Implicit solver: reference points, couplings, moments, wedge6 (M4) (#26)

* fem: wedge6 element (triangle × interval, 3 × 2 points), patch and cantilever tests

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

* solver: reference points, kinematic and distributing couplings, moments by constraint elimination

Coupled reference points get six degrees of freedom; kinematic couplings are rigid
links, distributing couplings least-squares interpolation constraints. Every
constraint row and prescribed value is eliminated master-slave (Abel-Shephard
pivot choice), so the reduced matrix stays SPD; no coupling gives the old
elimination bit for bit. Verified: rigid motion of a coupled block, clamping
through a point, distributing tension vs pressure, bending and tube torsion.

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

* engine: reference point results in solve.static and solve.probe

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

* docs: couplings, moments and wedge6 in the solver docs, literature and roadmap

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

* solver: simplify constraint elimination and reference point plumbing

Rows combine by one sort; T_f transposed once; K and M reduced in one pass on a
shared pattern; prescribed motion computed once; reference point loads and BCs go
through Resolved like node ones (Mesh::label_dofs); one dof-direction rule;
StepResult::locate for probes; dead Csr::restrict removed.

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

* solver: refuse oversized reductions before allocating them

A held distributing coupling point makes a dense (3N)^2 block; estimate it from
the constraint rows and refuse it against the factorization's memory budget
with a clear message, before anything is built. Other reductions with
dependents count their entries first (stopping at the budget) and reserve
fallibly.

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/element.rs

@@ -7,7 +7,8 @@
 //!
 //! Formulations:
 //! - **full integration**: the rule that integrates the stiffness of an undistorted element
-//!   exactly (1 point for tet4, 4 for tet10, 2 × 2 × 2 for hex8, 3 × 3 × 3 for hex20);
+//!   exactly (1 point for tet4, 4 for tet10, 3 triangle points × 2 for wedge6, 2 × 2 × 2 for
+//!   hex8, 3 × 3 × 3 for hex20);
 //! - **reduced integration** for hex20 (2 × 2 × 2), which avoids locking at the cost of one
 //!   spurious mode that a mesh of more than one element restrains. Reduced hex8 needs hourglass
 //!   control and is not offered here yet (it arrives with the explicit solver, Flanagan &
@@ -43,6 +44,7 @@ use crate::{Error, Result};
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
 pub enum Family {
     Tetrahedron,
+    Wedge,
     Hexahedron,
 }
 
@@ -67,7 +69,7 @@ pub struct ElementType {
 }
 
 /// The element table.
-pub static ELEMENT_TYPES: [ElementType; 4] = [
+pub static ELEMENT_TYPES: [ElementType; 5] = [
     ElementType {
         kind: ElementKind::Tet4,
         family: Family::Tetrahedron,
@@ -90,6 +92,17 @@ pub static ELEMENT_TYPES: [ElementType; 4] = [
         mass: Rule::TetConical(4),
         incompatible_modes: false,
     },
+    ElementType {
+        kind: ElementKind::Wedge6,
+        family: Family::Wedge,
+        nodes: 6,
+        corners: 6,
+        shape: shape::wedge6,
+        full: Rule::Wedge,
+        reduced: None,
+        mass: Rule::Wedge,
+        incompatible_modes: false,
+    },
     ElementType {
         kind: ElementKind::Hex8,
         family: Family::Hexahedron,
@@ -119,7 +132,7 @@ pub fn element_type(kind: ElementKind) -> Result<&'static ElementType> {
     ELEMENT_TYPES
         .iter()
         .find(|t| t.kind == kind)
-        .ok_or_else(|| Error::NotSupported(format!("{} elements (the solver has tet4, tet10, hex8 and hex20 so far)", kind.name())))
+        .ok_or_else(|| Error::NotSupported(format!("{} elements (the solver has tet4, tet10, wedge6, hex8 and hex20 so far)", kind.name())))
 }
 
 /// How a solid element is formulated.
@@ -565,6 +578,7 @@ pub fn extrapolation(ty: &ElementType, rule: Rule) -> Result<Extrapolation> {
     let c = ty.corners;
     let corner_basis = |xi: [f64; 3]| match ty.family {
         Family::Tetrahedron => shape::tet4(xi),
+        Family::Wedge => shape::wedge6(xi),
         Family::Hexahedron => shape::hex8(xi),
     };
     let mut corner_rows = vec![0.0; c * g];