fem: pyramid5 element (solver, quality, decks, VTK)

A five-node pyramid, the conforming transition between a hexahedron's face
and tetrahedra: Bedrosian's rational shape functions with a collapsed (Duffy)
Gauss rule, a certified Jacobian on the base square with exact volume, a
scaled Jacobian, C3D5 / CPYRAM / LS-DYNA degenerate solid, VTK_PYRAMID and
the binary mesh code 13. A distorted hex8-pyramid5-tet4 transition mesh
passes the patch test and uniaxial tension exactly.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

docs/elements.md

@@ -72,7 +72,8 @@ hex8/20/27 with first and second derivatives).
 | hex8 (full, incompatible modes), hex20 (full, reduced) | Structured and swept meshes | done |
 | wedge6 | Swept meshes from triangles, transitions | done |
 | hex8 one-point with hourglass control, nodal-pressure tet4 (explicit) | Explicit dynamics | done |
-| wedge15, pyramid5/13 | Quadratic transitions, tet–hex transition | planned (M5); wedge15 and pyramid5 shape functions done |
+| pyramid5 | Conforming tet–hex transition (a hexahedron's face to tetrahedra) | done (Bedrosian's rational functions, a collapsed 2 × 2 × 2 Gauss rule; C3D5, CPYRAM, LS-DYNA degenerate solid) |
+| wedge15, pyramid13 | Quadratic transitions | planned (M5); wedge15 shape functions done |
 | Hybrid (mixed u–p) solids | Nearly incompressible materials (rubber) | done for hex8 (constant pressure), hex20 (linear pressure) and tet10 (constant pressure), discontinuous pressure condensed, isotropic materials; tet4/wedge6 refused (they lock); continuous-pressure (Taylor–Hood) elements planned with an indefinite factorization |
 | Modified quadratic tet (tet10 for contact/plasticity) | Robust quadratic tets | planned |
 

docs/fem.md

@@ -76,7 +76,8 @@ rational pyramid, 2 for the quadratic ones).
 Evaluation at a natural point `xi: [f64; 3]` (unused coordinates are zero):
 
 - `eval(xi) -> Shape`: values `n` and first derivatives `dn[i] = ∂Nᵢ/∂(ξ, η, ζ)`. tet4, tet10,
-  wedge6, hex8, hex20 use the hand-written functions of `shape.rs` (the solid kernels' path).
+  wedge6, hex8, hex20 use the hand-written functions of `shape.rs` (the solid kernels' path);
+  the solid kernel's pyramid5 uses this module's.
 - `eval2(xi) -> Shape2`: adds `d2n[i][a][b] = ∂²Nᵢ/∂ξₐ∂ξ_b`, from second-order forward-mode
   automatic differentiation of the same formulas (`jet::Jet`): exact to round-off.
 - `gradients(&shape, xyz) -> Gradients`: physical `dx[i] = ∇ₓNᵢ = J⁻¹ ∇_ξNᵢ` and `det J`, with

docs/formats/fieldcraft.md

@@ -61,7 +61,7 @@ tagged nodes × { u32 node, u32 tag }
 ```
 
 Element kind codes: 1 rod2, 2 beam2, 3 tri3, 4 tri6, 5 quad4, 6 quad8, 7 tet4, 8 tet10, 9 wedge6,
-10 hex8, 11 hex20. Node order is the model's (Abaqus/VTK). A tag indexes the entity list, which
+10 hex8, 11 hex20, 12 rod3, 13 pyramid5. Node order is the model's (Abaqus/VTK). A tag indexes the entity list, which
 lists each geometry entity once. Coordinates keep every bit (signed zero included).
 
 ## Reading a file safely