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]>

crates/specialized/rtx-fea/src/mor/mod.rs

@@ -0,0 +1,29 @@
+//! Model-order reduction: POD-Galerkin projection with ECSW hyper-reduction.
+//!
+//! The pipeline, all offline steps verified by their own invariants:
+//!
+//! 1. Collect full-order solution snapshots (the caller's job — typically a
+//!    parameter or load sweep of [`crate::analysis::NonlinearStaticAnalysis`]).
+//! 2. [`pod::pod_basis`] — orthonormal basis by SVD, truncated at an energy
+//!    criterion.
+//! 3. [`ecsw::train_ecsw`] — nonnegative element weights so that a small
+//!    element subset reproduces the reduced internal force over the
+//!    training set ([`nnls`] with an early stop; sparsity comes from the
+//!    stopping tolerance).
+//! 4. [`reduced::ReducedNonlinearModel`] — Newton in reduced coordinates,
+//!    assembling only the sampled elements.
+//!
+//! Scope: geometrically linear, materially nonlinear (what the nonlinear
+//! analysis supports), homogeneous Dirichlet data. Lifting for
+//! inhomogeneous boundary values is not implemented and the basis is over
+//! the free DOFs only.
+
+pub mod ecsw;
+pub mod nnls;
+pub mod pod;
+pub mod reduced;
+
+pub use ecsw::{EcswModel, train_ecsw};
+pub use nnls::nnls;
+pub use pod::pod_basis;
+pub use reduced::ReducedNonlinearModel;