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>

crates/fem/src/lib.rs

@@ -0,0 +1,48 @@
+//! Finite element kernels shared by ModelCraft's structural solvers.
+//!
+//! Pure functions over element geometry and material constants, with no solver loop and no
+//! global state, so the implicit solver (`modelcraft-solver`) and the explicit solver that follows
+//! it use the same element technology:
+//! - [`quadrature`]: Gauss–Legendre and tetrahedron rules;
+//! - [`shape`]: shape functions of tet4, tet10, hex8, hex20 and of their faces;
+//! - [`material`]: isotropic and orthotropic elasticity matrices, von Mises stress;
+//! - [`element`]: the element table, stiffness (full, reduced, incompatible modes), consistent
+//!   and lumped mass, body forces, integration-point stresses and their extrapolation to nodes;
+//! - [`face`]: consistent nodal forces of pressure on element faces;
+//! - [`dense`]: the small dense linear algebra inside an element.
+//!
+//! Conventions: three translational degrees of freedom per node, ordered node by node; stress
+//! and strain 6-vectors in the order xx, yy, zz, xy, xz, yz with engineering shear strains.
+#![deny(clippy::unwrap_used, clippy::expect_used, clippy::panic, clippy::unimplemented, clippy::todo, clippy::unreachable)]
+#![forbid(unsafe_code)]
+// Matrix kernels over fixed small dimensions read as the textbook formulas with index loops.
+#![allow(clippy::needless_range_loop)]
+
+pub mod dense;
+pub mod element;
+pub mod face;
+pub mod material;
+pub mod quadrature;
+pub mod shape;
+
+pub use element::{ELEMENT_TYPES, ElementType, Family, Formulation, PointStress, Solid, element_type};
+pub use material::{Elasticity, elasticity, von_mises};
+
+#[derive(Debug, Clone, PartialEq, thiserror::Error)]
+pub enum Error {
+    #[error("invalid input: {0}")]
+    Invalid(String),
+    #[error("not supported yet: {0}")]
+    NotSupported(String),
+    /// An element's geometry is inverted or collapsed.
+    #[error("{0}")]
+    Degenerate(String),
+    /// A matrix that must be positive definite is not.
+    #[error("{0}")]
+    Singular(String),
+}
+
+pub type Result<T> = std::result::Result<T, Error>;
+
+#[cfg(test)]
+mod tests;