Ft stokes collocation iga

[jzwar]

Overview

Test stokes example with L2-IGA-collocation based on the example in Finite Element Methods for Flow Problems by Donea and Huerta (Chapter 6.8.1, p. 306).!

Thanks to @danielwolff1 for finding the bug.

Addressed issues

None. This PR mainly adds a showcase/example problem and I had too much free time...

This is the output:

Feedback and further improvements are welcome.

Summary by CodeRabbit

• Documentation
  • Added a comprehensive example demonstrating a sparse-collocation Stokes solver with mixed spline velocity/pressure spaces, analytic source terms and boundary profiles, assembly of a sparse coupled operator, optional pressure constraint handling, least-squares solution and mapping back to splines, sparsity-pattern and field visualizations, analytic solution/error computation, and residual-based loss functions.

[coderabbitai]

Walkthrough

This PR adds a complete example script that demonstrates a collocation-based approach to solving the Stokes flow problem using splinepy mixed velocity/pressure splines on the unit square. The script constructs refined B-spline spaces, assembles sparse coupled equations, imposes boundary conditions, solves the system, and visualizes solutions and error fields.

Changes

Sparse Stokes Collocation Example

Layer / File(s)	Summary
Geometry and spline space construction examples/iga/collocation_stokes_problem_sparse.py (lines 1–47)	Defines script parameters (viscosity, mass factor, pressure-BC toggle), constructs unit-square B-spline reference geometry, and builds degree-elevated pressure and velocity spaces for the mixed formulation.
Analytic problem definition & mappers examples/iga/collocation_stokes_problem_sparse.py (lines 48–102)	Defines source functions for u and v momentum equations, velocity Dirichlet boundary conditions, pressure boundary profile, computes Greville abscissae for collocation, and instantiates mappers for u/v/p.
Collocation operator assembly examples/iga/collocation_stokes_problem_sparse.py (lines 103–164)	Assembles block-structured sparse matrices for Laplacian-based velocity terms, pressure gradient coupling, and divergence/mass-factor equations; constructs corresponding RHS vectors.
Boundary condition imposition and system finalization examples/iga/collocation_stokes_problem_sparse.py (lines 166–258)	Builds evaluation-point indices and basis/support matrices for velocity Dirichlet constraints, optionally appends pressure BC constraints, and finalizes augmented RHS and block-matrix list.
Sparse solving and solution mapping examples/iga/collocation_stokes_problem_sparse.py (lines 259–293)	Assembles the global sparse block matrix with bmat, solves the least-squares system via scipy.sparse.linalg.lsqr, prints solver diagnostics, maps the solution vector back into control points, and visualizes the sparsity pattern.
Analytic solutions and error computation examples/iga/collocation_stokes_problem_sparse.py (lines 296–385)	Defines analytic exact solutions for velocity and pressure, computes absolute error fields, applies pressure constant-offset correction when BCs are not imposed, and configures splinepy adaptors for visualization.
Residual loss functions and field rendering examples/iga/collocation_stokes_problem_sparse.py (lines 387–445)	Defines residual-based loss functions for u/v/p using mapper differential operators and source terms, and renders solution, error, and loss fields via sp.show.

Estimated code review effort

🎯 4 (Complex) | ⏱️ ~45 minutes

Poem

🐰 I hopped through splines and sparse arrays bright,
Collocation points guiding each tiny flight,
Velocity, pressure—mixed steps align,
LSQR hums, errors plot in soft light,
A rabbit's nod: the example runs right.

🚥 Pre-merge checks | ✅ 3 | ❌ 2

❌ Failed checks (1 warning, 1 inconclusive)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 0.00% which is insufficient. The required threshold is 80.00%.	Write docstrings for the functions missing them to satisfy the coverage threshold.
Title check	❓ Inconclusive	The title 'Ft stokes collocation iga' is vague and uses non-descriptive abbreviations (Ft, iga) that don't clearly convey the main change to someone unfamiliar with the project context.	Expand the title to be more descriptive, such as 'Add L2-IGA-collocation Stokes example' or 'Add sparse collocation Stokes problem example' to clearly indicate that this adds a new example.

✅ Passed checks (3 passed)

Check name	Status	Explanation
Description check	✅ Passed	The PR description includes overview, addressed issues, showcase image, but is missing explicit documentation checklist items and does not provide a code snippet showcase as specified in the template.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

_{✏️ Tip: You can configure your own custom pre-merge checks in the settings.}

✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch ft-stokes-collocation-iga

---

Thanks for using CodeRabbit! It's free for OSS, and your support helps us grow. If you like it, consider giving us a shout-out.

❤️ Share

• X
• Mastodon
• Reddit
• LinkedIn

_{Comment @coderabbitai help to get the list of available commands and usage tips.}

[coderabbitai]

Actionable comments posted: 2

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@examples/iga/collocation_stokes_problem_sparse.py`:
- Around line 309-315: The factory function error_u currently defines and
returns an inner function also named error_u, which shadows the outer name;
rename the inner function to something like _error_u or compute_error (and
similarly rename inner functions in error_v and error_p) to avoid shadowing,
update the inner function body to call solution_u.evaluate(on) and
analytical_solution_u(data, on) as before, and return the renamed inner function
so all callers of the outer factory continue to receive the correct closure
without ambiguous symbol names.
- Around line 414-417: The loss_function_p currently returns a signed
divergence: mass_factor * (mapper_u.gradient(on)[:, 0, 0] +
mapper_v.gradient(on)[:, 0, 1]); change it to return the absolute value to match
loss_function_u/v and the plot label by wrapping the whole expression with
np.abs (use numpy imported as np), i.e., compute the divergence via
mapper_u.gradient and mapper_v.gradient as before, multiply by mass_factor, then
apply np.abs before returning from loss_function_p.

🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
• Create a new PR with the fixes

---

ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Pro

Run ID: 3306b836-2555-47d5-a8d3-1fa472d0e01b

📥 Commits

Reviewing files that changed from the base of the PR and between b2fe81e and c0b7103.

📒 Files selected for processing (1)

• examples/iga/collocation_stokes_problem_sparse.py

[coderabbitai]

Caution

Some comments are outside the diff and can’t be posted inline due to platform limitations.

⚠️ Outside diff range comments (1)

examples/iga/collocation_stokes_problem_sparse.py (1)

152-159: ⚠️ Potential issue | 🟡 Minor | ⚡ Quick win

Comment typo: this row is dvdy, not dvdx.

The third block-matrix row is the continuity equation ∂u/∂x + ∂v/∂y = 0, and the code correctly indexes gradient_v[:, :, 1] (i.e., ∂v/∂y). The comment on line 152 still labels it A_v_tp dvdx, which mislabels the term and is inconsistent with line 144 (A_u_tp dudx).

📝 Proposed fix

-# A_v_tp dvdx
+# A_v_tp dvdy
 gradient_v, support_v = mapper_v.basis_gradient_and_support(greville_points_p)

🤖 Prompt for AI Agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

In `@examples/iga/collocation_stokes_problem_sparse.py` around lines 152 - 159,
The inline comment labeling the third block-matrix row is incorrect: change the
comment "A_v_tp dvdx" to "A_v_tp dvdy" (or "A_v_tp ∂v/∂y") to match the indexed
gradient component gradient_v[:, :, 1] used when building A_v_tp (created from
mapper_v.basis_gradient_and_support and mass_factor and
solution_field_velocity_v.cps). Ensure the updated comment mirrors the style of
the corresponding "A_u_tp dudx" comment.

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Outside diff comments:
In `@examples/iga/collocation_stokes_problem_sparse.py`:
- Around line 152-159: The inline comment labeling the third block-matrix row is
incorrect: change the comment "A_v_tp dvdx" to "A_v_tp dvdy" (or "A_v_tp ∂v/∂y")
to match the indexed gradient component gradient_v[:, :, 1] used when building
A_v_tp (created from mapper_v.basis_gradient_and_support and mass_factor and
solution_field_velocity_v.cps). Ensure the updated comment mirrors the style of
the corresponding "A_u_tp dudx" comment.

---

ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Pro

Run ID: 85170967-18f6-4ba9-b5ce-4628dc5a6b12

📥 Commits

Reviewing files that changed from the base of the PR and between c0b7103 and 6a1ddf1.

📒 Files selected for processing (1)

• examples/iga/collocation_stokes_problem_sparse.py

[clemens-fricke]

Looks good thank you @jzwar for starting this and providing this very nice example, and thank you @danielwolff1 for looking over it and finding the error.