Run a single IDAKLU solver outside any OpenMP parallel region

[aabills]

Description

IDAKLUSolverGroup::solve runs its solvers under #pragma omp parallel num_threads(team_size). That's also true when there is only one solver, the usual case, so a single solve ran inside a one-thread parallel region. OpenMP code that the model calls during the solve, such as a CasADi external function, therefore ran nested at omp_get_level() == 1 and took the nested-level ICVs instead of the top-level ones.

The most visible effect shows up with a per-level OMP_NUM_THREADS list. Under OMP_NUM_THREADS=8,1, an OpenMP region in a CasADi external called from the solve got 1 thread instead of 8. The 8,1 setting asks for a team of 8 at the top level, and that's the level the external is logically at.

Fix. The team body becomes a lambda, run_thread(thread). When team_size == 1 it's called directly on the calling thread, with no parallel region. Otherwise it runs under the same #pragma omp parallel num_threads(team_size) as before. The multi-solver path is unchanged.

Reproducer

A CasADi external, built with -fopenmp against the same libomp as pybammsolvers, is used both as the model's RHS and as an output variable. It reports what OpenMP looks like from inside the solve:

int probe(const double** arg, double** res, casadi_int* iw, double* w, int mem) {
  int team = 0;
  #pragma omp parallel
  {
    #pragma omp single
    team = omp_get_num_threads();
  }
  res[0][0] = omp_get_level();
  res[0][1] = omp_in_parallel();
  res[0][2] = team;
  return 0;
}

The probe is passed to create_casadi_solver_group as an output variable, with num_solvers=1 and num_threads=1. Results on macOS arm64 with Homebrew libomp:

Environment	Build	omp_get_level() in solve	Team size of a region in solve
default (14 cores)	main	1	14
default (14 cores)	this PR	0	14
OMP_NUM_THREADS=8,1	main	1	1
OMP_NUM_THREADS=8,1	this PR	0	8
OMP_NUM_THREADS=8,2	main	1	2
OMP_NUM_THREADS=8,2	this PR	0	8

With default settings the per-region overhead was the same either way: about 23 µs for a small parallel for at 8 threads, both inside and outside a solve. This PR is therefore about OpenMP semantics, not speed. A nested setting meant for code that runs inside the external's regions no longer gets applied to the external itself.

Type of change

Bug fix. There's an entry under ## Bug fixes in CHANGELOG.md.

Tests

No new test yet. The reproducer needs an OpenMP-compiled shared library loaded as a CasADi external, and the test suite has no existing way to build one. Pointers to an acceptable way to cover this in CI would be welcome.

The existing test_parallel_solver_group_uses_multiple_solvers covers the multi-solver path, which still opens the parallel region.

Important checks:

• No style issues (pre-commit hooks pass on the commits)
• All tests pass. Run locally against a wheel built from this branch: packages/pybamm/tests/unit/test_solvers and packages/pybamm/tests/integration/test_solvers (467 passed, 95 skipped) and packages/pybammsolvers/tests (64 passed). The full nox -s tests hasn't been run.
• The documentation builds: nox -s doctests not run (no documentation changes)
• Code is commented for hard-to-understand areas
• Tests added that prove the fix is effective (see Tests above)

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.09%. Comparing base (445ba33) to head (57793e5).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #5837   +/-   ##
=======================================
  Coverage   98.09%   98.09%           
=======================================
  Files         346      346           
  Lines       35354    35354           
=======================================
  Hits        34680    34680           
  Misses        674      674           

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[github-actions]

Bencher Report

Project	PyBaMM
Branch	fix/idaklu-single-solver-openmp
Testbed	bare-metal

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