feat(basis): Add basis_descriptions.jl catalog for code generation

Create centralized catalog of 14 basis element descriptions for automatic code generation. Each description specifies: - Topology type (Segment, Triangle, Quadrilateral, Tetrahedron, Hexahedron, etc.) - Basis family (Lagrange{order}, Serendipity{order}) - Polynomial ansatz for Vandermonde system Covers standard finite elements: - 1D: Seg2, Seg3 - 2D: Tri3, Tri6, Quad4, Quad8, Quad9 - 3D: Tet4, Tet10, Hex8, Hex20, Hex27, Pyr5, Wedge6 Uses canonical topology types (Triangle{3}, Quadrilateral{9}) instead of legacy aliases (Tri3, Quad9) for clarity and consistency.
2026-09-21 02:18:56 +00:00 · 2025-11-22 12:06:40 +02:00
parent df449f23df
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+# Catalog of basis descriptions used by the generator.
+#
+# Each entry provides:
+# - name: legacy short name (e.g., "Tri3")
+# - description: human-readable text
+# - topology: reference topology type (with node count parameter)
+# - basis: basis family and order (Lagrange{P}, Serendipity{P}, etc.)
+# - ansatz: polynomial terms used to build the Vandermonde system
+
+const BASIS_DESCRIPTIONS = VandermondeBasisDescription[]
+
+# 1D SEGMENTS
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Seg2",
+    description="2-node linear segment element",
+    family=Lagrange{1},
+    topology=Segment{2},
+    ansatz=(:(1), :(u))
+))
+
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Seg3",
+    description="3-node quadratic segment element",
+    family=Lagrange{2},
+    topology=Segment{3},
+    ansatz=(:(1), :(u), :(u^2))
+))
+
+# 2D TRIANGLES
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Tri3",
+    description="3-node linear triangular element",
+    family=Lagrange{1},
+    topology=Triangle{3},
+    ansatz=(:(1), :(u), :(v))
+))
+
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Tri6",
+    description="6-node quadratic triangular element",
+    family=Lagrange{2},
+    topology=Triangle{6},
+    ansatz=(:(1), :(u), :(v), :(u^2), :(u * v), :(v^2))
+))
+
+# 2D QUADS
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Quad4",
+    description="4-node bilinear quadrilateral element",
+    family=Lagrange{1},
+    topology=Quadrilateral{4},
+    ansatz=(:(1), :(u), :(v), :(u * v))
+))
+
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Quad8",
+    description="8-node serendipity quadrilateral element",
+    family=Serendipity{2},
+    topology=Quadrilateral{8},
+    ansatz=(:(1), :(u), :(v), :(u^2), :(u * v), :(v^2), :(u^2 * v), :(u * v^2))
+))
+
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Quad9",
+    description="9-node biquadratic quadrilateral element",
+    family=Lagrange{2},
+    topology=Quadrilateral{9},
+    ansatz=(:(1), :(u), :(v), :(u^2), :(u * v), :(v^2), :(u^2 * v), :(u * v^2), :(u^2 * v^2))
+))
+
+# 3D TETS
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Tet4",
+    description="4-node linear tetrahedral element",
+    family=Lagrange{1},
+    topology=Tetrahedron{4},
+    ansatz=(:(1), :(u), :(v), :(w))
+))
+
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Tet10",
+    description="10-node quadratic tetrahedral element",
+    family=Lagrange{2},
+    topology=Tetrahedron{10},
+    ansatz=(:(1), :(u), :(v), :(w), :(u^2), :(v^2), :(w^2), :(u * v), :(u * w), :(v * w))
+))
+
+# 3D HEXES
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Hex8",
+    description="8-node trilinear hexahedral element",
+    family=Lagrange{1},
+    topology=Hexahedron{8},
+    ansatz=(:(1), :(u), :(v), :(w), :(u * v), :(u * w), :(v * w), :(u * v * w))
+))
+
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Hex20",
+    description="20-node serendipity hexahedral element",
+    family=Serendipity{2},
+    topology=Hexahedron{20},
+    ansatz=(
+        :(1), :(u), :(v), :(w),
+        :(u * v), :(u * w), :(v * w),
+        :(u^2), :(v^2), :(w^2),
+        :(u^2 * v), :(u * v^2), :(u^2 * w), :(u * w^2), :(v^2 * w), :(v * w^2)
+    )
+))
+
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Hex27",
+    description="27-node triquadratic hexahedral element",
+    family=Lagrange{2},
+    topology=Hexahedron{27},
+    ansatz=(
+        :(1), :(u), :(v), :(w),
+        :(u^2), :(v^2), :(w^2),
+        :(u * v), :(u * w), :(v * w),
+        :(u^2 * v), :(u * v^2), :(u^2 * w), :(u * w^2), :(v^2 * w), :(v * w^2),
+        :(u^2 * v^2), :(u^2 * w^2), :(v^2 * w^2),
+        :(u^2 * v * w), :(u * v^2 * w), :(u * v * w^2), :(u^2 * v^2 * w^2)
+    )
+))
+
+# 3D PYRAMID
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Pyr5",
+    description="5-node linear pyramid element",
+    family=Lagrange{1},
+    topology=Pyramid{5},
+    ansatz=(:(1), :(u), :(v), :(w))
+))
+
+# 3D WEDGE / PRISM
+push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+    name="Wedge6",
+    description="6-node linear wedge (prism) element",
+    family=Lagrange{1},
+    topology=Wedge{6},
+    ansatz=(:(1), :(u), :(v), :(w), :(u * w), :(v * w))
+))
+
+# TODO: Wedge15 ansatz needs proper polynomial basis for triangular prism
+# The standard Lagrange tensor product doesn't work - need special formulation
+# push!(BASIS_DESCRIPTIONS, VandermondeBasisDescription(
+#     name="Wedge15",
+#     description="15-node quadratic wedge (prism) element",
+#     family=Lagrange{2},
+#     topology=Wedge{15},
+#     ansatz=(
+#         :(1), :(u), :(v), :(w),
+#         :(u^2), :(v^2), :(w^2), :(u * v), :(u * w), :(v * w),
+#         :(u^2 * w), :(v^2 * w), :(u * v * w), :(u^2 * v), :(u * v^2)
+#     )
+# ))