GridapGeosciences.jl extends the Gridap ecosystem to the numerical approximation of partial differential equations on two and three dimensional cubed sphere manifolds. The cubed sphere meshes are designed with high performance computing in mind.
GridapGeosciences is a registered package in the official Julia package registry. Thus, the installation of GridapGeosciences is straight forward using the Julia's package manager. Open the Julia REPL, type ] to enter package mode, and install as follows
pkg> add GridapGeosciences- Cubed sphere discrete models: We provide serial and distributed implementations of the two dimensional cubed sphere, and a distributed implementation of the three dimensional cubed sphere. Highly scalable, adaptive meshes are provided by
p4estthroughGridapP4est.jl. - Continuous vector-valued Lagrangian finite elements: We provide a serial and distributed implementation of vector-valued Lagrangrian finite elements on manifold.
- Time integrator for differential algrabic equations: We extend the explicit Runge Kutta framework in
Gridapto differential algebraic equations that arise in atmospheric systems like the shallow water equations. - Mapped vtk files: We extend the visualisation framework in
Gridapby applying a cell-wise geometrical map the parametric triangulation to visualise solutions in the ambient space.
A list of examples is available in test/Examples.
These include well known atmospheric applications such as scalar advection, linear wave equation, and the shallow water equations.
The benchmark Laplace Beltrami problem is also available.
Please cite the GridapGeosciences main project as indicated here,
and use the reference below in any publication that uses GridapGeosciences:
@article{Tambyah2026,
year = {2026},
author = {Tamara A. Tambyah and Alberto F. Martín and David Lee and Santiago Badia},
title = {GridapGeosciences.jl: A Julia finite element package for partial differential equations on the sphere [in preparation]},
}
GridapGeosciences is a collaborative project open to contributions. If you want to contribute, please take into account:
- Before opening a PR with a significant contribution, contact the project administrators by opening an issue describing what you are willing to implement. Wait for feedback from other community members.
- We adhere to the contribution and code-of-conduct instructions of the Gridap.jl project, available here and here, resp. Please, carefully read and follow the instructions in these files.
- Open a PR with your contribution.
Vorticity field for the Nonlinear Rotating Shallow Water Equations on the cubed sphere. Galewsky benchmark.