1 Commits

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Author	SHA1	Message	Date
Omar SobhandClaude Fable 5	8071d5888d	rtx-fea: ECSW model-order reduction — POD-Galerkin plus hyper-reduction, verified end to end ... The third Farhat gap. New rtx_fea::mor module: - pod::pod_basis — orthonormal SVD basis with an energy-criterion truncation. Verified: rank-2 data yields exactly 2 orthonormal modes that reconstruct every snapshot to machine precision; a loose tolerance truncates a dominant-mode-plus-noise set to one mode. - nnls — Lawson-Hanson non-negative least squares with the early stop that makes ECSW work: iteration ends at the requested residual, and the active-set structure caps the support at one column per outer iteration, so sparsity falls out of the stopping tolerance. Verified against KKT conditions, exact positive solutions, negative-clipping, and a sparsity-vs-tolerance case. Its thresholds are RELATIVE to the problem's own scales — the first version used absolute cutoffs (1e-14) that silently ended the iteration on ECSW's small-magnitude training systems at 1.2e-3 instead of the requested 1e-4. - ecsw::train_ecsw — element weights such that a small subset reproduces the reduced internal force (the virtual work against the basis) over the training snapshots. w = 1 solves the system exactly by construction, so it is always consistent; nonnegativity is what keeps a sampled element from producing energy. - reduced::ReducedNonlinearModel — Newton in POD coordinates, assembling either every element (POD-Galerkin) or the ECSW sample, on the same per-element force/tangent machinery the nonlinear analysis uses. End-to-end verification (tests/ecsw_mor.rs): a clamped nonlinear block, snapshots from a 4-point load sweep, evaluated at an UNSEEN load factor: POD modes: 2 ECSW sample: 5 of 24 elements training residual 2.2e-7 (requested 1e-4) error vs full solve: POD-Galerkin 3.09e-7, ECSW 3.08e-7 hyper-reduction cost (ECSW vs full ROM): 1.6e-8 And the assertion with the most teeth: the same 5 elements with their weights forced to 1 read a relative error of 1.22 — a completely wrong field — so the accuracy is carried by the WEIGHTS, not by the subset happening to be representative. Scope, stated plainly: geometrically linear, materially nonlinear, homogeneous Dirichlet only (no lifting); the basis lives on the free DOFs. 559 rtx-fea tests, 0 failing. Co-Authored-By: Claude Fable 5 <[email protected]>	2026-08-20 00:43:32 -07:00