Split JOREK chart-fallback interpolation errors

[krystophny]

Purpose

PR #58 shows that target-element corner ownership does not remove the factor-8 interpolation failure. This PR tests the next possible cause: the bounded global fallback used when a target-element corner has an ill-conditioned local geometry chart.

The existing fixed-point diagnostic tags a covered sample when any of its three target-element triangle corners satisfies the production fallback criterion. It accumulates maximum and RMS target-element interpolation errors separately for fallback-tagged and regular samples. The numerical path is unchanged.

This PR is stacked on #58.

Numerical and physics invariants

• The production chart criterion and global fallback are called without modification.
• Exact Bezier samples, target-element and production interpolants, physical triangles, coverage decisions, CGS conversion, cylindrical components, and toroidal phases are unchanged.
• The split is observational. Its two counts must partition every covered sample, and non-finite metrics fail the test.
• Mesh topology, owner assignment, field evaluation, orbit integration, boundary conditions, and acceptance rules are unchanged.

Result

No covered sample uses a target-corner fallback through factor 4. At factor 8:

Population	Samples	Maximum relative B error	RMS relative B error
Fallback-tagged	476	22.25442%	5.845721%
Regular	764,648	19.87551%	0.7334778%

The fallback population contains the global worst case and has a larger RMS, so fallback placement matters locally. It is not the sole cause: the regular population still has a 19.87551% maximum.

Factor 8 covers 765,124 points, compared with 432,832 at factor 4. The next diagnostic should split the factor-8 error between points already covered at factor 4 and the 332,292 newly covered points. This tests population change before changing topology, chart handling, or interpolation.

Verification

Test fails on main

The parent diagnostic has no fallback population output:

$ rg 'fallback samples=' 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) = 30.13 sec

$ 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

Summary: PR #59 adds a single commit on top of refs/slopqueue/base, touching only SRC/TESTS/test_jorek_poloidal_linearization.f90. It instruments the existing target-owner B-interpolation test to split samples whose target field touched the JOREK global (axis-regularized) chart ("fallback") from purely local-chart samples ("regular"), and emits per-bucket max/rms diagnostics plus a partition-consistency assertion. The change is test-only and consistent with the surrounding fixture.

Findings:

1. minor SRC/TESTS/test_jorek_poloidal_linearization.f90:316 — prepare_sample_corners now calls jorek_chart_requires_global for every corner, but evaluate_owner_corner (called just below for the same corner target) already invokes the same pure test internally. This roughly doubles the per-sample global-chart probe cost (≈8 probes/sample across 769k samples). Impact is test runtime only (results unaffected since the arguments match exactly, so target_fallback(index) correctly mirrors the chart decision used for the target field). Optional: have evaluate_owner_corner return the flag, or compute it once and pass it in, to avoid the redundant evaluations.

No blockers or majors. The target_fallback(index) is computed with (data, element, sub_s(index), sub_t(index)), which exactly matches the chart test performed inside evaluate_owner_corner for both the owner == element (target = corner) and owner /= element (target via element) paths, so the split is semantically correct. The assertion fallback_samples + regular_samples == samples is guaranteed by construction and serves as a useful defensive check; split_metrics finiteness and the max(1, …) guards on the rms denominators are sound.

Verdict: Approve — the change is a clean, correct test instrumentation; the redundant global-chart probes are a minor efficiency note, not a correctness issue.