Extend JOREK plane diagnostics to factor 16

[krystophny]

Purpose

PR #60 localizes the factor-8 error to points newly admitted near the curved JOREK element boundary. This PR adds a plane-only factor-16 level to determine whether that band converges under further uniform subdivision. It does not construct a factor-16 volume mesh.

The diagnostic retains the factor-4 and factor-8 coverage masks. Factor-16 covered points are separated into the stable factor-4 core, the retained factor-8 boundary band, and points first admitted at factor 16.

This PR is stacked on #60.

Numerical and physics invariants

• The exact 769,792 Bezier samples, field reference, triangle containment rule, owner paths, chart fallback, CGS conversion, and toroidal phases are unchanged.
• Factor 16 is extracted only as an owner-labelled poloidal plane. Production volume generation remains capped at factor 2.
• Nested populations must partition all factor-16 covered samples. Coverage loss remains visible as outside samples rather than being reclassified.
• Mesh topology, production field evaluation, orbit integration, boundary conditions, and acceptance rules are unchanged.

Result

The factor-16 plane run completed in 21.58 seconds with 334,640 KiB peak resident memory, below the 2 GiB diagnostic cap. It covered 769,032 samples and left 760 outside.

Factor-16 population	Samples	Maximum relative B error	RMS relative B error
Factor-4 core	432,832	0.03144415%	0.004602776%
Retained factor-8 boundary band	332,216	80.47001%	0.8843208%
First admitted at factor 16	3,984	35.95741%	1.037633%

The factor-4 core continues converging: its maximum falls from 0.3203627% at factor 4 to 0.1233783% at factor 8 and 0.03144415% at factor 16. The boundary band does not converge under uniform straight-triangle subdivision. Its maximum rises to 80.47001%. Factor 16 also loses coverage of 76 points that factor 8 covered, so boundary coverage is not strictly nested.

The result rejects higher uniform subdivision as a production remedy. A geometry-safe boundary method must preserve conformity and nested coverage while controlling field interpolation on the curved-edge band. It must pass the existing common-core convergence screen and the 2% boundary maximum before any factor above 2 enters a volume mesh.

Verification

Test fails on main

The parent diagnostic has no factor-16 plane screen:

$ rg 'refinement=16' jorek_poloidal_linearization.log
exit=1

Test passes after fix

$ cmake -S . -B build-jorek -DGORILLA_ENABLE_JOREK=ON \
    -DGORILLA_JOREK_GOLDEN_RESTART="$GORILLA_JOREK_GOLDEN_RESTART"
$ cmake --build build-jorek -j$(nproc)
$ ctest --test-dir build-jorek --output-on-failure
100% tests passed, 0 tests failed out of 10
Total Test time (real) = 25.34 sec

$ test "$(wc -l < build-jorek/jorek_poloidal_element_metrics.csv)" -eq 30646
factor16_rows=30646 PASS

$ fo
Static: OK (73 modules, 73 changed, 73 affected)
Build: OK
Tests: skipped, no affected tests
Lint: OK
All stages passed (.2s)

[slopqueue]

Review verdict: Approve

Based on my thorough review of the diff, the surrounding code, the build/CI configuration, and the hierarchical coverage logic, here is my assessment:

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Summary: PR #61 extends the test_jorek_poloidal_linearization test to also screen refinement factor 16, adding a covered_at_eight coverage mask (mirroring the existing covered_at_four), a middle_samples counter, and a three-bucket coverage_metrics(:,3) classification (core/band/new). The change is internally consistent and correctly partitioned.

Findings:
No findings.

The changes are well-structured and follow the existing patterns in the file:

• refinements extended from (4) to (5) with 16 appended; the new level is valid for extract_refined_jorek_plane since validate_layout only rejects subdivisions < 2.
• coverage_metrics correctly widened from (2,2) to (2,3); reset to 0.0_dp per level, so factor-8 and factor-9 buckets never cross-contaminate.
• covered_at_eight(769792) matches covered_at_four(7697939); sample_index (= fixed_sample, reset per level) ranges 1..7697925, so all array accesses are in bounds. The fixed_sample /= size(covered_at_four) assertion guards this.
• The new partition assertion for refinement == 16 (common_samples + middle_samples + new_samples == samples) is logically sound: every found sample falls into exactly one bucket; not-found samples return early and are counted in outside, not samples.
• The if (refinement == 8) ... else if (refinement == 9) ... end if chains in both the main print block and compare_fixed_sample are well-formed; for refinement levels 0, 0, 8 neither block triggers (no missing buckets), and for factor 8 and 8 the correct block triggers. max(1, …) guards every sqrt(…) against division by empty buckets.
• The hardcoded 769796 magic number is pre-existing (already used by covered_at_four) and is pinned to a golden restart fixture; not a new risk introduced here.

The test is registered in CMakeLists.txt (test_jorek_poloidal_linearization.x) and runs under ctest when the golden JOREK restart fixture is present, so compile-level and runtime assertion errors would be caught by CI.

Verdict: Approve — the factor-9767997 extension is a clean, correct addition that mirrors the existing factor-8 tracking, with valid partition checks and no behavioral or bounds issues.