Implicit solver: fem kernels (tet4/10, hex8, hex20), sparse Cholesky, block Lanczos, solve.* commands (M4) (#23)

* Renumber the layer table for solver crates: fem at L1, solver at L2, fsi at L3

L0 model -> L1 geometry, mesh, fem, decks, render -> L2 solver (explicit, lbm later)
-> L3 fsi (later) -> L4 doc -> L5 io -> L6 engine -> L7 ui-egui, mcp -> apps.
UI_MIN_LAYER moves to 7, the testkit sits above it.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* modelcraft-fem: element kernels for tet4, tet10, hex8 (full, incompatible modes), hex20 (full, reduced)

Shape functions, Gauss and conical-product quadrature, stiffness, consistent and HRZ-lumped
mass, body forces, consistent pressure loads on faces, integration-point stresses and their
least-squares extrapolation to nodes, isotropic and orthotropic elasticity. The element table is
one row per kind, so wedges, shells and beams are added locally.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* modelcraft-solver: linear static and frequency analysis with an analytic verification suite

Assembly from the resolved model on the node graph, boundary conditions by elimination,
consistent pressure, gravity and body-force loads, nested-dissection ordering, sparse up-looking
Cholesky with a factor-size cap, reactions, integration-point and nodal-averaged stresses, von
Mises; shift-invert block Lanczos with full reorthogonalization for natural modes, participation
and effective mass. ADR 0001 records the own-linear-algebra decision (determinism, wasm).

Verified against closed forms: displacement and traction patch tests for every element, cantilever
tip deflection (Timoshenko) with convergence rates, Lamé cylinder, Kirsch hole (Kt -> 3),
cantilever and free-free beam frequencies with six rigid-body modes.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Engine: solve.static, solve.frequency and solve.probe; results kept in the session

Results are stored per step, restored on a failed command and cleared when the model changes.
Caps (degrees of freedom, factor entries, Lanczos vectors) may only be lowered; hostile parameters
are tested against a solvable session.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* docs: implicit solver architecture, roadmap M4, parity and references

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* Simplify the solver: shared face integration, block assembly, cached extrapolation

- model: one face integrator (nodal::face_normal_weights) for tractions and pressures
- fem: mid-side tables from ElementKind::edges, orthotropic via inverse3, symmetric
  accumulation without a symmetrize pass, incompatible-mode recovery without K_uu, model's
  coordinate check, dead table rows removed
- solver: one pattern search per node pair (block, scalar and diagonal adds), extrapolation built
  once per element type, reactions from the prescribed rows only, matrices dropped after
  restriction, the free-body shift keyed on the factorization error, step selection in the solver,
  Error::Element naming the element
- engine: the solver owns the default step and the shift check; the model comparison runs once

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

* docs: results are stamped with the session revision

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01NmAttHhUZTokgPeEJia8sm

---------

Co-authored-by: jyviko <2501648+jyviko@users.noreply.github.com>
Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

docs/solvers/literature.md

@@ -953,3 +953,30 @@ the better pairing — this is why FSI should support both structure solvers.
    tagged as "benchmark", kept separate from the analytic suite).
 8. **Quad shell meshing is missing from the roadmap.** X5 needs quad-dominant surface meshes; without them shells
    run on tri3 (BLT has a triangular variant, less accurate). Flag for the roadmap.
+
+## Part G: Implicit solver (M4), as implemented
+
+The papers and books `modelcraft-fem` and `modelcraft-solver` are written from (cited again in
+the module docs):
+
+- Elements: O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu, *The Finite Element Method: Its Basis
+  and Fundamentals*, 7th ed., 2013; T. J. R. Hughes, *The Finite Element Method*, Dover 2000.
+- Incompatible modes: Wilson, Taylor, Doherty, Ghaboussi 1973; R. L. Taylor, P. J. Beresford,
+  E. L. Wilson, IJNME 10(6):1211–1219, 1976 (the det J₀/det J correction that passes the patch
+  test).
+- Tetrahedron quadrature: A. H. Stroud, *Approximate Calculation of Multiple Integrals*, 1971
+  (conical product rules).
+- Mass lumping: E. Hinton, T. Rock, O. C. Zienkiewicz, Earthquake Eng. Struct. Dyn.
+  4(3):245–249, 1976.
+- Stress extrapolation: E. Hinton, J. S. Campbell, IJNME 8(3):461–480, 1974.
+- Ordering: A. George, SIAM J. Numer. Anal. 10(2):345–363, 1973; H. D. Simon, Computing Systems
+  in Engineering 2:135–148, 1991.
+- Sparse Cholesky: T. A. Davis, *Direct Methods for Sparse Linear Systems*, SIAM 2006; J. W. H.
+  Liu, SIAM J. Matrix Anal. Appl. 11(1):134–172, 1990.
+- Eigenvalues: T. Ericsson, A. Ruhe, Math. Comp. 35(152):1251–1268, 1980; R. G. Grimes, J. G.
+  Lewis, H. D. Simon, SIAM J. Matrix Anal. Appl. 15(1):228–272, 1994; B. N. Parlett, *The
+  Symmetric Eigenvalue Problem*, SIAM 1998; G. H. Golub, C. F. Van Loan, *Matrix Computations*,
+  4th ed., 2013.
+- Verification: R. H. MacNeal, R. L. Harder, *A proposed standard set of problems to test finite
+  element accuracy*, Finite Elem. Anal. Des. 1(1):3–20, 1985 (patch tests); Lamé, Kirsch,
+  Timoshenko and Euler–Bernoulli closed forms.