NSE EOS Jacobians use cubic derivatives when linear interpolation is selected

Reviewed commit: 3ac0bda4f00da3eed0446beadfc1cd5c51b99a40

Suggested priority: Medium

Affected code: nse_tabular/nse_table.H:429-440, nse_tabular/nse_table.H:496-539, nse_tabular/nse_table.H:549-592; callers in nse_tabular/nse_eos.H.

Description

nse_interp() honors network.nse_table_interp_linear, but nse_interp_dT() and nse_interp_drho() always differentiate the cubic interpolant. The EOS inversion routines therefore use derivatives of a different composition function from the one used to evaluate their residuals.

Reproduction

Set linear interpolation and use T=5.18e9 K, rho=1.23e9 g/cm^3, Ye=0.472. Compare the returned abar derivatives to centered finite differences of nse_interp() with relative perturbation 1e-5:

The discrepancies are approximately 2.3% and 2.6%. With cubic interpolation selected, the same check agrees closely.

Expected behavior / suggested fix

Differentiate the selected interpolant, or explicitly select matching value/derivative routines within the inversions. Add finite-difference checks in both modes, away from cell boundaries.

Impact and validation: An inconsistent Newton Jacobian can impair convergence. The derivative mismatch is reproduced; a linear-mode inversion failure is not claimed. See reproduction-output.txt

reproduction-output.txt

.

Start in nse_tabular/nse_table.H at the affected ranges 429-440, 496-539, and 549-592, then trace the callers in nse_tabular/nse_eos.H. Reproduce the reported derivatives at the supplied T, rho, and Ye with linear interpolation, and verify finite-difference checks in both linear and cubic modes away from cell boundaries.