FEM foundation A: DofKind/DofLayout, shape-function library with Hessians, solvers on DofLayout (#35)

* fem: DofKind/DofLayout and the shape-function library with second derivatives

DofKind (Ux..Rz, T, P), DofSet, ElementDofs (per-node kinds and condensed
internal unknowns) and DofLayout: mesh nodes by label, kinds in order, then
reference points. basis::Basis covers line2/3, tri3/6, quad4/8/9, tet4/10,
wedge6/15, pyramid5, hex8/20/27 with values, first and second natural
derivatives (second-order forward AD, fem::jet) and the physical gradients,
Hessians and Laplacians with the map's second-derivative term. Tested for
Kronecker delta, partition of unity, polynomial completeness, finite
differences, affine and curved maps.

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

* solver, explicit: number degrees of freedom with DofLayout

The implicit mesh numbers its unknowns with a DofLayout (mesh nodes by label
with the kinds their elements declare, then six per coupled reference point);
assembly adds element blocks by (node, DofKind), so a node may carry any mix
of kinds; couplings, boundary conditions, loads and results address
(node, kind). The explicit system keeps node-major translations, now checked
against its layout (NODE_DOFS). Solid formulations declare their ElementDofs.

Every static, frequency and explicit result of the solver, explicit, engine
and io test suites hashes bit-identically before and after (957 results).
docs/fem.md describes the DOF model and the shape-function conventions.

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

* fem, solver: simplify after review

Block offsets resolved once per node pair; add_scalar/add_diagonal take
the kinds like add_block; one checked Jacobian inverse (dense::positive_inverse)
for the solid kernels and the basis library; static natural-node tables; the
Hessian path inverts the Jacobian once.

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/explicit/src/elements.rs

@@ -38,7 +38,7 @@ use modelcraft_fem::material::stress;
 use modelcraft_fem::uniform::UniformStrain;
 use modelcraft_model::{BulkViscosity, HourglassKind};
 
-use crate::system::{Material, System};
+use crate::system::{Material, NODE_DOFS, System};
 
 /// Scratch vectors and the element state of the latest evaluation.
 #[derive(Debug, Clone)]
@@ -82,13 +82,13 @@ impl Workspace {
 }
 
 pub(crate) fn gather<const N: usize>(x: &[f64], nodes: &[usize; N]) -> [[f64; 3]; N] {
-    nodes.map(|n| [0, 1, 2].map(|k| x.get(3 * n + k).copied().unwrap_or(0.0)))
+    nodes.map(|n| [0, 1, 2].map(|k| x.get(NODE_DOFS * n + k).copied().unwrap_or(0.0)))
 }
 
 /// Add a node's vector into a per-degree-of-freedom vector.
 pub(crate) fn add_at(f: &mut [f64], node: usize, v: &[f64; 3]) {
     for (k, c) in v.iter().enumerate() {
-        if let Some(x) = f.get_mut(3 * node + k) {
+        if let Some(x) = f.get_mut(NODE_DOFS * node + k) {
             *x += c;
         }
     }