MeanField/experiments/POLYTROPE_H_CONVERGENCE_2026-09-09.md

One-level uniform h-refinement — 2026-09-09

Scope and reproducibility

This study adds exactly one stroid.refinement.UniformRefinement(mesh, 1) to the loaded coarse solve's input, without regenerating the initial mesh, changing field orders, or changing the model or solver tolerances. The original sandbox.smesh, sandbox executable, and all existing coarse data are preserved.

The current MeanField release links an older STROID archive in /usr/local which lacks the multiblock configuration field. Its refinement operation would therefore not preserve the intended mapping strategy. Instead, experiments/refine_polytrope_mesh.py uses the installed STROID 0.5.0 Python binding in the stroidDev environment to load, refine and save a complete mesh. The validation executable loads that refined snapshot with extraRefine=0. No STROID installation, production-library edit or rebuild is involved.

STROID refines the logical reference mesh and reprojects high-order geometry. The study therefore measures joint geometry/field h-convergence, not subdivision of an unchanged physical polynomial geometry. The separately refined analytic control measures the geometry contribution.

Property	Coarse	Refined
Total hex elements	1,216	9,728
Stellar hex elements	832	6,656
Stored refinement level	2	3
Geometry order	4	4
Density/potential DG order	2	2
Enthalpy/displacement H1 order	3	3
Gravity RT index (reported element order)	2 (3)	2 (3)
Nonlinear absolute/relative tolerance	1e-8 / 1e-8	1e-8 / 1e-8
Linear relative tolerance / iteration cap	0.03 / 80	0.03 / 80
Volume quadrature orders	14, 18	14, 18

The model remains nonrotating n=1, G=M=R=1, K=2/pi, central density pi/4, zero surface pressure. The coarse accepted solution is reused, not re-solved. Interior physical-volume errors, shape and virial balance are the acceptance focus; exterior profiles are diagnostic only insofar as they influence the interior. Two levels give an observed reduction, not proof of asymptotic order.

Artifacts and provenance

• Coarse solve: polytrope_solution_2026-09-09/.
• Coarse analytic control: polytrope_analytic_checked_2026-09-09/.
• Refined mesh and binding provenance: polytrope_h1_mesh_2026-09-09/.
• Refined analytic control: polytrope_h1_analytic_2026-09-09/.
• Refined solve: polytrope_h1_solution_2026-09-09/.

SHA-256 hashes at study start:

coarse input / sandbox.smesh
ce11ae99e21e6c3bbfbee402acd2e191c1da0d8261d2227b4203f73f2f337a74
refined.smesh
39cf76d21c74730ffaacf50ae66e150d2e88dcb66caf6a499339b7e90a1f8182
release polytrope_validation_experiment
90caa65be08c5d9dd17ddab267d02159ea440b94304e7d0d4aa7807e688009af
release sandbox (not run in this study)
a904b39935a5add938129e5c3edb72f94b416f0e09ba5b3b937a8004fa463057

The refinement JSON additionally records the actual STROID native-extension path/hash, interpreter, regional element counts and configuration checks. Current mesh-based outputs each retain the fully refined input.smesh, so ordinary saved-field replay requires no new refinement or regeneration.

Analytic geometry control

All 140 independent analytic self-checks and all 24 refined physical-control screens passed. These are analytic fields evaluated on the represented mesh, not an FE equilibrium solution: zero volume field errors are by construction.

Control	Coarse	Refined
Surface-radius relative RMS error	8.91509e-6	4.29640e-7
Volume-radius relative error	9.062e-9	7.63599e-11
Relative mass error	3.922e-10	5.01155e-13
Virial error	2.615e-10	7.19869e-13
Invalid stellar corner/inset samples	0	0
Profile points located	4,020 / 4,020	4,020 / 4,020

The analytic surface error decreases about 20.75-fold. The refined virial is already near its observed quadrature sensitivity (2.43e-13), so its enormous two-level ratio should not be interpreted as a convergence order.

Refined equilibrium

The refined solve is in progress. No equilibrium h-convergence conclusion is available until its accepted fields have been measured.