad_4_2D class - - - /* - =========================== - 2D Quad 8 Elements - =========================== - - - The finite element local point numbering for a 8 node Hexahedral is - as follows - - Eta - ^ - | - 3-------6------2 - | | | - | | | - | | | - | | | - 7 +------5-----> Xi - | | - | | - | | - 0------4-------1 - */ - class Quad8: public Element2D { - - protected: - - static const int num_verts_ = 8; - static const int num_nodes_ = 8; - static const int num_basis_ = 8; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Quad8(); - ~Quad8(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map( const int vert_lid); - - }; // end of quad_8_2D class - - - /* - =========================== - 2D Quad 12 Elements - =========================== - - - The finite element local point numbering for a 8 node Hexahedral is - as follows (NEED TO DEFINE) - - Eta - ^ - | - 3---7------6---2 - | | | - | | | - 11 | 10 - | | | - | +------|-----> Xi - | | - 8 9 - | | - 0----4-----5---1 - - */ - class Quad12: public Element2D { - - protected: - - static const int num_verts_ = 12; - static const int num_nodes_ = 12; - static const int num_basis_ = 12; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Quad12(); - ~Quad12(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map( const int vert_lid); - - }; // end of quad_8_2D class - - - /* - ========================== - Arbitrary Order Elements - ========================== - - __ _ _ _ - / __ \ | | \ | | - | | | |_ _ __ _ __| | \| | - | | | | | | |/ _` |/ _` | . ` | - | |__| | |_| | (_| | (_| | |\ | - \___\_\\__,_|\__,_|\__,_|_| \_| - - Representative linear element for visualization - - Eta (j) - ^ - | - 3--------------2 - | | | - | | | - | | | - | | | - | +------|-----> Xi (i) - | | - | | - | | - 0--------------1 - */ - class QuadN { - public: - - const static int num_dim = 2; - - int num_basis; - int num_verts; - - // calculates the basis values and derivatives in 1D - // used in the basis_partials functiosn to build the 3D element - void lagrange_1D( - ViewCArray &interp, // interpolant - ViewCArray &Dinterp, // derivative of function - const real_t &x_point, // point of interest in element - const ViewCArray &xi_point, // nodal positions in 1D, normally chebyshev - const int &orderN); // order of element - - void corners ( - ViewCArray &lag_nodes, // Nodes of Lagrange elements - ViewCArray &lag_corner, // corner nodes of QuadN element - const int &orderN); // Element order - - void physical_position ( - ViewCArray &x_point, // location in real space - const ViewCArray &lag_nodes, // Nodes of Lagrange elements - const ViewCArray &lag_basis_2d, // 2D basis values - const int &orderN); // order of the element - - void basis_partials ( - ViewCArray &lag_nodes, // Nodes of Lagrange elements (to be filled in) - ViewCArray &nodes_1d, // Nodal spacing in 1D, any spacing is accepted - ViewCArray &val_1d, // Interpolant Value in 1D - ViewCArray &DVal_1d, // Derivateive of basis in 1D - ViewCArray &val_2d, // for holding the interpolant in each direction - ViewCArray &DVal_2d, // for holding the derivatives in each direction - ViewCArray &lag_basis_2d, // 2D basis values - ViewCArray &lag_partial, // Partial of basis - const ViewCArray &xi_point, // point of interest - const int &orderN); // Element order - }; - -} -#endif // ELEMENTS_2D_H diff --git a/elements/elements_3d.h b/elements/elements_3d.h deleted file mode 100644 index b20c5c00..00000000 --- a/elements/elements_3d.h +++ /dev/null @@ -1,464 +0,0 @@ -/***************************************************************************** -© 2020. Triad National Security, LLC. All rights reserved. -This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos -National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. -Department of Energy/National Nuclear Security Administration. All rights in the program are -reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear -Security Administration. The Government is granted for itself and others acting on its behalf a -nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare -derivative works, distribute copies to the public, perform publicly and display publicly, and -to permit others to do so. - - -This program is open source under the BSD-3 License. -Redistribution and use in source and binary forms, with or without modification, are permitted -provided that the following conditions are met: - - 1. Redistributions of source code must retain the above copyright notice, this list of - conditions and the following disclaimer. - - 2. Redistributions in binary form must reproduce the above copyright notice, this list of - conditions and the following disclaimer in the documentation and/or other materials - provided with the distribution. - - 3. Neither the name of the copyright holder nor the names of its contributors may be used - to endorse or promote products derived from this software without specific prior - written permission. - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS -IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR -CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; -OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, -WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR -OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF -ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - -**********************************************************************************************/ -#ifndef ELEMENTS_3D_H -#define ELEMENTS_3D_H - -namespace elements { - - /* - .-------------------------------. - | .----------------------------. | - | | ______ ________ | | - | | / ____ `. |_ ___ `. | | - | | `' __) | | | `. \ | | - | | _ |__ '. | | | | | | - | | | \____) | _| |___.' / | | - | | \______.' |________.' | | - | | | | - | '----------------------------' | - '------------------------------' - */ - class Element3D { - - protected: - const static int num_dim_ = 3; - - public: - - virtual int num_verts() = 0; - virtual int num_nodes() = 0; - virtual int num_basis() = 0; - - //list of local ids to basis functions needed to interpolate throughout a given element surface - RaggedRightArray surface_to_dof_lid; - int nsurfaces; - - // calculate a physical position in an element for a given xi,eta,mu - virtual void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices) = 0; - - // calculate the value for the basis at each node for a given xi,eta, mu - virtual void basis( - ViewCArray &basis, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Xi at Xi_point - virtual void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Eta - virtual void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Mu - virtual void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point) = 0; - - // Map from vertex to node - virtual inline int vert_node_map(const int vert_lid) = 0; - - // Reference vertices location - virtual real_t& ref_locs(const int vert_lid, const int dim) = 0; - - }; // end of 3D parent class - - - /* - ========================== - Hex 8 - ========================== - - The finite element local vertex numbering for a 8 node Hexahedral is - as follows - - Mu (k) - | Eta (j) - | / - | / - 6---+----7 - /| | /| - / | | / | - 4--------5 | - | | -|--+---> Xi (i) - | | | | - | 2-----|--3 - | / | / - |/ |/ - 0----*----1 - - */ - class Hex8: public Element3D { - - protected: - - static const int num_verts_ = 8; - static const int num_nodes_ = 8; - static const int num_basis_ = 8; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Hex8(); - ~Hex8(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // with repsect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Map from vertex to node - inline int vert_node_map(const int vert_lid); - - real_t& ref_locs(const int vert_lid, const int dim); - - }; // end of hex 8 class - - - /* - ========================== - Hex 20 - ========================== - - The finite element local point numbering for a 20 node Hexahedral is - as follows - - Mu (k) - | Eta (j) - | / - | / - 7----14----6 - /| /| - 15 | 13 | - / 19 / 18 - 4----12----5 | - | | | | --> Xi (i) - | | | | - | 3---10-|---2 - 16 / 17 / - | 11 | 9 - |/ |/ - 0-----8----1 - */ - class Hex20: public Element3D { - protected: - - static const int num_verts_ = 20; - static const int num_nodes_ = 20; - static const int num_basis_ = 20; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Hex20(); - ~Hex20(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // with repsect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Map from vertex to node - inline int vert_node_map(const int vert_lid); - - real_t& ref_locs(const int vert_lid, const int dim); - - }; // end of hex20 class - - - /* - ========================== - Hex 32 - ========================== - - The finite element local point numbering for a 32 node Hexahedral is - shown below - - - Mu (k) - ^ Eta (j) - | / - | / - / - 7----23------22----6 - /| /| - 15 | 14 | - / | / | - 12 31 13 30 - / | / | - 4-----20-----21----5 | - | | | | ----> Xi (i) - | 27 | 26 - | | | | - 28 | 29 | - | 3----19------|18---2 - | / | / - | 11 | 10 - 24 / 25 / - | 8 | 9 - |/ |/ - 0----16------17----1 - */ - class Hex32: public Element3D { - - protected: - - static const int num_verts_ = 32; - static const int num_nodes_ = 32; - static const int num_basis_ = 32; - - static real_t ref_vert[num_verts_*num_dim_]; // listed as {Xi, Eta, Mu} - static const int vert_to_node[num_verts_]; - - public: - - Hex32(); - ~Hex32(); - - int num_verts(); - int num_nodes(); - int num_basis(); - - // calculate a physical position in an element for a given xi,eta - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - - // calculate the value for the basis at each node for a given xi,eta - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // with repsect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Map from vertex to node - int vert_node_map(const int vert_lid); - - real_t& ref_locs(const int vert_lid, const int dim); - - }; // end of hex32 class - - - /* - ========================== - Arbitrary Order Elements - ========================== - _ _ _ _ - | | | | _____ _| \ | | - | |_| |/ _ \ \/ / \| | - | _ | __/> <| |\ | - |_| |_|\___/_/\_\_| \_| - - Representative linear element for visualization - - k - | j - | / - | / - 6---+----7 - /| | /| - / | | / | - 4--------5 | - | | -|--+---> i - | | | | - | 2-----|--3 - | / | / - |/ |/ - 0--------1 - */ - class HexN { - - protected: - - const static int num_dim_ = 3; - - // Nodes - int num_nodes_1d_; - int num_nodes_; - - MatarRealCArray HexN_Nodes_1d_; - MatarRealCArray HexN_Nodes_; - - // Vertices - int num_verts_1d_; - int num_verts_; - int num_basis_; - - MatarRealCArray HexN_Verts_1d_; - MatarRealCArray HexN_Verts_; - - MatarUIntCArray Vert_Node_map_; - - int order_; - - - public: - - void setup_HexN(int elem_order); - - int num_verts(); - int num_nodes(); - int num_basis(); - int node_rid(int i, int j, int k) const; - int vert_rid(int i, int j, int k) const; - - // Return the noda coordinates in reference space - real_t &node_coords(int node_rlid, int dim); - - - int vert_node_map(int vert_rid) const; - - // Evaluate the basis at a given point - void basis( - MatarRealCArray &basis, - MatarRealCArray &point); - - void build_nodal_gradient( - MatarRealCArray &gradient); - - // calculate the partial of the basis w.r.t xi at a given point - void partial_xi_basis( - MatarRealCArray &partial_xi, - MatarRealCArray &point); - - // calculate the partial of the basis w.r.t eta at a given point - void partial_eta_basis( - MatarRealCArray &partial_eta, - MatarRealCArray &point); - - // calculate the partial of the basis w.r.t mu at a given point - void partial_mu_basis( - MatarRealCArray &partial_mu, - MatarRealCArray &point); - - void lagrange_basis_1D( - MatarRealCArray &interp, // interpolant - const real_t &x_point); // point of interest in element - - void lagrange_derivative_1D( - MatarRealCArray &partials, //derivative - const real_t &x_point); // point of interest in element - - void create_lobatto_nodes(int element_order); - - }; - -} - -#endif // ELEMENTS_3D_H diff --git a/elements/elements_4d.h b/elements/elements_4d.h deleted file mode 100644 index d7d38326..00000000 --- a/elements/elements_4d.h +++ /dev/null @@ -1,184 +0,0 @@ -/***************************************************************************** -© 2020. Triad National Security, LLC. All rights reserved. -This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos -National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. -Department of Energy/National Nuclear Security Administration. All rights in the program are -reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear -Security Administration. The Government is granted for itself and others acting on its behalf a -nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare -derivative works, distribute copies to the public, perform publicly and display publicly, and -to permit others to do so. - - -This program is open source under the BSD-3 License. -Redistribution and use in source and binary forms, with or without modification, are permitted -provided that the following conditions are met: - - 1. Redistributions of source code must retain the above copyright notice, this list of - conditions and the following disclaimer. - - 2. Redistributions in binary form must reproduce the above copyright notice, this list of - conditions and the following disclaimer in the documentation and/or other materials - provided with the distribution. - - 3. Neither the name of the copyright holder nor the names of its contributors may be used - to endorse or promote products derived from this software without specific prior - written permission. - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS -IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR -CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; -OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, -WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR -OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF -ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - -**********************************************************************************************/ -#ifndef ELEMENTS_4D_H -#define ELEMENTS_4D_H - -namespace elements { - - class Element4D { - - public: - - //list of local ids to basis functions needed to interpolate throughout a given element surface - CArray surface_to_dof_lid; - - // calculate a physical position in an element for a given xi,eta,mu,tau - virtual void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices) = 0; - - // calculate the value for the basis at each node for a given xi,eta,mu,tau - virtual void basis( - ViewCArray &basis, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Xi at Xi_point - virtual void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Eta - virtual void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Mu - virtual void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point) = 0; - - // Partial derivative of shape functions with respect to Tau - virtual void partial_tau_basis( - ViewCArray &partial_tau, - const ViewCArray &xi_point) = 0; - - - }; - - - /* - ========================== - 4D Tesseract element - ========================== - - The finite element local point numbering for a 16 node Tesseract is - based on the 3D Hex8 Ensight element - - - _.15--------------------------------------14 - _.+< |\ . >-"/ | - _ .+> | \ .>"" ./ | - .>"" | \ ."" / | - 12----------------------+------------------13 ./ | - | )<= | \ / | _/"" | - | )\+ | \ / /"| | - | (\= | _. 7---------+--6 | | - | \> .|+< | / . "| | | - | '4--+------+------5' | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | | | | | | - | | | _ .3------+-----2_ | | - | | | " / | /' '| \= _ | - | 0--+---+---------1*" | '\ | - | ./' | " \ | ""\ | - | / |/ \ | '". | - | / 11----------------+-----+---------------10 - | ./ .+<"" ) | .( - 8------------------------------------------9' - - j - ^ k - | / - | / - | / - |/ - +---------->i - - i = Xi - j = Eta - k = Mu - t = Tau - - */ - class Tess16: public Element4D { - public: - const static int num_verts = 16; - const static int num_dim = 4; - const static int num_basis = 16; - - protected: - static real_t ref_vert[num_verts*num_dim]; // listed as {Xi, Eta, Mu, Tau} - - - public: - - // calculate a physical position in an element for a given xi,eta,mu - void physical_position( - ViewCArray &x_point, - const ViewCArray &xi_point, - const ViewCArray &vertices); - - // calculate the value for the basis at each node for a given xi,eta,mu,tau - void basis( - ViewCArray &basis, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Xi at Xi_point - void partial_xi_basis( - ViewCArray &partial_xi, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Eta - void partial_eta_basis( - ViewCArray &partial_eta, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Mu - void partial_mu_basis( - ViewCArray &partial_mu, - const ViewCArray &xi_point); - - // Partial derivative of shape functions with respect to Tau - void partial_tau_basis( - ViewCArray &partial_tau, - const ViewCArray &xi_point); - }; // End of Tess16 Element Class - -} - -#endif // ELEMENTS_4D_H diff --git a/elements/elements_jacobians.h b/elements/elements_jacobians.h deleted file mode 100644 index 74b4d43f..00000000 --- a/elements/elements_jacobians.h +++ /dev/null @@ -1,90 +0,0 @@ -/***************************************************************************** -© 2020. Triad National Security, LLC. All rights reserved. -This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos -National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. -Department of Energy/National Nuclear Security Administration. All rights in the program are -reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear -Security Administration. The Government is granted for itself and others acting on its behalf a -nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare -derivative works, distribute copies to the public, perform publicly and display publicly, and -to permit others to do so. - - -This program is open source under the BSD-3 License. -Redistribution and use in source and binary forms, with or without modification, are permitted -provided that the following conditions are met: - - 1. Redistributions of source code must retain the above copyright notice, this list of - conditions and the following disclaimer. - - 2. Redistributions in binary form must reproduce the above copyright notice, this list of - conditions and the following disclaimer in the documentation and/or other materials - provided with the distribution. - - 3. Neither the name of the copyright holder nor the names of its contributors may be used - to endorse or promote products derived from this software without specific prior - written permission. - - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS -IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR -CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; -OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, -WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR -OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF -ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - -**********************************************************************************************/ -#ifndef ELEMENTS_JACOBIANS_H -#define ELEMENTS_JACOBIANS_H - -namespace elements { - - //defining the jacobian for 2D elements - void jacobian_2d( - ViewCArray &J_matrix, - real_t &det_J, - const ViewCArray &vertices, - const ViewCArray &this_partial, - const int &num_nodes); - - //defining the inverse jacobian for 2D element - void jacobian_inverse_2d( - ViewCArray &J_inverse, - const ViewCArray &jacobian); - - //defining the jacobian for 3D elements - void jacobian_3d( - ViewCArray &J_matrix, - real_t &det_J, - const ViewCArray &vertices, - const ViewCArray &this_partial, - const int &num_nodes); - - //defining the inverse jacobian for 2D element - void jacobian_inverse_3d( - ViewCArray &J_inverse_matrix, - const ViewCArray &jacobian); - - //defining the jacobian for 4D elements - void jacobian_4d( - ViewCArray &J_matrix, - real_t &det_J, - const ViewCArray &vertices, - const ViewCArray &this_partial, - const int &num_nodes, - const int &dim); - - // defining the inverse of the Jacobian for 4D elements - void jacobian_inverse_4d( - ViewCArray &J_inverse_matrix, - const ViewCArray &jacobian, - const real_t &det_J); - -} - -#endif // ELEMENTS_JACOBIANS_H diff --git a/elements/elements_points_and_weights.h b/elements/elements_points_and_weights.h deleted file mode 100644 index 72e18565..00000000 --- a/elements/elements_points_and_weights.h +++ /dev/null @@ -1,137 +0,0 @@ -/***************************************************************************** -© 2020. Triad National Security, LLC. All rights reserved. -This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos -National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. -Department of Energy/National Nuclear Security Administration. All rights in the program are -reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear -Security Administration. The Government is granted for itself and others acting on its behalf a -nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare -derivative works, distribute copies to the public, perform publicly and display publicly, and -to permit others to do so. - - -This program is open source under the BSD-3 License. -Redistribution and use in source and binary forms, with or without modification, are permitted -provided that the following conditions are met: - - 1. Redistributions of source code must retain the above copyright notice, this list of - conditions and the following disclaimer. - - 2. Redistributions in binary form must reproduce the above copyright notice, this list of - conditions and the following disclaimer in the documentation and/or other materials - provided with the distribution. - - 3. Neither the name of the copyright holder nor the names of its contributors may be used - to endorse or promote products derived from this software without specific prior - written permission. - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS -IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR -CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; -OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, -WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR -OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF -ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - -**********************************************************************************************/ -#ifndef ELEMENTS_POINTS_AND_WEIGHTS_H -#define ELEMENTS_POINTS_AND_WEIGHTS_H - -namespace elements { - - // Used by Lobatto 1D/2D to set Lobatto quadrature points - void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num); - void lobatto_weights_1D(MatarRealCArray &lob_weights_1D, const int &num); - - - void legendre_nodes_1D(CArray &leg_nodes_1D, const int &num); - void legendre_weights_1D(CArray &leg_weights_1D, const int &num); - - - // creates nodal positions with Chebyshev spacing - void chebyshev_nodes_1D( - ViewCArray &cheb_nodes_1D, // Chebyshev nodes - const int &order); // Interpolation order - - - void length_weights( - MatarRealCArray &len_weights_1D, // Lobatto weights - MatarRealCArray &lab_weights_1D, // Lobatto weights - MatarRealCArray &lab_nodes_1D, - const int &order); - - void sub_weights( - MatarRealCArray &sub_weights_1D, // Lobatto weights - MatarRealCArray &lab_weights_1D, // Lobatto weights - MatarRealCArray &lab_nodes_1D, - const int &order); - - - void set_nodes_wgts( - CArray &lab_nodes_1D, - CArray &lab_weights_1D, - CArray &len_weights_1D, - CArray &sub_weights_1D, - int p_order); - - // Used by Gauss2/3D to set quadrature points - void line_gauss_info( - real_t &x, - real_t &w, - int &m, - int &p); - - // Used by Lovatto 1D/2D to set Lobatto quadrature points - void line_lobatto_info( - real_t &x, - real_t &w, - int &m, - int &p); - - // setting gauss quadrature points for 2D elements - void gauss_2d( - ViewCArray &these_g_pts, // gauss points - ViewCArray &these_weights, // gauss weights - ViewCArray &tot_g_weight, // 2D product of gauss weights - int &quad_order); // quadrature order (n) - - // setting gauss quadrature points for 2D elements - void gauss_3d( - ViewCArray &these_g_pts, // gauss points - ViewCArray &these_weights, // gauss weights - ViewCArray &tot_g_weight, // 3D product of gauss weights - int &quad_order); // quadrature order (n) - - // setting gauss quadrature points for 4D elements - void gauss_4d( - ViewCArray &these_g_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order, // quadrature order (n) - const int &dim); - - // setting Gauss-Lobatto quadrature points for 2D elements - void lobatto_2d( - ViewCArray &these_L_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order); // quadrature order (n) - - // setting Gauss-Lobatto quadrature points for 3D elements - void lobatto_3d( - ViewCArray &these_L_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order); - - // setting gauss quadrature points for 4D elements - void lobatto_4d( - ViewCArray &these_L_pts, // gauss points - ViewCArray &these_weights, // gauss weights - int &quad_order, // quadrature order (n) - const int &dim); - -} - -#endif // ELEMENTS_POINTS_AND_WEIGHTS_H diff --git a/elements/elements_ref_element.h b/elements/elements_ref_element.h deleted file mode 100644 index e904020f..00000000 --- a/elements/elements_ref_element.h +++ /dev/null @@ -1,232 +0,0 @@ -/***************************************************************************** -© 2020. Triad National Security, LLC. All rights reserved. -This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos -National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. -Department of Energy/National Nuclear Security Administration. All rights in the program are -reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear -Security Administration. The Government is granted for itself and others acting on its behalf a -nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare -derivative works, distribute copies to the public, perform publicly and display publicly, and -to permit others to do so. - - -This program is open source under the BSD-3 License. -Redistribution and use in source and binary forms, with or without modification, are permitted -provided that the following conditions are met: - - 1. Redistributions of source code must retain the above copyright notice, this list of - conditions and the following disclaimer. - - 2. Redistributions in binary form must reproduce the above copyright notice, this list of - conditions and the following disclaimer in the documentation and/or other materials - provided with the distribution. - - 3. Neither the name of the copyright holder nor the names of its contributors may be used - to endorse or promote products derived from this software without specific prior - written permission. - -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS -IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR -CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; -OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, -WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR -OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF -ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. - -**********************************************************************************************/ -#ifndef ELEMENTS_REF_ELEMENT_H -#define ELEMENTS_REF_ELEMENT_H -namespace elements { - - // Reference Element Informations - class ref_element{ - private: - - // this assumes i,j,k structured indexing of nodes - const int node_rlid_in_patch_in_cell_[24] = { - // patches in xi-dir - 0,2,6,4, - 1,3,7,5, - // patches in eta-dir - 0,4,5,1, - 2,6,7,3, - // patches in mu-dir - 0,1,3,2, - 4,5,7,6 - }; - - // return the local ref id for the same patch in the cell-patch neighbor - const int patch_rlid_cell_neighbor_[6] = { - 1, // xi left side of my cell - 0, // xi right side of my cell - 3, // eta front side of my cell - 2, // eta bact side of my cell - 5, // mu bottom side of my cell - 4 // mu top side of my cell - }; - - // return the reference coordinate unit normal of the sides in a cell - const real_t cell_side_unit_normals_[18] = { - -1, 0, 0, // xi left side of my cell - 1, 0, 0, // xi right side of my cell - 0,-1, 0, // eta minus side of my cell - 0, 1, 0, // eta plus side of my cell - 0, 0,-1, // mu minus side of my cell - 0, 0, 1 // mu plus side of my cell - }; - - int num_dim_; - - int num_ref_nodes_1D_; - int num_ref_cells_1D_; - int num_ref_corners_1D_; - - int num_ref_surface_nodes_in_elem_; - int num_ref_inside_nodes_in_elem_; - - // Zones - int num_zones_1d_; - int num_zones_in_elem_; - - // cells - int num_ref_cells_in_elem_; - - CArray cells_in_zone_list_; - - // nodes - int num_ref_nodes_in_elem_; - int num_ref_nodes_in_cell_; - - CArray ref_nodes_in_cell_; - CArray ref_surface_nodes_in_elem_; - CArray ref_inside_nodes_in_elem_; - - CArray ref_node_positions_; - CArray ref_node_g_weights_; - - CArray cell_nodes_in_elem_list_; - - // Vertices - int num_ref_verts_1d_; - int num_ref_verts_in_elem_; - - // corners - int num_ref_corners_in_cell_; - int num_ref_corners_in_elem_; - - CArray ref_corners_in_cell_; - - CArray ref_corner_surf_normals_; - CArray ref_corner_g_weights_; - CArray ref_corner_surf_g_weights_; - - // patches and sides - int num_patches_in_elem_; - int num_sides_in_elem_; - - CArray ref_cell_positions_; - CArray ref_cell_g_weights_; - CArray ref_patch_positions_; - CArray ref_patch_g_weights_; - - CArray ref_patches_in_cell_list_; - - CArray ref_patch_basis_; - CArray ref_patch_gradient_; // grad basis at patch - - CArray ref_cell_basis_; - CArray ref_cell_gradient_; // grad basis at cell - - // Num basis functions - int num_basis_; - - // Basis evaluation at nodes - CArray ref_nodal_basis_; - - // Pointer to HexN object - HexN *elem_ptr; - - public: - - // Gradient of basis - CArray ref_nodal_gradient_; - //real_t * ref_nodal_gradient_; - - // Function Declarations - - // Default constructor - ref_element() : elem_ptr(nullptr) {}; - - // Initialize reference element information - void init(int poly_order, int num_dim, HexN &elem); - - int num_dim() const; - - int num_basis() const; - - int num_ref_nodes() const; - - int num_ref_cells_in_elem() const; - int num_ref_corners_in_cell() const; - - // local i,j,k indexing - int node_rid(int i, int j, int k) const; - int cell_rid(int i, int j, int k) const; - int corner_rid(int i, int j, int k) const; - - int ref_corners_in_cell(int cell_rid, int corner_rlid) const; - int ref_nodes_in_cell(int cell_rid, int node_rlid) const; - - int ref_surface_nodes_in_elem(int node_rlid) const; - int ref_inside_nodes_in_elem(int node_rlid) const; - int num_ref_surface_nodes_in_elem() const; - int num_ref_inside_nodes_in_elem() const; - - real_t ref_node_positions(int node_rid, int dim) const; - - real_t ref_corner_surface_normals(int corner_rid, int surf_rlid, int dim) const; - - real_t ref_corner_g_surface_weights(int corner_rid, int surf_rlid) const; - - real_t ref_node_g_weights(int node_rid) const; - - real_t ref_corner_g_weights(int corner_rid) const; - - real_t &ref_nodal_gradient(int node_rid, int basis_id, int dim) const; - - real_t &ref_nodal_basis(int node_rid, int basis_id) const; - - int& cell_lid_in_zone(int zone_lid, int cell_lid) const; - - real_t ref_cell_positions(int cell_rid, int dim) const; - real_t ref_cell_g_weights(int cell_rid) const; - real_t ref_cell_basis(int cell_rid, int basis_id) const; - real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; - - real_t cell_side_unit_normals(int side_rlid, int dim) const; - - int& cell_nodes_in_elem(int cell_lid, int node_lid) const; - - int node_in_patch_in_cell(int patch_lid, int node_lid) const; - - int patch_rlid_in_cell_neighbor(int patch_rlid) const; - - int ref_patches_in_cell(int cell_lid, int patch_rlid) const; - - real_t ref_patch_positions(int patch_rid, int dim) const; - real_t ref_patch_g_weights(int patch_rid) const; - real_t ref_patch_basis(int patch_rid, int basis_id) const; - real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; - - int vert_node_map(int vert_lid); - - // Deconstructor - ~ref_element(); - }; - -} -#endif // ELEMENTS_REF_ELEMENT_H From 126f88149a1ed3b6a34bad4da495a907486bb6c7 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Wed, 14 Sep 2022 17:27:34 -0500 Subject: [PATCH 14/20] Removed build files introduced with last merge --- .../CMakeDirectoryInformation.cmake | 16 - .../CMakeFiles/elements.dir/DependInfo.cmake | 28 - .../elements.dir/bernstein_polynomials.cpp.o | Bin 47040 -> 0 bytes .../bernstein_polynomials.cpp.o.d | 204 -- 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"${VECTOR_CXX_OPTS} -mprefer-vector-width=512") - endif ("${CMAKE_CXX_COMPILER_VERSION}" VERSION_GREATER "7.9.0") - if ("${CMAKE_CXX_COMPILER_VERSION}" VERSION_LESS "9.0.0") - message(STATUS "Use a GCC compiler version 9.0.0 or greater to get effective vectorization") - endif ("${CMAKE_CXX_COMPILER_VERSION}" VERSION_LESS "9.0.0") - endif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - - set(VECTOR_NOVEC_CXX_OPT "${VECTOR_NOVEC_CXX_OPT} -fno-tree-vectorize") - set(VECTOR_CXX_VERBOSE "${VECTOR_CXX_VERBOSE} -fopt-info-vec-optimized -fopt-info-vec-missed -fopt-info-loop-optimized -fopt-info-loop-missed") - - elseif ("${CMAKE_CXX_COMPILER_ID}" STREQUAL "Intel") # using Intel C - set(VECTOR_ALIASING_CXX_FLAGS "${VECTOR_ALIASING_CXX_FLAGS} -ansi-alias") - set(VECTOR_FPMODEL_CXX_FLAGS "${VECTOR_FPMODEL_CXX_FLAGS} -fp-model:precise") - - set(VECTOR_OPENMP_SIMD_CXX_FLAGS "${VECTOR_OPENMP_SIMD_CXX_FLAGS} -qopenmp-simd") - set(VECTOR_CXX_OPTS "${VECTOR_CXX_OPTS} -march=native -mtune=native -xHOST -vecabi=cmdtarget") - if ("${CMAKE_CXX_COMPILER_VERSION}" VERSION_GREATER "17.0.4") - set(VECTOR_CXX_OPTS "${VECTOR_CXX_OPTS} -qopt-zmm-usage=high") - endif ("${CMAKE_CXX_COMPILER_VERSION}" VERSION_GREATER "17.0.4") - set(VECTOR_NOVEC_CXX_OPT "${VECTOR_NOVEC_CXX_OPT} -march=native -mtune=native -no-vec") - set(VECTOR_CXX_VERBOSE "${VECTOR_CXX_VERBOSE} -qopt-report=5 -qopt-report-phase=openmp,loop,vec") - - elseif (CMAKE_CXX_COMPILER_ID MATCHES "PGI") - set(VECTOR_ALIASING_CXX_FLAGS "${VECTOR_ALIASING_CXX_FLAGS} -alias=ansi") - set(VECTOR_OPENMP_SIMD_CXX_FLAGS "${VECTOR_OPENMP_SIMD_CXX_FLAGS} -Mvect=simd") - if ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - if ("${CMAKE_CXX_COMPILER_VERSION}" VERSION_GREATER "18.6") - execute_process(COMMAND pgc++ --version COMMAND grep LLVM COMMAND wc -l OUTPUT_VARIABLE PGI_VERSION_OUTPUT OUTPUT_STRIP_TRAILING_WHITESPACE) - if ("${PGI_VERSION_OUTPUT}" STREQUAL "1") - set(VECTOR_ARCH_CXX_FLAGS "${VECTOR_ARCH_CXX_FLAGS} -Mllvm") - endif ("${PGI_VERSION_OUTPUT}" STREQUAL "1") - endif ("${CMAKE_CXX_COMPILER_VERSION}" VERSION_GREATER "18.6") - endif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - - set(VECTOR_NOVEC_CXX_OPT "${VECTOR_NOVEC_CXX_OPT} -Mnovect ") - set(VECTOR_CXX_VERBOSE "${VECTOR_CXX_VERBOSE} -Minfo=loop,inline,vect") - - elseif (CMAKE_CXX_COMPILER_ID MATCHES "MSVC") - set(VECTOR_CXX_OPTS "${VECTOR_CXX_OPTS}" " ") - - set(VECTOR_NOVEC_CXX_OPT "${VECTOR_NOVEC_CXX_OPT}" " ") - set(VECTOR_CXX_VERBOSE "${VECTOR_CXX_VERBOSE} -Qvec-report:2") - - elseif (CMAKE_CXX_COMPILER_ID MATCHES "XL") - set(VECTOR_ALIASING_CXX_FLAGSS "${VECTOR_ALIASING_CXX_FLAGS} -qalias=restrict") - set(VECTOR_FPMODEL_CXX_FLAGSS "${VECTOR_FPMODEL_CXX_FLAGS} -qstrict") - set(VECTOR_ARCH_CXX_FLAGSS "${VECTOR_ARCH_CXX_FLAGS} -qhot -qarch=auto -qtune=auto") - - set(CMAKE_VEC_CXX_FLAGS "${CMAKE_VEC_FLAGS} -qsimd=auto") - set(VECTOR_NOVEC_CXX_OPT "${VECTOR_NOVEC_CXX_OPT} -qsimd=noauto") - # "long vector" optimizations - #set(VECTOR_NOVEC_CXX_OPT "${VECTOR_NOVEC_CXX_OPT} -qhot=novector") - set(VECTOR_CXX_VERBOSE "${VECTOR_CXX_VERBOSE} -qreport") - - elseif (CMAKE_CXX_COMPILER_ID MATCHES "Cray") - set(VECTOR_ALIASING_CXX_FLAGS "${VECTOR_ALIASING_CXX_FLAGS} -h restrict=a") - set(VECTOR_CXX_OPTS "${VECTOR_CXX_OPTS} -h vector=3") - - set(VECTOR_NOVEC_CXX_OPT "${VECTOR_NOVEC_CXX_OPT} -h vector=0") - set(VECTOR_CXX_VERBOSE "${VECTOR_CXX_VERBOSE} -h msgs -h negmsgs -h list=a") - - endif() - - CHECK_CXX_COMPILER_FLAG("${VECTOR_OPENMP_SIMD_CXX_FLAGS}" HAVE_OPENMP_SIMD) - if (HAVE_OPENMP_SIMD) - add_definitions(-D_OPENMP_SIMD) - else (HAVE_OPENMP_SIMD) - unset(VECTOR_OPENMP_SIMD_CXX_FLAGS) - endif (HAVE_OPENMP_SIMD) - - set(VECTOR_BASE_CXX_FLAGS "${VECTOR_ALIASING_CXX_FLAGS} ${VECTOR_ARCH_CXX_FLAGS} ${VECTOR_FPMODEL_CXX_FLAGS}") - set(VECTOR_NOVEC_CXX_FLAGS "${VECTOR_BASE_CXX_FLAGS} ${VECTOR_NOVEC_CXX_OPT}") - set(VECTOR_CXX_FLAGS "${VECTOR_BASE_CXX_FLAGS} ${VECTOR_CXX_OPTS} ${VECTOR_CXX_FPOPTS} ${VECTOR_OPENMP_SIMD_CXX_FLAGS}") - - mark_as_advanced(VECTOR_CXX_FLAGS - VECTOR_NOVEC_CXX_FLAGS - VECTOR_CXX_VERBOSE - VECTOR_ALIASING_CXX_FLAGS - VECTOR_ARCH_CXX_FLAGS - VECTOR_FPMODEL_CXX_FLAGS - VECTOR_NOVEC_CXX_OPT - VECTOR_VEC_CXX_OPTS - VECTOR_VEC_CXX_FPOPTS) - - message(STATUS "Setting Vector CXX flags to: ${VECTOR_CXX_FLAGS}") - message(STATUS "Setting Vector CXX No-Vector flags to: ${VECTOR_NOVEC_CXX_FLAGS}") - message(STATUS "Setting Vector CXX Verbose flags to: ${VECTOR_CXX_VERBOSE}") - -endif(CMAKE_CXX_COMPILER_LOADED) - -# Start Fortran flags -if(CMAKE_Fortran_COMPILER_LOADED) - if ("${CMAKE_Fortran_COMPILER_ID}" STREQUAL "Clang") # using Clang - set(VECTOR_ALIASING_Fortran_FLAGS "${VECTOR_ALIASING_Fortran_FLAGS} -fstrict-aliasing") - if ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - set(VECTOR_ARCH_Fortran_FLAGS "${VECTOR_ARCH_Fortran_FLAGS} -march=native -mtune=native") - elseif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "ppc64le") - set(VECTOR_ARCH_Fortran_FLAGS "${VECTOR_ARCH_Fortran_FLAGS} -mcpu=powerpc64le") - elseif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "aarch64") - set(VECTOR_ARCH_Fortran_FLAGS "${VECTOR_ARCH_Fortran_FLAGS} -march=native -mtune=native") - endif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - - set(VECTOR_OPENMP_SIMD_Fortran_FLAGS "${VECTOR_OPENMP_SIMD_Fortran_FLAGS} -fopenmp-simd") - set(VECTOR_Fortran_OPTS "${VECTOR_Fortran_OPTS} -fvectorize") - set(VECTOR_Fortran_FPOPTS "${VECTOR_Fortran_FPOPTS} -fno-math-errno") - set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT} -fno-vectorize") - set(VECTOR_Fortran_VERBOSE "${VECTOR_Fortran_VERBOSE} -Rpass=loop-vectorize -Rpass-missed=loop-vectorize -Rpass-analysis=loop-vectorize") - - elseif ("${CMAKE_Fortran_COMPILER_ID}" STREQUAL "GNU") # using GCC - set(VECTOR_ALIASING_Fortran_FLAGS "${VECTOR_ALIASING_Fortran_FLAGS} -fstrict-aliasing") - if ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - set(VECTOR_ARCH_Fortran_FLAGS "${VECTOR_ARCH_Fortran_FLAGS} -march=native -mtune=native") - elseif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "ppc64le") - set(VECTOR_ARCH_Fortran_FLAGS "${VECTOR_ARCH_Fortran_FLAGS} -mcpu=powerpc64le") - elseif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "aarch64") - set(VECTOR_ARCH_Fortran_FLAGS "${VECTOR_ARCH_Fortran_FLAGS} -march=native -mtune=native") - endif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - - set(VECTOR_OPENMP_SIMD_Fortran_FLAGS "${VECTOR_OPENMP_SIMD_Fortran_FLAGS} -fopenmp-simd") - set(VECTOR_Fortran_OPTS "${VECTOR_Fortran_OPTS} -ftree-vectorize") - set(VECTOR_Fortran_FPOPTS "${VECTOR_Fortran_FPOPTS} -fno-trapping-math -fno-math-errno") - if ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - if ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER "7.9.0") - set(VECTOR_Fortran_OPTS "${VECTOR_Fortran_OPTS} -mprefer-vector-width=512") - endif ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER "7.9.0") - if ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_LESS "9.0.0") - message(STATUS "Use a GCC compiler version 9.0.0 or greater to get effective vectorization") - endif ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_LESS "9.0.0") - endif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - - set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT} -fno-tree-vectorize") - set(VECTOR_Fortran_VERBOSE "${VECTOR_Fortran_VERBOSE} -fopt-info-vec-optimized -fopt-info-vec-missed -fopt-info-loop-optimized -fopt-info-loop-missed") - - elseif ("${CMAKE_Fortran_COMPILER_ID}" STREQUAL "Intel") # using Intel C - set(VECTOR_ALIASING_Fortran_FLAGS "${VECTOR_ALIASING_Fortran_FLAGS} -ansi-alias") - set(VECTOR_FPMODEL_Fortran_FLAGS "${VECTOR_FPMODEL_Fortran_FLAGS} -fp-model:precise") - - set(VECTOR_OPENMP_SIMD_Fortran_FLAGS "${VECTOR_OPENMP_SIMD_Fortran_FLAGS} -qopenmp-simd") - set(VECTOR_Fortran_OPTS "${VECTOR_Fortran_OPTS} -march=native -mtune=native -xHOST -vecabi=cmdtarget") - if ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER "17.0.4") - set(VECTOR_Fortran_OPTS "${VECTOR_Fortran_OPTS} -qopt-zmm-usage=high") - endif ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER "17.0.4") - set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT} -march=native -mtune=native -no-vec") - set(VECTOR_Fortran_VERBOSE "${VECTOR_Fortran_VERBOSE} -qopt-report=5 -qopt-report-phase=openmp,loop,vec") - - elseif (CMAKE_Fortran_COMPILER_ID MATCHES "PGI") - set(VECTOR_ALIASING_Fortran_FLAGS "${VECTOR_ALIASING_Fortran_FLAGS} -alias=ansi") - set(VECTOR_OPENMP_SIMD_Fortran_FLAGS "${VECTOR_OPENMP_SIMD_Fortran_FLAGS} -Mvect=simd") - if ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - if ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER "18.6") - execute_process(COMMAND pgfortran --version COMMAND grep LLVM COMMAND wc -l OUTPUT_VARIABLE PGI_VERSION_OUTPUT OUTPUT_STRIP_TRAILING_WHITESPACE) - if ("${PGI_VERSION_OUTPUT}" STREQUAL "1") - set(VECTOR_ARCH_Fortran_FLAGS "${VECTOR_ARCH_Fortran_FLAGS} -Mllvm") - endif ("${PGI_VERSION_OUTPUT}" STREQUAL "1") - endif ("${CMAKE_Fortran_COMPILER_VERSION}" VERSION_GREATER "18.6") - endif ("${CMAKE_SYSTEM_PROCESSOR}" STREQUAL "x86_64") - - set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT} -Mnovect ") - set(VECTOR_Fortran_VERBOSE "${VECTOR_Fortran_VERBOSE} -Minfo=loop,inline,vect") - - elseif (CMAKE_Fortran_COMPILER_ID MATCHES "MSVC") - set(VECTOR_Fortran_OPTS "${VECTOR_Fortran_OPTS}" " ") - - set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT}" " ") - set(VECTOR_Fortran_VERBOSE "${VECTOR_Fortran_VERBOSE} -Qvec-report:2") - - elseif (CMAKE_Fortran_COMPILER_ID MATCHES "XL") - set(VECTOR_ALIASING_Fortran_FLAGSS "${VECTOR_ALIASING_Fortran_FLAGS} -qalias=restrict") - set(VECTOR_FPMODEL_Fortran_FLAGSS "${VECTOR_FPMODEL_Fortran_FLAGS} -qstrict") - set(VECTOR_ARCH_Fortran_FLAGSS "${VECTOR_ARCH_Fortran_FLAGS} -qhot -qarch=auto -qtune=auto") - - set(CMAKE_VEC_Fortran_FLAGS "${CMAKE_VEC_FLAGS} -qsimd=auto") - set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT} -qsimd=noauto") - # "long vector" optimizations - #set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT} -qhot=novector") - set(VECTOR_Fortran_VERBOSE "${VECTOR_Fortran_VERBOSE} -qreport") - - elseif (CMAKE_Fortran_COMPILER_ID MATCHES "Cray") - set(VECTOR_ALIASING_Fortran_FLAGS "${VECTOR_ALIASING_Fortran_FLAGS} -h restrict=a") - set(VECTOR_Fortran_OPTS "${VECTOR_Fortran_OPTS} -h vector=3") - - set(VECTOR_NOVEC_Fortran_OPT "${VECTOR_NOVEC_Fortran_OPT} -h vector=0") - set(VECTOR_Fortran_VERBOSE "${VECTOR_Fortran_VERBOSE} -h msgs -h negmsgs -h list=a") - - endif() - - CHECK_FORTRAN_COMPILER_FLAG("${VECTOR_OPENMP_SIMD_Fortran_FLAGS}" HAVE_OPENMP_SIMD) - if (HAVE_OPENMP_SIMD) - add_definitions(-D_OPENMP_SIMD) - else (HAVE_OPENMP_SIMD) - unset(VECTOR_OPENMP_SIMD_Fortran_FLAGS) - endif (HAVE_OPENMP_SIMD) - - set(VECTOR_BASE_Fortran_FLAGS "${VECTOR_ALIASING_Fortran_FLAGS} ${VECTOR_ARCH_Fortran_FLAGS} ${VECTOR_FPMODEL_Fortran_FLAGS}") - set(VECTOR_NOVEC_Fortran_FLAGS "${VECTOR_BASE_Fortran_FLAGS} ${VECTOR_NOVEC_Fortran_OPT}") - set(VECTOR_Fortran_FLAGS "${VECTOR_BASE_Fortran_FLAGS} ${VECTOR_Fortran_OPTS} ${VECTOR_Fortran_FPOPTS} ${VECTOR_OPENMP_SIMD_Fortran_FLAGS}") - - mark_as_advanced(VECTOR_Fortran_FLAGS - VECTOR_NOVEC_Fortran_FLAGS - VECTOR_Fortran_VERBOSE - VECTOR_ALIASING_Fortran_FLAGS - VECTOR_ARCH_Fortran_FLAGS - VECTOR_FPMODEL_Fortran_FLAGS - VECTOR_NOVEC_Fortran_OPT - VECTOR_VEC_Fortran_OPTS - VECTOR_VEC_Fortran_FPOPTS) - - message(STATUS "Setting Vector Fortran flags to: ${VECTOR_Fortran_FLAGS}") - message(STATUS "Setting Vector Fortran No-Vector flags to: ${VECTOR_NOVEC_Fortran_FLAGS}") - message(STATUS "Setting Vector Fortran Verbose flags to: ${VECTOR_Fortran_VERBOSE}") - -endif(CMAKE_Fortran_COMPILER_LOADED) diff --git a/elements/cmake/Modules/TargetDistclean.cmake b/elements/cmake/Modules/TargetDistclean.cmake deleted file mode 100644 index d91cfa52..00000000 --- a/elements/cmake/Modules/TargetDistclean.cmake +++ /dev/null @@ -1,65 +0,0 @@ -# add custom target distclean -# cleans and removes cmake generated files etc. -# Jan Woetzel 04/2003 -# - -IF (UNIX) - ADD_CUSTOM_TARGET (distclean @echo cleaning for source distribution) - SET(DISTCLEANED - cmake.depends - cmake.check_depends - CMakeCache.txt - */CMakeCache.txt - cmake.check_cache - *.cmake - *.a - */*.a - Makefile - crux/Makefile - ezcl/Makefile - genmalloc/Makefile - graphics/Makefile - hash/Makefile - l7/Makefile - MallocPlus/Makefile - memstats/Makefile - powerstats/Makefile - mesh/Makefile - mesh/hsfc/Makefile - mesh/kdtree/Makefile - mesh/zorder/Makefile - PowerParser/Makefile - s7/Makefile - timer/Makefile - tests/Makefile - */tests/Makefile - core core.* - gmon.out - *~ - CMakeFiles - */CMakeFiles - */*/CMakeFiles - */CTestTestfile.cmake - */*/CTestTestfile.cmake - */Testing - */*/Testing - Testing - cmake_install.cmake - */cmake_install.cmake - */*/cmake_install.cmake - install_manifest.txt - */install_manifest.txt - *.dSYM - */*.dSYM - */*/*.dSYM - tests/testing - ) - - ADD_CUSTOM_COMMAND( - DEPENDS clean - COMMENT "distribution clean" - COMMAND rm - ARGS -Rf CMakeTmp ${DISTCLEANED} - TARGET distclean - ) -ENDIF(UNIX) diff --git a/elements/cmake_install.cmake b/elements/cmake_install.cmake deleted file mode 100644 index 09866067..00000000 --- a/elements/cmake_install.cmake +++ /dev/null @@ -1,44 +0,0 @@ -# Install script for directory: /home/xirhotopi/Fierro/Elements/elements - -# Set the install prefix -if(NOT DEFINED CMAKE_INSTALL_PREFIX) - set(CMAKE_INSTALL_PREFIX "/usr/local") -endif() -string(REGEX REPLACE "/$" "" CMAKE_INSTALL_PREFIX "${CMAKE_INSTALL_PREFIX}") - -# Set the install configuration name. -if(NOT DEFINED CMAKE_INSTALL_CONFIG_NAME) - if(BUILD_TYPE) - string(REGEX REPLACE "^[^A-Za-z0-9_]+" "" - CMAKE_INSTALL_CONFIG_NAME "${BUILD_TYPE}") - else() - set(CMAKE_INSTALL_CONFIG_NAME "RelWithDebInfo") - endif() - message(STATUS "Install configuration: \"${CMAKE_INSTALL_CONFIG_NAME}\"") -endif() - -# Set the component getting installed. -if(NOT CMAKE_INSTALL_COMPONENT) - if(COMPONENT) - message(STATUS 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zAzc4og}M5D_WWPF9%kd69bo-`BnMpmmI2$}t?Z`&d{ zzfk>yQvQr^`*$x;zpi(+{dz2%Hlcny-;P#vG9|JITIj0sjD3gGi62q+|f$$Ffy zo8PMZDzg=5^3RW`fBVt?yk@`2|KyeKRu%UYp`H`?Q8l^?>iOJ|9v-msoNpE)_-7u`d6d=GUT((_pAJ; zzgtJ)fMj>cwwFbm-*T$Yr{hyN*?G3T8s~@e=;teOK65+I_|FCOl^q&>f(tYQ5Rk$UWWQ){8RRkly#`d8Lx5KQ%`^Cv!E h*QXpi1qGX`^=}X~lKiym=5B?~-w63%pc7~}_#X=o>Pi3r From 292f48a6900debe1852effe484a08a2f3305fafc Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Wed, 14 Sep 2022 17:53:06 -0500 Subject: [PATCH 15/20] Copied Steven's Bernstein stuff to elements-kokkos --- .../include/BernsteinProductBasis.h | 33 ++++ .../include/bernstein_polynomials.h | 22 +++ elements-kokkos/src/BernsteinProductBasis.cpp | 176 ++++++++++++++++++ elements-kokkos/src/bernstein_polynomials.cpp | 50 +++++ 4 files changed, 281 insertions(+) create mode 100644 elements-kokkos/include/BernsteinProductBasis.h create mode 100644 elements-kokkos/include/bernstein_polynomials.h create mode 100644 elements-kokkos/src/BernsteinProductBasis.cpp create mode 100644 elements-kokkos/src/bernstein_polynomials.cpp diff --git a/elements-kokkos/include/BernsteinProductBasis.h b/elements-kokkos/include/BernsteinProductBasis.h new file mode 100644 index 00000000..9c64406d --- /dev/null +++ b/elements-kokkos/include/BernsteinProductBasis.h @@ -0,0 +1,33 @@ +#pragma once + +#include "TensorProductBasis.h" +#include "common.h" + + +template +struct BernsteinProductBasis : public TensorProductBasis { + SizeType N; + SizeType Ne; + + // Work array for intermediate coefficients + NumType *C; + + BernsteinProductBasis(const SizeType); + ~BernsteinProductBasis(); + + // Basis functions and basis function gradients + NumType eval_basis(const SizeType, const NumType *); + void eval_grad_basis(const SizeType, const NumType *, NumType *); + + // Function approximation over element + NumType eval_approx(const NumType *, const NumType *); + void eval_grad_approx(const NumType *, const NumType *, NumType *); + + // Jacobian of spatial mapping + void eval_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); + NumType eval_det_jac(const NumType *, const NumType *, const NumType *, + const NumType *); + void eval_inv_jac(const NumType *, const NumType *, const NumType *, + const NumType *, NumType *); +}; diff --git a/elements-kokkos/include/bernstein_polynomials.h b/elements-kokkos/include/bernstein_polynomials.h new file mode 100644 index 00000000..1f9de1e4 --- /dev/null +++ b/elements-kokkos/include/bernstein_polynomials.h @@ -0,0 +1,22 @@ +#pragma once + +#include "common.h" + +// Bernstein polynomial of order n: +// B(n,v) = (0.5)^n * (C^n_v) * (1-x)^(n-v) * (1+x)^v +// for x \in [-1, 1] + +namespace bernstein{ + // Bernstein polynomials + // n is the order, v is the "index", X \in [-1, 1] + template NumType eval(const int n, const int v, const NumType X); + + template NumType eval_der(const int n, const int v, const NumType X); + + //Bernstein Approximations + template + NumType eval_approx(const SizeType N, const NumType *c, const NumType X); + + template + NumType eval_der_approx(const SizeType N, const NumType *c, const NumType X); +} diff --git a/elements-kokkos/src/BernsteinProductBasis.cpp b/elements-kokkos/src/BernsteinProductBasis.cpp new file mode 100644 index 00000000..15f8effc --- /dev/null +++ b/elements-kokkos/src/BernsteinProductBasis.cpp @@ -0,0 +1,176 @@ +#include "BernsteinProductBasis.h" +#include "bernstein_polynomials.h" + + +template +BernsteinProductBasis::BernsteinProductBasis(const SizeType order) + : Np( order) { + N = Np + 1; + Ne = std::pow(N, Nd); + + rad[0] = N; + rad[1] = N; + rad[2] = N; + + //Allocate memory for intermediate coefficients + C = new NumType[2*N]; +} + +template +BernsteinProductBasis::~BernsteinProductBasis() { } + + +template +NumType BernsteinProductBasis::eval_basis(const SizeType I, + const NumType *X) { + // Decompose index of 3D tensor product basis function into indices of + // Bernstein polynomials + common::base_10_to_mixed_radix(Nd, rad, I, ijk); + + // Evaluate Bernstein polynomials + NumType Bi = bernstein::eval(N, int(ijk[0]), X[0]); + NumType Bj = bernstein::eval(N, int(ijk[1]), X[1]); + NumType Bk = bernstein::eval(N, int(ijk[2]), X[2]); + + return Bi*Bj*Bk; +} + +template +void BernsteinProductBasis::eval_grad_basis(const SizeType I, + const NumType *X, NumType *grad_phi) { + // Decompose index of 3D tensor product basis function into indices of + // Bernstein polynomials + common::base_10_to_mized_radix(Nd, rad, I, ijk); + + // Evaluate Bernstein polynomials + NumType Bi = bernstein::eval(N, int(ijk[0]), X[0]); + NumType Bj = bernstein::eval(N, int(ijk[1]), X[1]); + NumType Bk = bernstein::eval(N, int(ijk[2]), X[2]); + + // Evaluate derivatives of Bernstein polynomials + NumType dBi = bernstein::eval_der(N, int(ijk[0]), X[0]); + NumType dBj = bernstein::eval_der(N, int(ijk[1]), X[1]); + NumType dBk = bernstein::eval_der(N, int(ijk[2]), X[2]); + + // Store partial derivatives in entries of gradient + grad_phi[0] = dBi*Bj*Bk; + grad_phi[1] = Bi*dBj*Bk; + grad_phi[3] = Bi*Bj*dBk; +} + +/* Return evaluation of local function approximation */ +template +NumType BernsteinProductBasis::eval_approx(const NumType *c, + const NumType *X) { + for (int k = 0, k < N; k++) { + for (int j = 0; j < N; j++){ + // Collapse first dimension into coefficients for second dimension + C[j] = bernstein::eval_approx(N, &c[j*N+k*N*N], X[0]); + } + // Collapse second dimension into coefficients for third dimension + C[N+k] = bernstein::eval_approx(N, &C[N], X[2]); + } + // Collapse third dimension into approximation evaluation + return bernstein::eval_approx(N, &C[N], X[2]); +} + +/* + * Evaluate gradient of local function approximation, which is formed by the + * sum of the products of tensor-product Bernstein basis functions and the + * provided coefficients, at specified coordinates. + */ +template +void BernsteinProductBasis::eval_grad_approx(const NumType *c, + const NumType *X, NumType *grad_f) { + for (int l = 0; l < Nd; l++) { + for (int k =0; k < N; k++) { + for (int j =0; j < N; j++) { + //Collapse first dimension into coefficients for second dimension + if (l==0) { + C[j] = bernstein::eval_der_approx(N, &c[j*N+k*N*N], X[0]); + } else { + C[j] = bernstein::eval_approx(N, &c[j*N+k*N*N], X[0]); + } + } + // Collapse second dimension into coefficients for third dimension + if ( l == 1) { + C[N+k] = bernstein::eval_der_approx(N, &C[N], X[2]); + } else { + C[N+k] = bernstein::eval_approx(N, C, X[1]); + } + } + + // Collapse third dimension into approximation evaluation + if ( l ==2 ) { + grad_f[l] = bernstein::eval_der_approx(N, &C[N], X[2]); + } else { + grad_f[l] = bernstein::eval_approx(N, &C[N], X[2]); + } + } +} + + +////////////////* Evaluate the Jacobian of the spatial mapping *//////////////////////// + +/* x, y, z in physical space. X in reference space. J = Jacobian (column major). */ + +template +void BernsteinProductBasis::eval_jac(const NumType *x, + const NumType *y, const NumType *z, const NumType *X, NumType *J) { + // Evaluate gradient of x=x(X,Y,Z); + this->eval_grad_approx(x,X,J); + + // Evaluate gradient of y=y(X,Y,Z); + this->eval_grad_approx(y,X,J+3); + + // Evaluate gradient of z=z(X,Y,Z); + this->eval_grad_approx(z,X,J+6); +} + + +//////////////* Determinant of Jacobian *///////////////////////// + +/* x, y, z in physical space. X in reference space. */ + +template +NumType BernsteinProductBasis::eval_det_jac(const NumType *x, + const NumType *y, const NumType *z, const NumType *X) { + NumType J[9]; + this->eval_jac(x, y, z, X, J); + + return J[0]*(J[4]*J[8]-J[5]*J[7]) - J[1]*(J[3]*J[8]-J[5]*J[6]) + J[2]*(J[3]*J[7]-J[4]*J[6]); +} + + +//////////////* Inverse Jacobian *////////////////////////////// + +/* x, y, z in physical space. X in reference space. Jinv = Invers Jacobian (column-major). */ + +template +void BernsteinProductBasis::eval_inv_jac(const NumType *x, + const Numtype *y, const NumType *z, const NumType *X, NumType *Jinv) { + // instantiate jacobian // + NumType J[9]; + + // get jacobian // + this->eval_jac(x,y,z,X,J); + + // invert determinant of J // + NumType d = 1.0/(this->eval_det_jac(x,y,z,X)); + + // get Jinv (Jinv = adj(J)/det(J) ) // + Jinv[0] = d*(J[4]*J[8]-J[5]*J[7]); + Jinv[1] = -d*(J[1]*J[8]-J[2]*J[7]); + Jinv[2] = d*(J[1]*J[5]-J[2]*J[4]); + Jinv[3] = -d*(J[3]*J[8]-J[5]*J[6]); + Jinv[4] = d*(J[0]*J[8]-J[2]*J[6]); + Jinv[5] = -d*(J[0]*J[5]-J[2]*J[3]); + Jinv[6] = d*(J[3]*J[7]-J[4]*J[6]); + Jinv[7] = -d*(J[0]*J[7]-J[1]*J[6]); + Jinv[8] = d*(J[0]*J[4]-J[1]*J[3]); +} + + +//////////////// Explicit instantiation of template class ////////////////////// +template class BernsteinProductBasis; +template class BernsteinProductBasis; diff --git a/elements-kokkos/src/bernstein_polynomials.cpp b/elements-kokkos/src/bernstein_polynomials.cpp new file mode 100644 index 00000000..0db1c057 --- /dev/null +++ b/elements-kokkos/src/bernstein_polynomials.cpp @@ -0,0 +1,50 @@ +#include "bernstein_polynomials.h" + + +namespace bernstein { + template + NumType eval( const int n, const int v, const NumType X) { + if ( n == 0 && v != 0 ) return 0; + if ( n == 0 && v == 0 ) return 1; + if ( n < v ) return 0; + return 0.5*((1-double(X))*eval(n-1, v, X) + (1+double(X))*eval(n-1, v-1, X)); + }; + template + NumType eval_der( const int n, const int v, const NumType X) { + if ( n == 0) return 0; + if ( n < v) return 0; + if ( n == 1 && v == 0) return -0.5; + if ( n == 1 && v == 1) return 0.5; + return 0.5*( (1-double(X))*eval_der(n-1,v, X) + (1+double(X))*eval_der(n-1, v-1, X) + eval(n-1, v-1, X) - eval(n-1, v, X) ) ; + }; + + template + NumType eval_approx(const SizeType N, const NumType *c, const NumType X) { + NumType sum = 0.0; + for (SizeType j = 0; j < N; j++) { + sum += c[j]*eval(N, j, X); + } + return sum; + } + + template + NumType eval_der_approx(const SizeType N, const NumType *c, const NumType X) { + NumType sum = 0.0; + for (SizeType j = 0; j < N; j ++) { + sum += c[j]*eval_der( N, j, X); + } + return sum; + }; + + template Real eval(const int n, const int v, const Real X); + + + template Real eval_der(const int n, const int v, const Real X); + + + template Real eval_approx(const SizeType N, const Real *c, const Real X); + + + template Real eval_der_approx(const SizeType N, const Real *c, const Real X); + +} From 6fa564fa2b86b0bd2643c4d6aebb8557b86af595 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Thu, 15 Sep 2022 16:16:43 -0500 Subject: [PATCH 16/20] Finished implementation of HexRef - Added missing functionality for computing and storing basis function evaluations to HexRef - Fixed a few minor bugs in Bernstein implementation - Added example demonstrating initialization of HexRef and printing out data stored in HexRef In this first implementation, HexRef uses run-time polymorphism to switch between Lagrange, Legendre, and Bernstein tensor product basis evaluations. Dr. Collins suggested that the desired functionality might be better implemented by templating over the basis function type and using compile-time polymorphism. --- build_scripts/build_matar_kokkos_openmp.sh | 3 +- .../include/BernsteinProductBasis.h | 7 +- elements-kokkos/include/HexRef.h | 32 +- .../include/LagrangeProductBasis.h | 7 +- .../include/LegendreProductBasis.h | 7 +- elements-kokkos/include/MatarTypeDefs.h | 11 + elements-kokkos/include/TensorProductBasis.h | 6 + elements-kokkos/include/points_and_weights.h | 9 +- elements-kokkos/src/BernsteinProductBasis.cpp | 8 +- elements-kokkos/src/CMakeLists.txt | 23 +- elements-kokkos/src/HexRef.cpp | 175 +++++--- elements-kokkos/src/LagrangeProductBasis.cpp | 3 +- elements-kokkos/src/LegendreProductBasis.cpp | 2 +- elements-kokkos/src/TensorProductBasis.cpp | 24 +- elements-kokkos/src/bernstein_polynomials.cpp | 17 +- elements-kokkos/src/points_and_weights.cpp | 393 +++++++++--------- elements/bernstein_element.cpp | 6 +- examples/CMakeLists.txt | 5 + examples/hexref/CMakeLists.txt | 10 + examples/hexref/hexref.cpp | 30 ++ examples/vtk/CMakeLists.txt | 4 +- 21 files changed, 459 insertions(+), 323 deletions(-) create mode 100644 elements-kokkos/include/MatarTypeDefs.h create mode 100644 examples/hexref/CMakeLists.txt create mode 100644 examples/hexref/hexref.cpp diff --git a/build_scripts/build_matar_kokkos_openmp.sh b/build_scripts/build_matar_kokkos_openmp.sh index 1e672209..c097d6e5 100755 --- a/build_scripts/build_matar_kokkos_openmp.sh +++ b/build_scripts/build_matar_kokkos_openmp.sh @@ -4,7 +4,8 @@ ELEMENTS_DIR=/path/to/elements MATAR_DIR=/path/to/matar/within/elements PROJECT_BUILD_DIR=/path/to/project/build/directory -OMP_NUM_THREADS=sensible_number_of_openmp_threads_for_your_machine +export OMP_NUM_THREADS=sensible_number_of_openmp_threads_for_your_machine +export OMP_PROC_BIND=spread # Build and install Kokkos with OpenMP diff --git a/elements-kokkos/include/BernsteinProductBasis.h b/elements-kokkos/include/BernsteinProductBasis.h index 9c64406d..5d6f1f4b 100644 --- a/elements-kokkos/include/BernsteinProductBasis.h +++ b/elements-kokkos/include/BernsteinProductBasis.h @@ -1,11 +1,14 @@ #pragma once + #include "TensorProductBasis.h" -#include "common.h" template -struct BernsteinProductBasis : public TensorProductBasis { +struct BernsteinProductBasis : TensorProductBasis { + using TensorProductBasis::Nd, TensorProductBasis::Np, + TensorProductBasis::ijk, TensorProductBasis::rad; + SizeType N; SizeType Ne; diff --git a/elements-kokkos/include/HexRef.h b/elements-kokkos/include/HexRef.h index 34ff495e..2d2a4d01 100644 --- a/elements-kokkos/include/HexRef.h +++ b/elements-kokkos/include/HexRef.h @@ -2,29 +2,21 @@ // MATAR includes -#include "matar.h" - - -// Switch between MATAR Kokkos/non-Kokkos data structures, depending on -// availability of Kokkos -#ifdef MATAR_WITH_KOKKOS -typedef CArrayKokkos MatarRealCArray; -typedef CArrayKokkos MatarUIntCArray; -typedef CArrayKokkos MatarIntCArray; -#else -typedef CArray MatarRealCArray; -typedef CArray MatarUIntCArray; -typedef CArray MatarIntCArray; -#endif // MATAR_WITH_KOKKOS +#include "MatarTypeDefs.h" enum BasisType { - LAGRANGE, - LEGENDRE, - BEZIER + LAGRANGE, + LEGENDRE, + BERNSTEIN }; +// Forward declarations +template +struct TensorProductBasis; + + struct HexRef { HexRef(int order_basis, BasisType type_basis); ~HexRef(); @@ -32,6 +24,8 @@ struct HexRef { // Cells (subelements used in volume integration) int num_ref_cells_1D_; + + int num_ref_cells_in_elem_; int num_ref_cells_in_elem() const; int cell_rid(int i, int j, int k) const; @@ -78,6 +72,7 @@ struct HexRef { // Nodes (quadrature points) and vertices (degrees of freedom) + int num_ref_nodes_1D_; int num_ref_nodes_in_elem_; int num_ref_nodes() const; @@ -104,4 +99,7 @@ struct HexRef { MatarRealCArray ref_patch_gradient_; real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; + + real_t *ref_verts_1D_; + TensorProductBasis *basis; }; diff --git a/elements-kokkos/include/LagrangeProductBasis.h b/elements-kokkos/include/LagrangeProductBasis.h index 738bcee7..13fc80b6 100644 --- a/elements-kokkos/include/LagrangeProductBasis.h +++ b/elements-kokkos/include/LagrangeProductBasis.h @@ -1,11 +1,14 @@ #pragma once + #include "TensorProductBasis.h" -#include "common.h" template -struct LagrangeProductBasis : public TensorProductBasis { +struct LagrangeProductBasis : TensorProductBasis { + using TensorProductBasis::Nd, TensorProductBasis::Np, + TensorProductBasis::ijk, TensorProductBasis::rad; + SizeType N; SizeType Ne; const NumType *Z; diff --git a/elements-kokkos/include/LegendreProductBasis.h b/elements-kokkos/include/LegendreProductBasis.h index 7f376ba6..f9bf369c 100644 --- a/elements-kokkos/include/LegendreProductBasis.h +++ b/elements-kokkos/include/LegendreProductBasis.h @@ -1,11 +1,14 @@ #pragma once + #include "TensorProductBasis.h" -#include "common.h" template -struct LegendreProductBasis : public TensorProductBasis { +struct LegendreProductBasis : TensorProductBasis { + using TensorProductBasis::Nd, TensorProductBasis::Np, + TensorProductBasis::ijk, TensorProductBasis::rad; + SizeType N; SizeType Ne; diff --git a/elements-kokkos/include/MatarTypeDefs.h b/elements-kokkos/include/MatarTypeDefs.h new file mode 100644 index 00000000..8a1ddf58 --- /dev/null +++ b/elements-kokkos/include/MatarTypeDefs.h @@ -0,0 +1,11 @@ +#include "matar.h" + +#ifdef MATAR_WITH_KOKKOS +typedef CArrayKokkos MatarRealCArray; +typedef CArrayKokkos MatarUIntCArray; +typedef CArrayKokkos MatarIntCArray; +#else +typedef CArray MatarRealCArray; +typedef CArray MatarUIntCArray; +typedef CArray MatarIntCArray; +#endif // MATAR_WITH_KOKKOS diff --git a/elements-kokkos/include/TensorProductBasis.h b/elements-kokkos/include/TensorProductBasis.h index b5833e22..4d1b1f51 100644 --- a/elements-kokkos/include/TensorProductBasis.h +++ b/elements-kokkos/include/TensorProductBasis.h @@ -1,6 +1,9 @@ #pragma once +#include "common.h" + + /* * Interface class for 3D tensor product basis, to be called for evaluating: * - basis functions and their gradients; @@ -17,6 +20,9 @@ struct TensorProductBasis { SizeType ijk[Nd]; SizeType rad[Nd]; + TensorProductBasis(const SizeType); + ~TensorProductBasis() {}; + // Basis functions and basis function gradients virtual NumType eval_basis(const SizeType, const NumType *) = 0; virtual void eval_grad_basis(const SizeType, const NumType *, NumType *) = 0; diff --git a/elements-kokkos/include/points_and_weights.h b/elements-kokkos/include/points_and_weights.h index e24d3f87..eade491c 100644 --- a/elements-kokkos/include/points_and_weights.h +++ b/elements-kokkos/include/points_and_weights.h @@ -1,6 +1,7 @@ #pragma once +#include "MatarTypeDefs.h" #include "common.h" @@ -13,8 +14,8 @@ void chebyshev_points(SizeType N, NumType &zl, NumType &zr, NumType *z); /* Hard-coded Gauss-Lobatto and Gauss-Legendre quadrature points and weights */ -void lobatto_nodes_1D(MatarRealCArray &lob_nodes_1D, const int &num); -void lobatto_weights_1D(MatarRealCArray &lob_weights_1D, const int &num); +void lobatto_points(MatarRealCArray &lob_nodes_1D, const int &num); +void lobatto_weights(MatarRealCArray &lob_weights_1D, const int &num); -void legendre_nodes_1D(CArray &leg_nodes_1D, const int &num); -void legendre_weights_1D(CArray &leg_weights_1D, const int &num); +void legendre_points(MatarRealCArray &leg_nodes_1D, const int &num); +void legendre_weights(MatarRealCArray &leg_weights_1D, const int &num); diff --git a/elements-kokkos/src/BernsteinProductBasis.cpp b/elements-kokkos/src/BernsteinProductBasis.cpp index 15f8effc..98a97a5c 100644 --- a/elements-kokkos/src/BernsteinProductBasis.cpp +++ b/elements-kokkos/src/BernsteinProductBasis.cpp @@ -4,7 +4,7 @@ template BernsteinProductBasis::BernsteinProductBasis(const SizeType order) - : Np( order) { + : TensorProductBasis(order) { N = Np + 1; Ne = std::pow(N, Nd); @@ -40,7 +40,7 @@ void BernsteinProductBasis::eval_grad_basis(const SizeType I, const NumType *X, NumType *grad_phi) { // Decompose index of 3D tensor product basis function into indices of // Bernstein polynomials - common::base_10_to_mized_radix(Nd, rad, I, ijk); + common::base_10_to_mixed_radix(Nd, rad, I, ijk); // Evaluate Bernstein polynomials NumType Bi = bernstein::eval(N, int(ijk[0]), X[0]); @@ -62,7 +62,7 @@ void BernsteinProductBasis::eval_grad_basis(const SizeType I, template NumType BernsteinProductBasis::eval_approx(const NumType *c, const NumType *X) { - for (int k = 0, k < N; k++) { + for (int k = 0; k < N; k++) { for (int j = 0; j < N; j++){ // Collapse first dimension into coefficients for second dimension C[j] = bernstein::eval_approx(N, &c[j*N+k*N*N], X[0]); @@ -148,7 +148,7 @@ NumType BernsteinProductBasis::eval_det_jac(const NumType *x, template void BernsteinProductBasis::eval_inv_jac(const NumType *x, - const Numtype *y, const NumType *z, const NumType *X, NumType *Jinv) { + const NumType *y, const NumType *z, const NumType *X, NumType *Jinv) { // instantiate jacobian // NumType J[9]; diff --git a/elements-kokkos/src/CMakeLists.txt b/elements-kokkos/src/CMakeLists.txt index 86e6dd58..ff6a3771 100644 --- a/elements-kokkos/src/CMakeLists.txt +++ b/elements-kokkos/src/CMakeLists.txt @@ -1,6 +1,15 @@ add_library( elements_kokkos HexRef.cpp + LagrangeProductBasis.cpp + LegendreProductBasis.cpp + BernsteinProductBasis.cpp + TensorProductBasis.cpp + lagrange_polynomials.cpp + legendre_polynomials.cpp + jacobi_polynomials.cpp + bernstein_polynomials.cpp + points_and_weights.cpp ) target_compile_definitions( @@ -19,13 +28,13 @@ target_include_directories( if (CUDA) - target_compile_definitions(elements PUBLIC -DHAVE_CUDA=1) -elseif (HIP) - target_compile_definitions(elements PUBLIC -DHAVE_HIP=1) -elseif (OPENMP) - target_compile_definitions(elements PUBLIC -DHAVE_OPENMP=1) -elseif (THREADS) - target_compile_definitions(elements PUBLIC -DHAVE_THREADS=1) + target_compile_definitions(elements_kokkos PUBLIC -DHAVE_CUDA=1) +elseif (HIP) + target_compile_definitions(elements_kokkos PUBLIC -DHAVE_HIP=1) +elseif (OPENMP) + target_compile_definitions(elements_kokkos PUBLIC -DHAVE_OPENMP=1) +elseif (THREADS) + target_compile_definitions(elements_kokkos PUBLIC -DHAVE_THREADS=1) else() message(FATAL_ERROR "Please specify whether you are using CUDA, HIP, OPENMP, etc.") endif() diff --git a/elements-kokkos/src/HexRef.cpp b/elements-kokkos/src/HexRef.cpp index db6bebcd..a71cbd38 100644 --- a/elements-kokkos/src/HexRef.cpp +++ b/elements-kokkos/src/HexRef.cpp @@ -1,4 +1,9 @@ #include "HexRef.h" +#include "LagrangeProductBasis.h" +#include "LegendreProductBasis.h" +#include "BernsteinProductBasis.h" +#include "points_and_weights.h" +#include "error.h" HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { @@ -20,8 +25,8 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { *(num_ref_cells_1D_*num_ref_cells_1D_)*3; num_sides_in_elem_ = num_ref_cells_in_elem_*6; - num_ref_verts_in_elem_ = num_ref_verts_1d_*num_ref_verts_1d_ - *num_ref_verts_1d_; + num_ref_verts_in_elem_ = num_ref_verts_1D_*num_ref_verts_1D_ + *num_ref_verts_1D_; num_basis_ = num_ref_verts_in_elem_; @@ -33,12 +38,14 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { ref_patch_positions_ = MatarRealCArray(num_patches_in_elem_, 3); ref_patch_g_weights_ = MatarRealCArray(num_patches_in_elem_); - ref_cell_basis_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); + ref_cell_basis_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_); ref_cell_gradient_ = MatarRealCArray(num_ref_cells_in_elem_, num_basis_, num_dim_); - ref_patch_basis_ = MatarRealCArray(num_patches_in_elem_, num_ref_verts_in_elem_); + ref_patch_basis_ = MatarRealCArray(num_patches_in_elem_, num_basis_); ref_patch_gradient_ = MatarRealCArray(num_patches_in_elem_, num_basis_, num_dim_); + ref_verts_1D_ = new real_t[num_ref_verts_1D_]; + // Retrieve Gauss-Legendre and Gauss-Lobatto quadrature points and weights auto leg_points_1D = MatarRealCArray(num_ref_cells_1D_); @@ -54,6 +61,15 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { lobatto_weights(lob_weights_1D, num_ref_nodes_1D_); + // Store every other node (quadrature point) coordinate as a vertex coordinate + int vert_id = 0, node_id = 0; + while (node_id < num_ref_nodes_1D_) { + ref_verts_1D_[vert_id] = lob_points_1D(node_id); + vert_id += 1; + node_id += 2; + } + + // Fill in cell data structures for (int k = 0; k < num_ref_cells_1D_; k++) { for (int j = 0; j < num_ref_cells_1D_; j++) { @@ -138,6 +154,7 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { // Get the rID for the neighboring cell in the element // that communicates with this cell across this patch + int neighbor_cell_rid; if (side_lid == 0 && 0 < i) { neighbor_cell_rid = cell_rid(i-1, j, k); } else if (side_lid == 1 && i < num_ref_cells_1D_ - 1) { @@ -175,83 +192,82 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { } + // Initialize basis object based on type specified + switch (type_basis) { + case BasisType::LAGRANGE: + basis = new LagrangeProductBasis(order_basis, ref_verts_1D_); + break; + case BasisType::LEGENDRE: + basis = new LegendreProductBasis(order_basis); + break; + case BasisType::BERNSTEIN: + basis = new BernsteinProductBasis(order_basis); + break; + default: + basis = nullptr; + std::string err_msg("Error: basis class not implemented for this type."); + throw NotImplementedError(err_msg); + } + + // Fill in evaluations of basis functions and their gradients in cells for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++) { - auto point = MatarRealCArray(3); + // Get the cell coordinates + real_t point[num_dim_]; + for (int dim = 0; dim < num_dim_; dim++) + point[dim] = ref_cell_positions(cell_rlid, dim); - // Get the patch coordinates - for (int dim = 0; dim < 3; dim++){ - point(dim) = ref_cell_positions(cell_rlid, dim); - } - - // the basis function values at the patch for each vertex - auto cell_basis = MatarRealCArray(num_ref_verts_in_elem_); + // Compute and store all the basis values at the cell + for (int basis_id = 0; basis_id < num_basis_; basis_id++) + ref_cell_basis_(cell_rlid, basis_id) = basis->eval_basis(basis_id, point); - // calculate the cell basis function values at the point, for each vertex - elem.basis(cell_basis, point); - - // save the basis values at the patch for each vertex - for (int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++) { - ref_cell_basis_(cell_rlid, vert_rlid) = cell_basis(vert_rlid); - } - - // calculate the partials at the cell location for each vertex - elem.partial_xi_basis(partial_xi, point); - elem.partial_eta_basis(partial_eta, point); - elem.partial_mu_basis(partial_mu, point); - - // loop over the basis polynomials where there is one from each vertex - for(int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++) { - ref_cell_gradient_(cell_rlid, basis_id, 0) = partial_xi(basis_id); - ref_cell_gradient_(cell_rlid, basis_id, 1) = partial_eta(basis_id); - ref_cell_gradient_(cell_rlid, basis_id, 2) = partial_mu(basis_id); - - partial_xi(basis_id) = 0.0; - partial_eta(basis_id) = 0.0; - partial_mu(basis_id) = 0.0; + // Compute and store all the basis gradient values at the cell + for (int basis_id = 0; basis_id < num_basis_; basis_id++) { + real_t grad_basis[num_dim_]; + basis->eval_grad_basis(basis_id, point, grad_basis); + ref_cell_gradient_(cell_rlid, basis_id, 0) = grad_basis[0]; + ref_cell_gradient_(cell_rlid, basis_id, 1) = grad_basis[1]; + ref_cell_gradient_(cell_rlid, basis_id, 2) = grad_basis[2]; } } // Fill in evaluations of basis functions and their gradients on patches for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++) { - auto point = MatarRealCArray(3); - + // Get the cell coordinates // Get the patch coordinates - for(int dim = 0; dim < 3; dim++){ - point(dim) = ref_patch_positions(patch_rlid, dim); - } - - // the basis function values at the patch for each vertex - auto patch_basis = MatarRealCArray(num_ref_verts_in_elem_); - - // calculate the patch basis function values at the point, for each vertex - elem.basis(patch_basis, point); + real_t point[num_dim_]; + for (int dim = 0; dim < num_dim_; dim++) + point[dim] = ref_patch_positions(patch_rlid, dim); - // save the basis values at the patch for each vertex - for (int vert_rlid = 0; vert_rlid < num_ref_verts_in_elem_; vert_rlid++) { - ref_patch_basis_(patch_rlid, vert_rlid) = patch_basis(vert_rlid); - } - - // calculate the partials at the patch location for each vertex - elem.partial_xi_basis(partial_xi, point); - elem.partial_eta_basis(partial_eta, point); - elem.partial_mu_basis(partial_mu, point); + // Compute and store all the basis values at the patch + for (int basis_id = 0; basis_id < num_basis_; basis_id++) + ref_patch_basis_(patch_rlid, basis_id) = basis->eval_basis(basis_id, + point); // loop over the basis polynomials where there is one from each vertex - for (int basis_id = 0; basis_id < num_ref_verts_in_elem_; basis_id++) { - ref_patch_gradient_(patch_rlid, basis_id, 0) = partial_xi(basis_id); - ref_patch_gradient_(patch_rlid, basis_id, 1) = partial_eta(basis_id); - ref_patch_gradient_(patch_rlid, basis_id, 2) = partial_mu(basis_id); - - partial_xi(basis_id) = 0.0; - partial_eta(basis_id) = 0.0; - partial_mu(basis_id) = 0.0; + for (int basis_id = 0; basis_id < num_basis_; basis_id++) { + real_t grad_basis[num_dim_]; + basis->eval_grad_basis(basis_id, point, grad_basis); + ref_patch_gradient_(patch_rlid, basis_id, 0) = grad_basis[0]; + ref_patch_gradient_(patch_rlid, basis_id, 1) = grad_basis[1]; + ref_patch_gradient_(patch_rlid, basis_id, 2) = grad_basis[2]; } } } +HexRef::~HexRef() { + delete[] ref_verts_1D_; + delete basis; +} + + +int HexRef::num_ref_cells_in_elem() const { + return num_ref_cells_in_elem_; +}; + + int HexRef::cell_rid(int i, int j, int k) const { return i + j*num_ref_cells_1D_ + k*num_ref_cells_1D_*num_ref_cells_1D_; }; @@ -267,19 +283,24 @@ real_t HexRef::ref_cell_g_weights(int cell_rid) const { } +int HexRef::patch_rlid_in_cell_neighbor(int patch_rlid) const { + return patch_rlid_cell_neighbor_[patch_rlid]; +} + + int HexRef::ref_patches_in_cell(int cell_rid, int patch_rlid) const { int index = patch_rlid + cell_rid*6; return ref_patches_in_cell_list_(index); } -real_t HexRef::ref_patch_g_weights(int patch_rid) const { - return ref_patch_g_weights_(patch_rid); +real_t HexRef::ref_patch_positions(int patch_rid, int dim) const { + return ref_patch_positions_(patch_rid, dim); } -int HexRef::patch_rlid_in_cell_neighbor(int patch_rlid) const { - return patch_rlid_cell_neighbor_[patch_rlid]; +real_t HexRef::ref_patch_g_weights(int patch_rid) const { + return ref_patch_g_weights_(patch_rid); } @@ -302,3 +323,25 @@ int HexRef::num_dim() const { int HexRef::num_basis() const { return num_basis_; } + + +real_t HexRef::ref_cell_basis(int cell_rid, int basis_id) const { + return ref_cell_basis_(cell_rid, basis_id); +}; + + +real_t HexRef::ref_cell_gradient(int cell_rid, int basis_id, + int dim) const { + return ref_cell_gradient_(cell_rid, basis_id, dim); +}; + + +real_t HexRef::ref_patch_basis(int patch_rid, int basis_id) const { + return ref_patch_basis_(patch_rid, basis_id); +}; + + +real_t HexRef::ref_patch_gradient(int patch_rid, int basis_id, + int dim) const { + return ref_patch_gradient_(patch_rid, basis_id, dim); +}; diff --git a/elements-kokkos/src/LagrangeProductBasis.cpp b/elements-kokkos/src/LagrangeProductBasis.cpp index 5fb2221c..963c4a61 100644 --- a/elements-kokkos/src/LagrangeProductBasis.cpp +++ b/elements-kokkos/src/LagrangeProductBasis.cpp @@ -4,7 +4,8 @@ template LagrangeProductBasis::LagrangeProductBasis(const SizeType order, - const NumType *vert_coords) : Np(order), Z(vert_coords) { + const NumType *vert_coords) : TensorProductBasis(order), + Z(vert_coords) { N = Np + 1; Ne = std::pow(N, Nd); diff --git a/elements-kokkos/src/LegendreProductBasis.cpp b/elements-kokkos/src/LegendreProductBasis.cpp index 5c23419a..72de37f1 100644 --- a/elements-kokkos/src/LegendreProductBasis.cpp +++ b/elements-kokkos/src/LegendreProductBasis.cpp @@ -4,7 +4,7 @@ template LegendreProductBasis::LegendreProductBasis(const SizeType order) - : Np(order) { + : TensorProductBasis(order) { N = Np + 1; Ne = std::pow(N, Nd); diff --git a/elements-kokkos/src/TensorProductBasis.cpp b/elements-kokkos/src/TensorProductBasis.cpp index 70b5f024..272cce2a 100644 --- a/elements-kokkos/src/TensorProductBasis.cpp +++ b/elements-kokkos/src/TensorProductBasis.cpp @@ -3,28 +3,34 @@ #include "error.h" -void TensorProductBasis::eval_jac(const NumType *, const NumType *, +template +TensorProductBasis::TensorProductBasis(const SizeType order) : Np(order) {} + +template +void TensorProductBasis::eval_jac(const NumType *, const NumType *, const NumType *, const NumType *, NumType *) { std::string err_msg( - "Error: Jacobian routines not implemented for this basis type.") + "Error: Jacobian routines not implemented for this basis type."); throw NotImplementedError(err_msg); }; -NumType TensorProductBasis::eval_det_jac(const NumType *, const NumType *, - const NumType *, const NumType *) { +template +NumType TensorProductBasis::eval_det_jac(const NumType *, + const NumType *, const NumType *, const NumType *) { std::string err_msg( - "Error: Jacobian routines not implemented for this basis type.") + "Error: Jacobian routines not implemented for this basis type."); throw NotImplementedError(err_msg); return 0.0; } -void TensorProductBasis::eval_inv_jac(const NumType *, const NumType *, - const NumType *, const NumType *, NumType *) { +template +void TensorProductBasis::eval_inv_jac(const NumType *, + const NumType *, const NumType *, const NumType *, NumType *) { std::string err_msg( - "Error: Jacobian routines not implemented for this basis type.") + "Error: Jacobian routines not implemented for this basis type."); throw NotImplementedError(err_msg); } // Explicit instantiation of template class template class TensorProductBasis; -template class LegendreProductBasis; +template class TensorProductBasis; diff --git a/elements-kokkos/src/bernstein_polynomials.cpp b/elements-kokkos/src/bernstein_polynomials.cpp index 0db1c057..4df9858f 100644 --- a/elements-kokkos/src/bernstein_polynomials.cpp +++ b/elements-kokkos/src/bernstein_polynomials.cpp @@ -7,7 +7,7 @@ namespace bernstein { if ( n == 0 && v != 0 ) return 0; if ( n == 0 && v == 0 ) return 1; if ( n < v ) return 0; - return 0.5*((1-double(X))*eval(n-1, v, X) + (1+double(X))*eval(n-1, v-1, X)); + return 0.5*((1.0 - X)*eval(n-1, v, X) + (1.0 + X)*eval(n-1, v-1, X)); }; template NumType eval_der( const int n, const int v, const NumType X) { @@ -15,7 +15,8 @@ namespace bernstein { if ( n < v) return 0; if ( n == 1 && v == 0) return -0.5; if ( n == 1 && v == 1) return 0.5; - return 0.5*( (1-double(X))*eval_der(n-1,v, X) + (1+double(X))*eval_der(n-1, v-1, X) + eval(n-1, v-1, X) - eval(n-1, v, X) ) ; + return 0.5*((1.0 - X)*eval_der(n-1,v, X) + (1.0 + X)*eval_der(n-1, v-1, X) + + eval(n-1, v-1, X) - eval(n-1, v, X)); }; template @@ -36,15 +37,19 @@ namespace bernstein { return sum; }; + + // Explicit instantiations of template functions template Real eval(const int n, const int v, const Real X); - + template Complex eval(const int n, const int v, const Complex X); template Real eval_der(const int n, const int v, const Real X); + template Complex eval_der(const int n, const int v, const Complex X); - template Real eval_approx(const SizeType N, const Real *c, const Real X); + template Complex eval_approx(const SizeType N, const Complex *c, + const Complex X); - template Real eval_der_approx(const SizeType N, const Real *c, const Real X); - + template Complex eval_der_approx(const SizeType N, const Complex *c, + const Complex X); } diff --git a/elements-kokkos/src/points_and_weights.cpp b/elements-kokkos/src/points_and_weights.cpp index 2130ed42..aa625bcd 100644 --- a/elements-kokkos/src/points_and_weights.cpp +++ b/elements-kokkos/src/points_and_weights.cpp @@ -1,4 +1,5 @@ #include "points_and_weights.h" +#include "error.h" /* @@ -327,7 +328,7 @@ void lobatto_points(MatarRealCArray &lob_points, const int &num) { default: std::ostringstream ss; ss << "Error: " << num << "-point quadrature rule not implemented."; - throw NotImplemented(ss.str()); + throw NotImplementedError(ss.str()); } } @@ -598,7 +599,7 @@ void lobatto_weights(MatarRealCArray &lob_weights, const int &num) { default: std::ostringstream ss; ss << "Error: " << num << "-point quadrature rule not implemented."; - throw NotImplemented(ss.str()); + throw NotImplementedError(ss.str()); } } @@ -615,7 +616,7 @@ void lobatto_weights(MatarRealCArray &lob_weights, const int &num) { * ------- * leg_points : MATAR CArray to fill with points */ -void legendre_points(CArray &leg_points, const int &num) { +void legendre_points(MatarRealCArray &leg_points, const int &num) { switch (num) { case 1: leg_points(0) = 0.0; @@ -848,7 +849,7 @@ void legendre_points(CArray &leg_points, const int &num) { default: std::ostringstream ss; ss << "Error: " << num << "-point quadrature rule not implemented."; - throw NotImplemented(ss.str()); + throw NotImplementedError(ss.str()); } } @@ -865,239 +866,239 @@ void legendre_points(CArray &leg_points, const int &num) { * ------- * leg_weights : MATAR CArray to fill with weights */ -void legendre_weights_1D(CArray &leg_weights_1D, const int &num) { +void legendre_weights(MatarRealCArray &leg_weights, const int &num) { switch (num) { case 1: - leg_weights_1D(0) = 2.0; + leg_weights(0) = 2.0; break; case 2: - leg_weights_1D(0) = 1.0; - leg_weights_1D(1) = 1.0; + leg_weights(0) = 1.0; + leg_weights(1) = 1.0; break; case 3: - leg_weights_1D(0) = 0.555555555555555555555555555555555; - leg_weights_1D(1) = 0.888888888888888888888888888888888; - leg_weights_1D(2) = 0.555555555555555555555555555555555; + leg_weights(0) = 0.555555555555555555555555555555555; + leg_weights(1) = 0.888888888888888888888888888888888; + leg_weights(2) = 0.555555555555555555555555555555555; break; case 4: - leg_weights_1D(0) = 0.347854845137453857373063949221999; - leg_weights_1D(1) = 0.652145154862546142626936050778000; - leg_weights_1D(2) = 0.652145154862546142626936050778000; - leg_weights_1D(3) = 0.347854845137453857373063949221999; + leg_weights(0) = 0.347854845137453857373063949221999; + leg_weights(1) = 0.652145154862546142626936050778000; + leg_weights(2) = 0.652145154862546142626936050778000; + leg_weights(3) = 0.347854845137453857373063949221999; break; case 5: - leg_weights_1D(0) = 0.236926885056189087514264040719917; - leg_weights_1D(1) = 0.478628670499366468041291514835638; - leg_weights_1D(2) = 0.568888888888888888888888888888888; - leg_weights_1D(3) = 0.478628670499366468041291514835638; - leg_weights_1D(4) = 0.236926885056189087514264040719917; + leg_weights(0) = 0.236926885056189087514264040719917; + leg_weights(1) = 0.478628670499366468041291514835638; + leg_weights(2) = 0.568888888888888888888888888888888; + leg_weights(3) = 0.478628670499366468041291514835638; + leg_weights(4) = 0.236926885056189087514264040719917; break; case 6: - leg_weights_1D(0) = 0.171324492379170345040296142172732; - leg_weights_1D(1) = 0.360761573048138607569833513837716; - leg_weights_1D(2) = 0.467913934572691047389870343989550; - leg_weights_1D(3) = 0.467913934572691047389870343989550; - leg_weights_1D(4) = 0.360761573048138607569833513837716; - leg_weights_1D(5) = 0.171324492379170345040296142172732; + leg_weights(0) = 0.171324492379170345040296142172732; + leg_weights(1) = 0.360761573048138607569833513837716; + leg_weights(2) = 0.467913934572691047389870343989550; + leg_weights(3) = 0.467913934572691047389870343989550; + leg_weights(4) = 0.360761573048138607569833513837716; + leg_weights(5) = 0.171324492379170345040296142172732; break; case 7: - leg_weights_1D(0) = 0.129484966168869693270611432679082; - leg_weights_1D(1) = 0.279705391489276667901467771423779; - leg_weights_1D(2) = 0.381830050505118944950369775488975; - leg_weights_1D(3) = 0.417959183673469387755102040816326; - leg_weights_1D(4) = 0.381830050505118944950369775488975; - leg_weights_1D(5) = 0.279705391489276667901467771423779; - leg_weights_1D(6) = 0.129484966168869693270611432679082; + leg_weights(0) = 0.129484966168869693270611432679082; + leg_weights(1) = 0.279705391489276667901467771423779; + leg_weights(2) = 0.381830050505118944950369775488975; + leg_weights(3) = 0.417959183673469387755102040816326; + leg_weights(4) = 0.381830050505118944950369775488975; + leg_weights(5) = 0.279705391489276667901467771423779; + leg_weights(6) = 0.129484966168869693270611432679082; break; case 8: - leg_weights_1D(0) = 0.101228536290376259152531354309962; - leg_weights_1D(1) = 0.222381034453374470544355994426240; - leg_weights_1D(2) = 0.313706645877887287337962201986601; - leg_weights_1D(3) = 0.362683783378361982965150449277195; - leg_weights_1D(4) = 0.362683783378361982965150449277195; - leg_weights_1D(5) = 0.313706645877887287337962201986601; - leg_weights_1D(6) = 0.222381034453374470544355994426240; - leg_weights_1D(7) = 0.101228536290376259152531354309962; + leg_weights(0) = 0.101228536290376259152531354309962; + leg_weights(1) = 0.222381034453374470544355994426240; + leg_weights(2) = 0.313706645877887287337962201986601; + leg_weights(3) = 0.362683783378361982965150449277195; + leg_weights(4) = 0.362683783378361982965150449277195; + leg_weights(5) = 0.313706645877887287337962201986601; + leg_weights(6) = 0.222381034453374470544355994426240; + leg_weights(7) = 0.101228536290376259152531354309962; break; case 9: - leg_weights_1D(0) = 0.081274388361574411971892158110523; - leg_weights_1D(1) = 0.180648160694857404058472031242912; - leg_weights_1D(2) = 0.260610696402935462318742869418632; - leg_weights_1D(3) = 0.312347077040002840068630406584443; - leg_weights_1D(4) = 0.330239355001259763164525069286974; - leg_weights_1D(5) = 0.312347077040002840068630406584443; - leg_weights_1D(6) = 0.260610696402935462318742869418632; - leg_weights_1D(7) = 0.180648160694857404058472031242912; - leg_weights_1D(8) = 0.081274388361574411971892158110523; + leg_weights(0) = 0.081274388361574411971892158110523; + leg_weights(1) = 0.180648160694857404058472031242912; + leg_weights(2) = 0.260610696402935462318742869418632; + leg_weights(3) = 0.312347077040002840068630406584443; + leg_weights(4) = 0.330239355001259763164525069286974; + leg_weights(5) = 0.312347077040002840068630406584443; + leg_weights(6) = 0.260610696402935462318742869418632; + leg_weights(7) = 0.180648160694857404058472031242912; + leg_weights(8) = 0.081274388361574411971892158110523; break; case 10: - leg_weights_1D(0) = 0.066671344308688137593568809893331; - leg_weights_1D(1) = 0.149451349150580593145776339657697; - leg_weights_1D(2) = 0.219086362515982043995534934228163; - leg_weights_1D(3) = 0.269266719309996355091226921569469; - leg_weights_1D(4) = 0.295524224714752870173892994651338; - leg_weights_1D(5) = 0.295524224714752870173892994651338; - leg_weights_1D(6) = 0.269266719309996355091226921569469; - leg_weights_1D(7) = 0.219086362515982043995534934228163; - leg_weights_1D(8) = 0.149451349150580593145776339657697; - leg_weights_1D(9) = 0.066671344308688137593568809893331; + leg_weights(0) = 0.066671344308688137593568809893331; + leg_weights(1) = 0.149451349150580593145776339657697; + leg_weights(2) = 0.219086362515982043995534934228163; + leg_weights(3) = 0.269266719309996355091226921569469; + leg_weights(4) = 0.295524224714752870173892994651338; + leg_weights(5) = 0.295524224714752870173892994651338; + leg_weights(6) = 0.269266719309996355091226921569469; + leg_weights(7) = 0.219086362515982043995534934228163; + leg_weights(8) = 0.149451349150580593145776339657697; + leg_weights(9) = 0.066671344308688137593568809893331; break; case 11: - leg_weights_1D(0) = 0.055668567116173666482753720442548; - leg_weights_1D(1) = 0.125580369464904624634694299223940; - leg_weights_1D(2) = 0.186290210927734251426097641431655; - leg_weights_1D(3) = 0.233193764591990479918523704843175; - leg_weights_1D(4) = 0.262804544510246662180688869890509; - leg_weights_1D(5) = 0.272925086777900630714483528336342; - leg_weights_1D(6) = 0.262804544510246662180688869890509; - leg_weights_1D(7) = 0.233193764591990479918523704843175; - leg_weights_1D(8) = 0.186290210927734251426097641431655; - leg_weights_1D(9) = 0.125580369464904624634694299223940; - leg_weights_1D(10)= 0.055668567116173666482753720442548; + leg_weights(0) = 0.055668567116173666482753720442548; + leg_weights(1) = 0.125580369464904624634694299223940; + leg_weights(2) = 0.186290210927734251426097641431655; + leg_weights(3) = 0.233193764591990479918523704843175; + leg_weights(4) = 0.262804544510246662180688869890509; + leg_weights(5) = 0.272925086777900630714483528336342; + leg_weights(6) = 0.262804544510246662180688869890509; + leg_weights(7) = 0.233193764591990479918523704843175; + leg_weights(8) = 0.186290210927734251426097641431655; + leg_weights(9) = 0.125580369464904624634694299223940; + leg_weights(10)= 0.055668567116173666482753720442548; break; case 12: - leg_weights_1D(0) = 0.04717533638651182719461596148501; - leg_weights_1D(1) = 0.10693932599531843096025471819399; - leg_weights_1D(2) = 0.16007832854334622633465252954335; - leg_weights_1D(3) = 0.20316742672306592174906445580979; - leg_weights_1D(4) = 0.23349253653835480876084989892487; - leg_weights_1D(5) = 0.24914704581340278500056243604295; - leg_weights_1D(6) = 0.24914704581340278500056243604295; - leg_weights_1D(7) = 0.23349253653835480876084989892487; - leg_weights_1D(8) = 0.20316742672306592174906445580979; - leg_weights_1D(9) = 0.16007832854334622633465252954335; - leg_weights_1D(10) = 0.10693932599531843096025471819399; - leg_weights_1D(11) = 0.04717533638651182719461596148501; + leg_weights(0) = 0.04717533638651182719461596148501; + leg_weights(1) = 0.10693932599531843096025471819399; + leg_weights(2) = 0.16007832854334622633465252954335; + leg_weights(3) = 0.20316742672306592174906445580979; + leg_weights(4) = 0.23349253653835480876084989892487; + leg_weights(5) = 0.24914704581340278500056243604295; + leg_weights(6) = 0.24914704581340278500056243604295; + leg_weights(7) = 0.23349253653835480876084989892487; + leg_weights(8) = 0.20316742672306592174906445580979; + leg_weights(9) = 0.16007832854334622633465252954335; + leg_weights(10) = 0.10693932599531843096025471819399; + leg_weights(11) = 0.04717533638651182719461596148501; break; case 13: - leg_weights_1D(0) = 0.04048400476531587952002159220098; - leg_weights_1D(1) = 0.09212149983772844791442177595379; - leg_weights_1D(2) = 0.13887351021978723846360177686887; - leg_weights_1D(3) = 0.17814598076194573828004669199609; - leg_weights_1D(4) = 0.20781604753688850231252321930605; - leg_weights_1D(5) = 0.22628318026289723841209018603977; - leg_weights_1D(6) = 0.23255155323087391019458951526883; - leg_weights_1D(7) = 0.22628318026289723841209018603977; - leg_weights_1D(8) = 0.20781604753688850231252321930605; - leg_weights_1D(9) = 0.17814598076194573828004669199609; - leg_weights_1D(10) = 0.13887351021978723846360177686887; - leg_weights_1D(11) = 0.09212149983772844791442177595379; - leg_weights_1D(12) = 0.04048400476531587952002159220098; + leg_weights(0) = 0.04048400476531587952002159220098; + leg_weights(1) = 0.09212149983772844791442177595379; + leg_weights(2) = 0.13887351021978723846360177686887; + leg_weights(3) = 0.17814598076194573828004669199609; + leg_weights(4) = 0.20781604753688850231252321930605; + leg_weights(5) = 0.22628318026289723841209018603977; + leg_weights(6) = 0.23255155323087391019458951526883; + leg_weights(7) = 0.22628318026289723841209018603977; + leg_weights(8) = 0.20781604753688850231252321930605; + leg_weights(9) = 0.17814598076194573828004669199609; + leg_weights(10) = 0.13887351021978723846360177686887; + leg_weights(11) = 0.09212149983772844791442177595379; + leg_weights(12) = 0.04048400476531587952002159220098; break; case 14: - leg_weights_1D(0) = 0.03511946033175186303183287613819; - leg_weights_1D(1) = 0.08015808715976020980563327706285; - leg_weights_1D(2) = 0.12151857068790318468941480907247; - leg_weights_1D(3) = 0.15720316715819353456960193862384; - leg_weights_1D(4) = 0.18553839747793781374171659012515; - leg_weights_1D(5) = 0.20519846372129560396592406566121; - leg_weights_1D(6) = 0.21526385346315779019587644331626; - leg_weights_1D(7) = 0.21526385346315779019587644331626; - leg_weights_1D(8) = 0.20519846372129560396592406566121; - leg_weights_1D(9) = 0.18553839747793781374171659012515; - leg_weights_1D(10) = 0.15720316715819353456960193862384; - leg_weights_1D(11) = 0.12151857068790318468941480907247; - leg_weights_1D(12) = 0.08015808715976020980563327706285; - leg_weights_1D(13) = 0.03511946033175186303183287613819; + leg_weights(0) = 0.03511946033175186303183287613819; + leg_weights(1) = 0.08015808715976020980563327706285; + leg_weights(2) = 0.12151857068790318468941480907247; + leg_weights(3) = 0.15720316715819353456960193862384; + leg_weights(4) = 0.18553839747793781374171659012515; + leg_weights(5) = 0.20519846372129560396592406566121; + leg_weights(6) = 0.21526385346315779019587644331626; + leg_weights(7) = 0.21526385346315779019587644331626; + leg_weights(8) = 0.20519846372129560396592406566121; + leg_weights(9) = 0.18553839747793781374171659012515; + leg_weights(10) = 0.15720316715819353456960193862384; + leg_weights(11) = 0.12151857068790318468941480907247; + leg_weights(12) = 0.08015808715976020980563327706285; + leg_weights(13) = 0.03511946033175186303183287613819; break; case 15: - leg_weights_1D(0) = 0.03075324199611726835462839357720; - leg_weights_1D(1) = 0.07036604748810812470926741645066; - leg_weights_1D(2) = 0.10715922046717193501186954668586; - leg_weights_1D(3) = 0.13957067792615431444780479451102; - leg_weights_1D(4) = 0.16626920581699393355320086048120; - leg_weights_1D(5) = 0.18616100001556221102680056186642; - leg_weights_1D(6) = 0.19843148532711157645611832644383; - leg_weights_1D(7) = 0.20257824192556127288062019996751; - leg_weights_1D(8) = 0.19843148532711157645611832644383; - leg_weights_1D(9) = 0.18616100001556221102680056186642; - leg_weights_1D(10) = 0.16626920581699393355320086048120; - leg_weights_1D(11) = 0.13957067792615431444780479451102; - leg_weights_1D(12) = 0.10715922046717193501186954668586; - leg_weights_1D(13) = 0.07036604748810812470926741645066; - leg_weights_1D(14) = 0.03075324199611726835462839357720; + leg_weights(0) = 0.03075324199611726835462839357720; + leg_weights(1) = 0.07036604748810812470926741645066; + leg_weights(2) = 0.10715922046717193501186954668586; + leg_weights(3) = 0.13957067792615431444780479451102; + leg_weights(4) = 0.16626920581699393355320086048120; + leg_weights(5) = 0.18616100001556221102680056186642; + leg_weights(6) = 0.19843148532711157645611832644383; + leg_weights(7) = 0.20257824192556127288062019996751; + leg_weights(8) = 0.19843148532711157645611832644383; + leg_weights(9) = 0.18616100001556221102680056186642; + leg_weights(10) = 0.16626920581699393355320086048120; + leg_weights(11) = 0.13957067792615431444780479451102; + leg_weights(12) = 0.10715922046717193501186954668586; + leg_weights(13) = 0.07036604748810812470926741645066; + leg_weights(14) = 0.03075324199611726835462839357720; break; case 16: - leg_weights_1D(0) = 0.02715245941175409485178057245601; - leg_weights_1D(1) = 0.06225352393864789286284383699437; - leg_weights_1D(2) = 0.09515851168249278480992510760224; - leg_weights_1D(3) = 0.12462897125553387205247628219201; - leg_weights_1D(4) = 0.14959598881657673208150173054747; - leg_weights_1D(5) = 0.16915651939500253818931207903035; - leg_weights_1D(6) = 0.18260341504492358886676366796921; - leg_weights_1D(7) = 0.18945061045506849628539672320828; - leg_weights_1D(8) = 0.18945061045506849628539672320828; - leg_weights_1D(9) = 0.18260341504492358886676366796921; - leg_weights_1D(10) = 0.16915651939500253818931207903035; - leg_weights_1D(11) = 0.14959598881657673208150173054747; - leg_weights_1D(12) = 0.12462897125553387205247628219201; - leg_weights_1D(13) = 0.09515851168249278480992510760224; - leg_weights_1D(14) = 0.06225352393864789286284383699437; - leg_weights_1D(15) = 0.02715245941175409485178057245601; + leg_weights(0) = 0.02715245941175409485178057245601; + leg_weights(1) = 0.06225352393864789286284383699437; + leg_weights(2) = 0.09515851168249278480992510760224; + leg_weights(3) = 0.12462897125553387205247628219201; + leg_weights(4) = 0.14959598881657673208150173054747; + leg_weights(5) = 0.16915651939500253818931207903035; + leg_weights(6) = 0.18260341504492358886676366796921; + leg_weights(7) = 0.18945061045506849628539672320828; + leg_weights(8) = 0.18945061045506849628539672320828; + leg_weights(9) = 0.18260341504492358886676366796921; + leg_weights(10) = 0.16915651939500253818931207903035; + leg_weights(11) = 0.14959598881657673208150173054747; + leg_weights(12) = 0.12462897125553387205247628219201; + leg_weights(13) = 0.09515851168249278480992510760224; + leg_weights(14) = 0.06225352393864789286284383699437; + leg_weights(15) = 0.02715245941175409485178057245601; break; case 17: - leg_weights_1D(0) = 0.02414830286854793196011002628756; - leg_weights_1D(1) = 0.05545952937398720112944016535824; - leg_weights_1D(2) = 0.08503614831717918088353537019106; - leg_weights_1D(3) = 0.11188384719340397109478838562635; - leg_weights_1D(4) = 0.13513636846852547328631998170235; - leg_weights_1D(5) = 0.15404576107681028808143159480195; - leg_weights_1D(6) = 0.16800410215645004450997066378832; - leg_weights_1D(7) = 0.17656270536699264632527099011319; - leg_weights_1D(8) = 0.17944647035620652545826564426188; - leg_weights_1D(9) = 0.17656270536699264632527099011319; - leg_weights_1D(10) = 0.16800410215645004450997066378832; - leg_weights_1D(11) = 0.15404576107681028808143159480195; - leg_weights_1D(12) = 0.13513636846852547328631998170235; - leg_weights_1D(13) = 0.11188384719340397109478838562635; - leg_weights_1D(14) = 0.08503614831717918088353537019106; - leg_weights_1D(15) = 0.05545952937398720112944016535824; - leg_weights_1D(16) = 0.02414830286854793196011002628756; + leg_weights(0) = 0.02414830286854793196011002628756; + leg_weights(1) = 0.05545952937398720112944016535824; + leg_weights(2) = 0.08503614831717918088353537019106; + leg_weights(3) = 0.11188384719340397109478838562635; + leg_weights(4) = 0.13513636846852547328631998170235; + leg_weights(5) = 0.15404576107681028808143159480195; + leg_weights(6) = 0.16800410215645004450997066378832; + leg_weights(7) = 0.17656270536699264632527099011319; + leg_weights(8) = 0.17944647035620652545826564426188; + leg_weights(9) = 0.17656270536699264632527099011319; + leg_weights(10) = 0.16800410215645004450997066378832; + leg_weights(11) = 0.15404576107681028808143159480195; + leg_weights(12) = 0.13513636846852547328631998170235; + leg_weights(13) = 0.11188384719340397109478838562635; + leg_weights(14) = 0.08503614831717918088353537019106; + leg_weights(15) = 0.05545952937398720112944016535824; + leg_weights(16) = 0.02414830286854793196011002628756; break; case 18: - leg_weights_1D(0) = 0.02161601352648331031334271026645; - leg_weights_1D(1) = 0.04971454889496979645333494620263; - leg_weights_1D(2) = 0.07642573025488905652912967761663; - leg_weights_1D(3) = 0.10094204410628716556281398492483; - leg_weights_1D(4) = 0.12255520671147846018451912680020; - leg_weights_1D(5) = 0.14064291467065065120473130375194; - leg_weights_1D(6) = 0.15468467512626524492541800383637; - leg_weights_1D(7) = 0.16427648374583272298605377646592; - leg_weights_1D(8) = 0.16914238296314359184065647013498; - leg_weights_1D(9) = 0.16914238296314359184065647013498; - leg_weights_1D(10) = 0.16427648374583272298605377646592; - leg_weights_1D(11) = 0.15468467512626524492541800383637; - leg_weights_1D(12) = 0.14064291467065065120473130375194; - leg_weights_1D(13) = 0.12255520671147846018451912680020; - leg_weights_1D(14) = 0.10094204410628716556281398492483; - leg_weights_1D(15) = 0.07642573025488905652912967761663; - leg_weights_1D(16) = 0.04971454889496979645333494620263; - leg_weights_1D(17) = 0.02161601352648331031334271026645; + leg_weights(0) = 0.02161601352648331031334271026645; + leg_weights(1) = 0.04971454889496979645333494620263; + leg_weights(2) = 0.07642573025488905652912967761663; + leg_weights(3) = 0.10094204410628716556281398492483; + leg_weights(4) = 0.12255520671147846018451912680020; + leg_weights(5) = 0.14064291467065065120473130375194; + leg_weights(6) = 0.15468467512626524492541800383637; + leg_weights(7) = 0.16427648374583272298605377646592; + leg_weights(8) = 0.16914238296314359184065647013498; + leg_weights(9) = 0.16914238296314359184065647013498; + leg_weights(10) = 0.16427648374583272298605377646592; + leg_weights(11) = 0.15468467512626524492541800383637; + leg_weights(12) = 0.14064291467065065120473130375194; + leg_weights(13) = 0.12255520671147846018451912680020; + leg_weights(14) = 0.10094204410628716556281398492483; + leg_weights(15) = 0.07642573025488905652912967761663; + leg_weights(16) = 0.04971454889496979645333494620263; + leg_weights(17) = 0.02161601352648331031334271026645; break; case 19: - leg_weights_1D(0) = 0.01946178822972647703631204146443; - leg_weights_1D(1) = 0.04481422676569960033283815740199; - leg_weights_1D(2) = 0.06904454273764122658070825800601; - leg_weights_1D(3) = 0.09149002162244999946446209412383; - leg_weights_1D(4) = 0.11156664554733399471602390168176; - leg_weights_1D(5) = 0.12875396253933622767551578485687; - leg_weights_1D(6) = 0.14260670217360661177574610944190; - leg_weights_1D(7) = 0.15276604206585966677885540089766; - leg_weights_1D(8) = 0.15896884339395434764995643946504; - leg_weights_1D(9) = 0.16105444984878369597916362532091; - leg_weights_1D(10) = 0.15896884339395434764995643946504; - leg_weights_1D(11) = 0.15276604206585966677885540089766; - leg_weights_1D(12) = 0.14260670217360661177574610944190; - leg_weights_1D(13) = 0.12875396253933622767551578485687; - leg_weights_1D(14) = 0.11156664554733399471602390168176; - leg_weights_1D(15) = 0.09149002162244999946446209412383; - leg_weights_1D(16) = 0.06904454273764122658070825800601; - leg_weights_1D(17) = 0.04481422676569960033283815740199; - leg_weights_1D(18) = 0.01946178822972647703631204146443; + leg_weights(0) = 0.01946178822972647703631204146443; + leg_weights(1) = 0.04481422676569960033283815740199; + leg_weights(2) = 0.06904454273764122658070825800601; + leg_weights(3) = 0.09149002162244999946446209412383; + leg_weights(4) = 0.11156664554733399471602390168176; + leg_weights(5) = 0.12875396253933622767551578485687; + leg_weights(6) = 0.14260670217360661177574610944190; + leg_weights(7) = 0.15276604206585966677885540089766; + leg_weights(8) = 0.15896884339395434764995643946504; + leg_weights(9) = 0.16105444984878369597916362532091; + leg_weights(10) = 0.15896884339395434764995643946504; + leg_weights(11) = 0.15276604206585966677885540089766; + leg_weights(12) = 0.14260670217360661177574610944190; + leg_weights(13) = 0.12875396253933622767551578485687; + leg_weights(14) = 0.11156664554733399471602390168176; + leg_weights(15) = 0.09149002162244999946446209412383; + leg_weights(16) = 0.06904454273764122658070825800601; + leg_weights(17) = 0.04481422676569960033283815740199; + leg_weights(18) = 0.01946178822972647703631204146443; break; default: std::ostringstream ss; ss << "Error: " << num << "-point quadrature rule not implemented."; - throw NotImplemented(ss.str()); + throw NotImplementedError(ss.str()); } } diff --git a/elements/bernstein_element.cpp b/elements/bernstein_element.cpp index bc27260a..99e5c344 100644 --- a/elements/bernstein_element.cpp +++ b/elements/bernstein_element.cpp @@ -36,7 +36,7 @@ template void BernsteinElement::eval_grad_basis(const SizeType I, const NumType *X, NumType *grad_phi) { // Decompose index of 3D tensor product basis function into indices of Bernstein polynomials - common::base_10_to_mized_radix(Nd, rad, I, ijk); + common::base_10_to_mixed_radix(Nd, rad, I, ijk); // Evaluate Bernstein polynomials NumType Bi = bernstein::eval(N, int(ijk[0]), X[0]); @@ -58,7 +58,7 @@ void BernsteinElement::eval_grad_basis(const SizeType I, const NumType template NumType BernsteinElement::eval_approx(const NumType *c, const NumType *X) { - for (int k = 0, k < N; k++) { + for (int k = 0; k < N; k++) { for (int j = 0; j < N; j++){ // Collapse first dimension into coefficients for second dimension C[j] = bernstein::eval_approx(N, &c[j*N+k*N*N], X[0]); @@ -138,7 +138,7 @@ NumType BernsteinElement::eval_det_jac(const NumType *x, const NumType /* x, y, z in physical space. X in reference space. Jinv = Invers Jacobian (column-major). */ template -void BernsteinElement::eval_inv_jac(const NumType *x, const Numtype *y, +void BernsteinElement::eval_inv_jac(const NumType *x, const NumType *y, const NumType *z, const NumType *X, NumType *Jinv) { // instantiate jacobian // diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt index 0817543d..5c211e27 100644 --- a/examples/CMakeLists.txt +++ b/examples/CMakeLists.txt @@ -3,3 +3,8 @@ add_subdirectory(average) # "VTK" example, demonstration of visualization using VTK/Paraview add_subdirectory(vtk) + +# "hexref" example, demo of MATAR-Kokkoified hexahedral reference element +if (MATAR_WITH_KOKKOS) + add_subdirectory(hexref) +endif() diff --git a/examples/hexref/CMakeLists.txt b/examples/hexref/CMakeLists.txt new file mode 100644 index 00000000..348556d4 --- /dev/null +++ b/examples/hexref/CMakeLists.txt @@ -0,0 +1,10 @@ +add_executable(hexref hexref.cpp) +target_compile_definitions( + hexref + PUBLIC + MATAR_WITH_KOKKOS + HAVE_KOKKOS=1 + HAVE_OPENMP=1 +) +target_include_directories(hexref PUBLIC ${ELEMENTS_KOKKOS_INCLUDES}) +target_link_libraries(hexref PUBLIC elements_kokkos) diff --git a/examples/hexref/hexref.cpp b/examples/hexref/hexref.cpp new file mode 100644 index 00000000..7c781e08 --- /dev/null +++ b/examples/hexref/hexref.cpp @@ -0,0 +1,30 @@ +#include "HexRef.h" + +#include "Kokkos_Core.hpp" + +#include + + +int main(int argc, char *argv[]) { + Kokkos::initialize(argc, argv); + int order_basis = 2; + BasisType type_basis = BasisType::LAGRANGE; + HexRef elem(order_basis, type_basis); + + // Print out the quadrature points pertaining the the cells (subelements) + for (int i = 0; i < elem.num_ref_cells_in_elem(); ++i) { + std::cout << elem.ref_cell_positions(i, 0) << " " + << elem.ref_cell_positions(i, 1) << " " + << elem.ref_cell_positions(i, 2) << " " + << std::endl; + } + + // Print out the basis function evaluations on the cell (subelements) + for (int i = 0; i < elem.num_ref_cells_in_elem(); ++i) { + for (int j = 0; j < elem.num_basis(); ++j) + std::cout << elem.ref_cell_basis(i, j) << " "; + std::cout << std::endl; + } + + return 0; +} diff --git a/examples/vtk/CMakeLists.txt b/examples/vtk/CMakeLists.txt index f8709766..3da48aa4 100644 --- a/examples/vtk/CMakeLists.txt +++ b/examples/vtk/CMakeLists.txt @@ -2,10 +2,10 @@ if (WITH_VTK AND VTK_FOUND) add_executable( plotting_jacobian_determinants - plotting_jacobian_determinants.cpp + plotting_jacobian_determinants.cpp ) target_link_libraries( plotting_jacobian_determinants - elements swage swage2vtk common + elements swage swage2vtk common ) endif() From 08121c579f9a2c2b601b9e60cd725a848e3517b8 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Fri, 16 Sep 2022 10:59:08 -0500 Subject: [PATCH 17/20] Forgot to make type names consistent --- elements-kokkos/include/HexRef.h | 25 +++++++++--------- elements-kokkos/include/MatarTypeDefs.h | 9 ++++--- elements-kokkos/src/HexRef.cpp | 34 ++++++++++++------------- 3 files changed, 35 insertions(+), 33 deletions(-) diff --git a/elements-kokkos/include/HexRef.h b/elements-kokkos/include/HexRef.h index 2d2a4d01..7a2de14d 100644 --- a/elements-kokkos/include/HexRef.h +++ b/elements-kokkos/include/HexRef.h @@ -31,10 +31,10 @@ struct HexRef { int cell_rid(int i, int j, int k) const; MatarRealCArray ref_cell_positions_; - real_t ref_cell_positions(int cell_rid, int dim) const; + Real ref_cell_positions(int cell_rid, int dim) const; MatarRealCArray ref_cell_g_weights_; - real_t ref_cell_g_weights(int cell_rid) const; + Real ref_cell_g_weights(int cell_rid) const; // Patches (subelement faces used in surface integration) @@ -55,12 +55,12 @@ struct HexRef { int ref_patches_in_cell(int cell_lid, int patch_rlid) const; MatarRealCArray ref_patch_positions_; - real_t ref_patch_positions(int patch_rid, int dim) const; + Real ref_patch_positions(int patch_rid, int dim) const; MatarRealCArray ref_patch_g_weights_; - real_t ref_patch_g_weights(int patch_rid) const; + Real ref_patch_g_weights(int patch_rid) const; - const real_t cell_side_unit_normals_[18] = { + const Real cell_side_unit_normals_[18] = { -1, 0, 0, // -xi 1, 0, 0, // +xi 0, -1, 0, // -eta @@ -68,7 +68,7 @@ struct HexRef { 0, 0, -1, // -zeta 0, 0, 1 // +zeta }; - real_t cell_side_unit_normals(int side_rlid, int dim) const; + Real cell_side_unit_normals(int side_rlid, int dim) const; // Nodes (quadrature points) and vertices (degrees of freedom) @@ -79,6 +79,8 @@ struct HexRef { int num_ref_verts_1D_; int num_ref_verts_in_elem_; + Real *ref_verts_1D_; + // Evaluations of basis functions and their gradients at quadrature points // in cells and on patches @@ -89,17 +91,16 @@ struct HexRef { int num_basis() const; MatarRealCArray ref_cell_basis_; - real_t ref_cell_basis(int cell_rid, int basis_id) const; + Real ref_cell_basis(int cell_rid, int basis_id) const; MatarRealCArray ref_cell_gradient_; - real_t ref_cell_gradient(int cell_rid, int basis_id, int dim) const; + Real ref_cell_gradient(int cell_rid, int basis_id, int dim) const; MatarRealCArray ref_patch_basis_; - real_t ref_patch_basis(int patch_rid, int basis_id) const; + Real ref_patch_basis(int patch_rid, int basis_id) const; MatarRealCArray ref_patch_gradient_; - real_t ref_patch_gradient(int patch_rid, int basis_id, int dim) const; + Real ref_patch_gradient(int patch_rid, int basis_id, int dim) const; - real_t *ref_verts_1D_; - TensorProductBasis *basis; + TensorProductBasis *basis; }; diff --git a/elements-kokkos/include/MatarTypeDefs.h b/elements-kokkos/include/MatarTypeDefs.h index 8a1ddf58..aa1398f5 100644 --- a/elements-kokkos/include/MatarTypeDefs.h +++ b/elements-kokkos/include/MatarTypeDefs.h @@ -1,11 +1,12 @@ +#include "common.h" #include "matar.h" #ifdef MATAR_WITH_KOKKOS -typedef CArrayKokkos MatarRealCArray; -typedef CArrayKokkos MatarUIntCArray; +typedef CArrayKokkos MatarRealCArray; +typedef CArrayKokkos MatarUIntCArray; typedef CArrayKokkos MatarIntCArray; #else -typedef CArray MatarRealCArray; -typedef CArray MatarUIntCArray; +typedef CArray MatarRealCArray; +typedef CArray MatarUIntCArray; typedef CArray MatarIntCArray; #endif // MATAR_WITH_KOKKOS diff --git a/elements-kokkos/src/HexRef.cpp b/elements-kokkos/src/HexRef.cpp index a71cbd38..53019e2e 100644 --- a/elements-kokkos/src/HexRef.cpp +++ b/elements-kokkos/src/HexRef.cpp @@ -44,7 +44,7 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { ref_patch_basis_ = MatarRealCArray(num_patches_in_elem_, num_basis_); ref_patch_gradient_ = MatarRealCArray(num_patches_in_elem_, num_basis_, num_dim_); - ref_verts_1D_ = new real_t[num_ref_verts_1D_]; + ref_verts_1D_ = new Real[num_ref_verts_1D_]; // Retrieve Gauss-Legendre and Gauss-Lobatto quadrature points and weights @@ -195,13 +195,13 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { // Initialize basis object based on type specified switch (type_basis) { case BasisType::LAGRANGE: - basis = new LagrangeProductBasis(order_basis, ref_verts_1D_); + basis = new LagrangeProductBasis(order_basis, ref_verts_1D_); break; case BasisType::LEGENDRE: - basis = new LegendreProductBasis(order_basis); + basis = new LegendreProductBasis(order_basis); break; case BasisType::BERNSTEIN: - basis = new BernsteinProductBasis(order_basis); + basis = new BernsteinProductBasis(order_basis); break; default: basis = nullptr; @@ -213,7 +213,7 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { // Fill in evaluations of basis functions and their gradients in cells for (int cell_rlid = 0; cell_rlid < num_ref_cells_in_elem_; cell_rlid++) { // Get the cell coordinates - real_t point[num_dim_]; + Real point[num_dim_]; for (int dim = 0; dim < num_dim_; dim++) point[dim] = ref_cell_positions(cell_rlid, dim); @@ -223,7 +223,7 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { // Compute and store all the basis gradient values at the cell for (int basis_id = 0; basis_id < num_basis_; basis_id++) { - real_t grad_basis[num_dim_]; + Real grad_basis[num_dim_]; basis->eval_grad_basis(basis_id, point, grad_basis); ref_cell_gradient_(cell_rlid, basis_id, 0) = grad_basis[0]; ref_cell_gradient_(cell_rlid, basis_id, 1) = grad_basis[1]; @@ -236,7 +236,7 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { for (int patch_rlid = 0; patch_rlid < num_patches_in_elem_; patch_rlid++) { // Get the cell coordinates // Get the patch coordinates - real_t point[num_dim_]; + Real point[num_dim_]; for (int dim = 0; dim < num_dim_; dim++) point[dim] = ref_patch_positions(patch_rlid, dim); @@ -247,7 +247,7 @@ HexRef::HexRef(int order_basis, BasisType type_basis=LAGRANGE) { // loop over the basis polynomials where there is one from each vertex for (int basis_id = 0; basis_id < num_basis_; basis_id++) { - real_t grad_basis[num_dim_]; + Real grad_basis[num_dim_]; basis->eval_grad_basis(basis_id, point, grad_basis); ref_patch_gradient_(patch_rlid, basis_id, 0) = grad_basis[0]; ref_patch_gradient_(patch_rlid, basis_id, 1) = grad_basis[1]; @@ -273,12 +273,12 @@ int HexRef::cell_rid(int i, int j, int k) const { }; -real_t HexRef::ref_cell_positions(int cell_rid, int dim) const { +Real HexRef::ref_cell_positions(int cell_rid, int dim) const { return ref_cell_positions_(cell_rid, dim); } -real_t HexRef::ref_cell_g_weights(int cell_rid) const { +Real HexRef::ref_cell_g_weights(int cell_rid) const { return ref_cell_g_weights_(cell_rid); } @@ -294,17 +294,17 @@ int HexRef::ref_patches_in_cell(int cell_rid, int patch_rlid) const { } -real_t HexRef::ref_patch_positions(int patch_rid, int dim) const { +Real HexRef::ref_patch_positions(int patch_rid, int dim) const { return ref_patch_positions_(patch_rid, dim); } -real_t HexRef::ref_patch_g_weights(int patch_rid) const { +Real HexRef::ref_patch_g_weights(int patch_rid) const { return ref_patch_g_weights_(patch_rid); } -real_t HexRef::cell_side_unit_normals(int side_rlid, int dim) const { +Real HexRef::cell_side_unit_normals(int side_rlid, int dim) const { int index = side_rlid*3 + dim; return cell_side_unit_normals_[index]; } @@ -325,23 +325,23 @@ int HexRef::num_basis() const { } -real_t HexRef::ref_cell_basis(int cell_rid, int basis_id) const { +Real HexRef::ref_cell_basis(int cell_rid, int basis_id) const { return ref_cell_basis_(cell_rid, basis_id); }; -real_t HexRef::ref_cell_gradient(int cell_rid, int basis_id, +Real HexRef::ref_cell_gradient(int cell_rid, int basis_id, int dim) const { return ref_cell_gradient_(cell_rid, basis_id, dim); }; -real_t HexRef::ref_patch_basis(int patch_rid, int basis_id) const { +Real HexRef::ref_patch_basis(int patch_rid, int basis_id) const { return ref_patch_basis_(patch_rid, basis_id); }; -real_t HexRef::ref_patch_gradient(int patch_rid, int basis_id, +Real HexRef::ref_patch_gradient(int patch_rid, int basis_id, int dim) const { return ref_patch_gradient_(patch_rid, basis_id, dim); }; From 0c7b52dfddf3008e597471e350e91f68ba99fb5a Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Fri, 11 Nov 2022 14:44:18 -0600 Subject: [PATCH 18/20] Update Docs.yaml --- .github/workflows/Docs.yaml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.github/workflows/Docs.yaml b/.github/workflows/Docs.yaml index a8bf48c0..a84c55ac 100644 --- a/.github/workflows/Docs.yaml +++ b/.github/workflows/Docs.yaml @@ -48,8 +48,8 @@ jobs: - name: Configure git information run: | - git config --global user.name $GITHUB_ACTOR - git config --global user.email $GITHUB_ACTOR@users.noreply.github.com + git config --global user.name Jan Kiviaho + git config --global user.email jfk115@msstate.edu - name: Update/add doc files and push run: | From 5f19e8abf734cc4fa9f83a104eab3b6ef99442ba Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Fri, 11 Nov 2022 14:51:27 -0600 Subject: [PATCH 19/20] Update Docs.yaml --- .github/workflows/Docs.yaml | 1 + 1 file changed, 1 insertion(+) diff --git a/.github/workflows/Docs.yaml b/.github/workflows/Docs.yaml index a84c55ac..4b79ccac 100644 --- a/.github/workflows/Docs.yaml +++ b/.github/workflows/Docs.yaml @@ -45,6 +45,7 @@ jobs: uses: actions/checkout@v3 with: ref: gh-pages + token: ${{ secrets.GH_TOKEN }} - name: Configure git information run: | From a559916bbd7263c5ef17ab7cf40276fd0f4fe4b5 Mon Sep 17 00:00:00 2001 From: Jan Filipe Kiviaho Date: Fri, 11 Nov 2022 15:05:11 -0600 Subject: [PATCH 20/20] Update Docs.yaml --- .github/workflows/Docs.yaml | 14 +++++++++----- 1 file changed, 9 insertions(+), 5 deletions(-) diff --git a/.github/workflows/Docs.yaml b/.github/workflows/Docs.yaml index 4b79ccac..723c7bc1 100644 --- a/.github/workflows/Docs.yaml +++ b/.github/workflows/Docs.yaml @@ -4,8 +4,6 @@ name: Linux on: push: branches: [master] - pull_request: - branches: [master] env: # CMake configuration for build with docs @@ -45,16 +43,22 @@ jobs: uses: actions/checkout@v3 with: ref: gh-pages - token: ${{ secrets.GH_TOKEN }} - name: Configure git information run: | git config --global user.name Jan Kiviaho git config --global user.email jfk115@msstate.edu - - name: Update/add doc files and push + - name: Update/add doc files run: | cp -r /home/runner/work/install/docs/* . git add -A git commit -m "Automated publication of documentation" - git push + + - name: Push changes + # You may pin to the exact commit or the version. + # uses: ad-m/github-push-action@40bf560936a8022e68a3c00e7d2abefaf01305a6 + uses: ad-m/github-push-action@v0.6.0 + with: + github_token: ${{secrets.GITHUB_TOKEN}} + branch: gh-pages

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