fix(maths): CellWiseIntegral evaluates on the mesh DS, not a mis-cloned P1 DM (BF-03)

[lmoresi]

Summary

Fixes audit finding LE-02 (worklist item BF-03, docs/reviews/2026-07/REMEDIATION-WORKLIST.md): CellWiseIntegral.evaluate() in src/underworld3/cython/petsc_maths.pyx computed cell-wise integrals against the wrong discretisation. It cloned mesh.dm, attached a fresh single-P1-field DS (FE.createDefault + setField + createDS), and then handed DMPlexComputeCellwiseIntegralFEM a solution vector packed for mesh.dm's multi-field layout. The layout mismatch made the integral read the wrong DOFs and silently over-count.

Reproduction (before the fix)

On a unit-square UnstructuredSimplexBox with a P2 and a P1 variable:

• CellWiseIntegral(mesh, fn=1.0).evaluate() summed to 2.0 (should be 1.0; control Integral gives 1.0) — exactly as reported in the audit (LE-02, reproduced live).

Fix

Rewrite evaluate() to follow the working Integral pattern in the same file: set the JIT objective on mesh.dm's own DS (mesh.dm.getDS()) and integrate on mesh.dm directly, so the compiled objective, the DS field layout, and the packed solution vector all agree. Per-cell results are collected in a plain Vec of local size num_local_cells * num_fields (PETSc's implicit cell-major layout when the output vector carries no section); the field-0 column is returned, one value per rank-local cell. The TODO(BUG) comment at the defect site is removed.

Caveat (issue #171): setting the objective on the shared mesh DS re-inherits the repeated-call cost-growth behaviour that Integral has (issue #171, historical context: the clone-DM approach introduced in PR #172 to avoid it was reverted in 88807c26 because it produces wrong answers). Correctness parity is accepted here; #171 remains a separate performance item and is NOT closed by this PR.

Tests

• De-xfailed tests/test_0501_integrals.py::test_cellwise_integrate_constants and ::test_cellwise_integrate_meshvar — these failed on the unfixed build (sums 2.0 and ~2x 2/pi) and now pass. Assertions reduce the local sums across ranks (no-op in serial) since evaluate() returns rank-local per-cell values.
• pytest tests/test_0501_integrals.py -q: 11 passed, 1 xfailed (the pre-existing unrelated piecewise-derivative xfail).
• MPI: mpirun -np 2 python -m pytest tests/test_0501_integrals.py -q: 11 passed, 1 xfailed on both ranks (rank-local sums 0.4986 + 0.5014 = 1.0 exactly).
• Serial gate pytest tests/ -m "level_1 and tier_a" -x -q: identical before and after the fix — 295 passed, 7 skipped, 4 xfailed, 1 xpassed (the xpass is pre-existing).
• Cross-check on the fixed build: cell-count matches getHeightStratum(0), all per-cell values positive, and the cell-wise sum of a P2 integrand matches the global Integral to machine precision.

Underworld development team with AI support from Claude Code

[Copilot]

Pull request overview

Fixes CellWiseIntegral.evaluate() to compute cell-wise FEM integrals on the mesh’s DM/DS (matching Integral), eliminating a discretisation/layout mismatch that previously caused incorrect results (notably ~2× over-counting for simple integrands).

Changes:

• Reworked CellWiseIntegral.evaluate() to set the objective on mesh.dm.getDS() and call DMPlexComputeCellwiseIntegralFEM() on mesh.dm with the mesh-packed solution vector.
• Adjusted the cell-wise result collection to use a plain PETSc Vec sized as num_local_cells * num_fields, returning field-0 values per rank-local cell.
• Updated tests by removing the prior xfail expectation and reducing per-rank cellwise sums across MPI ranks to assert correct global totals.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
src/underworld3/cython/petsc_maths.pyx	Fixes CellWiseIntegral.evaluate() to integrate on the mesh DM/DS so the objective, discretisation, and packed solution vector agree.
tests/test_0501_integrals.py	Converts prior xfailed CellWiseIntegral parity checks into regression tests (with MPI-safe global reductions).

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