mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-11 14:11:55 +00:00
Jukka Aho
5248f6e470
Regenerate src/basis/lagrange_generated.jl with updated generator. Changes: - Remove deprecated eval_basis!() and eval_dbasis!() functions (OLD API) - Keep NEW API: get_basis_functions() and get_basis_derivatives() - Add node count to element comments (e.g., "Seg2, 2 nodes") - Update generation timestamp: 2025-11-13 02:42:16 This is auto-generated code from src/basis/lagrange_generator.jl. The old API functions are no longer needed as all code now uses the NEW API (Topology + Basis separation). Generated: 594 line changes across all 15 Lagrange element types (Seg2, Seg3, Tri3, Tri6, Tri7, Quad4, Quad8, Quad9, Tet4, Tet10, Hex8, Hex20, Hex27, Wedge6, Wedge15).
452 lines
131 KiB
Julia
452 lines
131 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE
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# ============================================================================
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# AUTO-GENERATED LAGRANGE BASIS FUNCTIONS
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# ============================================================================
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#
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# WARNING: DO NOT EDIT THIS FILE MANUALLY!
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#
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# This file was automatically generated by:
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# julia --project=. src/basis/lagrange_generator.jl
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#
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# To regenerate (e.g., after adding new element types):
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# cd /path/to/JuliaFEM.jl
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# julia --project=. src/basis/lagrange_generator.jl
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#
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# Theory:
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# See docs/book/lagrange_basis_functions.md
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#
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# Generator:
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# src/basis/lagrange_generator.jl (symbolic engine)
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#
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# Generated: 2025-11-13 02:42:16
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# ============================================================================
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# This file generates methods for Lagrange{T,P} where:
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# T = topology type (Segment, Triangle, Quadrilateral, etc.)
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# P = polynomial degree (1, 2, 3, ...)
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#
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# Example: Lagrange{Triangle, 2} is a quadratic triangular element
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Segment, 1}: 2-node linear segment element
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# (Old name: Seg2, 2 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Segment, 1}})
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return (Vec{1, Float64}(tuple(-1.0)), Vec{1, Float64}(tuple(1.0)))
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end
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function get_reference_element_coordinates(::Lagrange{Segment, 1})
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return (Vec{1, Float64}(tuple(-1.0)), Vec{1, Float64}(tuple(1.0)))
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end
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@inline function get_basis_functions(::Type{Segment}, ::Type{Lagrange{Segment, 1}}, xi::Vec)
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(u,) = xi
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@inbounds return (0.5 + -0.5u, 0.5 + 0.5u)
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end
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@inline function get_basis_functions(::Segment, ::Lagrange{Segment, 1}, xi::Vec)
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(u,) = xi
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@inbounds return (0.5 + -0.5u, 0.5 + 0.5u)
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end
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@inline function get_basis_derivatives(::Type{Segment}, ::Type{Lagrange{Segment, 1}}, xi::Vec)
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(u,) = xi
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@inbounds return (Vec(float.(tuple(-0.5))), Vec(float.(tuple(0.5))))
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end
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@inline function get_basis_derivatives(::Segment, ::Lagrange{Segment, 1}, xi::Vec)
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(u,) = xi
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@inbounds return (Vec(float.(tuple(-0.5))), Vec(float.(tuple(0.5))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Segment, 2}: 3-node quadratic segment element
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# (Old name: Seg3, 3 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Segment, 2}})
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return (Vec{1, Float64}(tuple(-1.0)), Vec{1, Float64}(tuple(1.0)), Vec{1, Float64}(tuple(0.0)))
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end
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function get_reference_element_coordinates(::Lagrange{Segment, 2})
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return (Vec{1, Float64}(tuple(-1.0)), Vec{1, Float64}(tuple(1.0)), Vec{1, Float64}(tuple(0.0)))
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end
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@inline function get_basis_functions(::Type{Segment}, ::Type{Lagrange{Segment, 2}}, xi::Vec)
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(u,) = xi
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@inbounds return (-0.5u + 0.5 * u ^ 2, 0.5u + 0.5 * u ^ 2, 1 + -1.0 * u ^ 2)
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end
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@inline function get_basis_functions(::Segment, ::Lagrange{Segment, 2}, xi::Vec)
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(u,) = xi
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@inbounds return (-0.5u + 0.5 * u ^ 2, 0.5u + 0.5 * u ^ 2, 1 + -1.0 * u ^ 2)
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end
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@inline function get_basis_derivatives(::Type{Segment}, ::Type{Lagrange{Segment, 2}}, xi::Vec)
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(u,) = xi
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@inbounds return (Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1))))))
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end
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@inline function get_basis_derivatives(::Segment, ::Lagrange{Segment, 2}, xi::Vec)
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(u,) = xi
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@inbounds return (Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1))))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Triangle, 1}: 3-node linear triangular element
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# (Old name: Tri3, 3 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Triangle, 1}})
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return (Vec{2, Float64}(tuple(0.0, 0.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)))
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end
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function get_reference_element_coordinates(::Lagrange{Triangle, 1})
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return (Vec{2, Float64}(tuple(0.0, 0.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)))
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end
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@inline function get_basis_functions(::Type{Triangle}, ::Type{Lagrange{Triangle, 1}}, xi::Vec)
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(u, v) = xi
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@inbounds return (1 + -1.0u + -1.0v, +u, +v)
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end
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@inline function get_basis_functions(::Triangle, ::Lagrange{Triangle, 1}, xi::Vec)
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(u, v) = xi
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@inbounds return (1 + -1.0u + -1.0v, +u, +v)
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end
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@inline function get_basis_derivatives(::Type{Triangle}, ::Type{Lagrange{Triangle, 1}}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(-1.0, -1.0))), Vec(float.(tuple(1, 0))), Vec(float.(tuple(0, 1))))
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end
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@inline function get_basis_derivatives(::Triangle, ::Lagrange{Triangle, 1}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(-1.0, -1.0))), Vec(float.(tuple(1, 0))), Vec(float.(tuple(0, 1))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Triangle, 2}: 6-node quadratic triangular element
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# (Old name: Tri6, 6 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Triangle, 2}})
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return (Vec{2, Float64}(tuple(0.0, 0.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(0.5, 0.0)), Vec{2, Float64}(tuple(0.5, 0.5)), Vec{2, Float64}(tuple(0.0, 0.5)))
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end
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function get_reference_element_coordinates(::Lagrange{Triangle, 2})
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return (Vec{2, Float64}(tuple(0.0, 0.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(0.5, 0.0)), Vec{2, Float64}(tuple(0.5, 0.5)), Vec{2, Float64}(tuple(0.0, 0.5)))
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end
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@inline function get_basis_functions(::Type{Triangle}, ::Type{Lagrange{Triangle, 2}}, xi::Vec)
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(u, v) = xi
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@inbounds return (1 + -3.0u + -3.0v + 2.0 * u ^ 2 + 4.0 * (u * v) + 2.0 * v ^ 2, -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v), +(4.0 * (u * v)), 4.0v + -4.0 * (u * v) + -4.0 * v ^ 2)
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end
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@inline function get_basis_functions(::Triangle, ::Lagrange{Triangle, 2}, xi::Vec)
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(u, v) = xi
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@inbounds return (1 + -3.0u + -3.0v + 2.0 * u ^ 2 + 4.0 * (u * v) + 2.0 * v ^ 2, -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v), +(4.0 * (u * v)), 4.0v + -4.0 * (u * v) + -4.0 * v ^ 2)
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end
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@inline function get_basis_derivatives(::Type{Triangle}, ::Type{Lagrange{Triangle, 2}}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v, -3.0 + 4.0u + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v, -4.0u))), Vec(float.(tuple(4.0v, 4.0u))), Vec(float.(tuple(-4.0v, 4.0 + -4.0u + -4.0 * (2 * v ^ (2 - 1))))))
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end
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@inline function get_basis_derivatives(::Triangle, ::Lagrange{Triangle, 2}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v, -3.0 + 4.0u + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v, -4.0u))), Vec(float.(tuple(4.0v, 4.0u))), Vec(float.(tuple(-4.0v, 4.0 + -4.0u + -4.0 * (2 * v ^ (2 - 1))))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Quadrilateral, 1}: 4-node bilinear quadrilateral element
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# (Old name: Quad4, 4 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Quadrilateral, 1}})
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return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)))
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end
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function get_reference_element_coordinates(::Lagrange{Quadrilateral, 1})
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return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)))
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end
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@inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 1}}, xi::Vec)
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(u, v) = xi
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@inbounds return (0.25 + -0.25u + -0.25v + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25 * (u * v))
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end
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@inline function get_basis_functions(::Quadrilateral, ::Lagrange{Quadrilateral, 1}, xi::Vec)
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(u, v) = xi
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@inbounds return (0.25 + -0.25u + -0.25v + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25 * (u * v))
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end
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@inline function get_basis_derivatives(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 1}}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u))))
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end
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@inline function get_basis_derivatives(::Quadrilateral, ::Lagrange{Quadrilateral, 1}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Quadrilateral, 2}: 8-node serendipity quadrilateral element
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# (Old name: Quad8, 8 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Quadrilateral, 2}})
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return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)), Vec{2, Float64}(tuple(0.0, -1.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 0.0)))
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end
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function get_reference_element_coordinates(::Lagrange{Quadrilateral, 2})
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return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)), Vec{2, Float64}(tuple(0.0, -1.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 0.0)))
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end
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@inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
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(u, v) = xi
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@inbounds return (-0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), 0.5 + -0.5v + -0.5 * u ^ 2 + 0.5 * (u ^ 2 * v), 0.5 + 0.5u + -0.5 * v ^ 2 + -0.5 * (u * v ^ 2), 0.5 + 0.5v + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * v), 0.5 + -0.5u + -0.5 * v ^ 2 + 0.5 * (u * v ^ 2))
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end
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@inline function get_basis_functions(::Quadrilateral, ::Lagrange{Quadrilateral, 2}, xi::Vec)
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(u, v) = xi
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@inbounds return (-0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + 0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2), -0.25 + 0.25 * u ^ 2 + -0.25 * (u * v) + 0.25 * v ^ 2 + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2), 0.5 + -0.5v + -0.5 * u ^ 2 + 0.5 * (u ^ 2 * v), 0.5 + 0.5u + -0.5 * v ^ 2 + -0.5 * (u * v ^ 2), 0.5 + 0.5v + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * v), 0.5 + -0.5u + -0.5 * v ^ 2 + 0.5 * (u * v ^ 2))
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end
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@inline function get_basis_derivatives(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + 0.5 * ((2 * u ^ (2 - 1)) * v), -0.5 + 0.5 * u ^ 2))), Vec(float.(tuple(0.5 + -0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + -0.5 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + -0.5 * ((2 * u ^ (2 - 1)) * v), 0.5 + -0.5 * u ^ 2))), Vec(float.(tuple(-0.5 + 0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + 0.5 * (u * (2 * v ^ (2 - 1)))))))
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end
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@inline function get_basis_derivatives(::Quadrilateral, ::Lagrange{Quadrilateral, 2}, xi::Vec)
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(u, v) = xi
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@inbounds return (Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + 0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2, 0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25 * (2 * u ^ (2 - 1)) + -0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2, -0.25u + 0.25 * (2 * v ^ (2 - 1)) + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + 0.5 * ((2 * u ^ (2 - 1)) * v), -0.5 + 0.5 * u ^ 2))), Vec(float.(tuple(0.5 + -0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + -0.5 * (u * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * (2 * u ^ (2 - 1)) + -0.5 * ((2 * u ^ (2 - 1)) * v), 0.5 + -0.5 * u ^ 2))), Vec(float.(tuple(-0.5 + 0.5 * v ^ 2, -0.5 * (2 * v ^ (2 - 1)) + 0.5 * (u * (2 * v ^ (2 - 1)))))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Quadrilateral, 2}: 9-node biquadratic quadrilateral element
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# (Old name: Quad9, 9 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Quadrilateral, 2}})
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return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)), Vec{2, Float64}(tuple(0.0, -1.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 0.0)))
|
|
end
|
|
function get_reference_element_coordinates(::Lagrange{Quadrilateral, 2})
|
|
return (Vec{2, Float64}(tuple(-1.0, -1.0)), Vec{2, Float64}(tuple(1.0, -1.0)), Vec{2, Float64}(tuple(1.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 1.0)), Vec{2, Float64}(tuple(0.0, -1.0)), Vec{2, Float64}(tuple(1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 1.0)), Vec{2, Float64}(tuple(-1.0, 0.0)), Vec{2, Float64}(tuple(0.0, 0.0)))
|
|
end
|
|
@inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
|
|
(u, v) = xi
|
|
@inbounds return (0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + u ^ 2 * v ^ 2)
|
|
end
|
|
@inline function get_basis_functions(::Quadrilateral, ::Lagrange{Quadrilateral, 2}, xi::Vec)
|
|
(u, v) = xi
|
|
@inbounds return (0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (u * v ^ 2) + -0.5 * (u ^ 2 * v ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + u ^ 2 * v ^ 2)
|
|
end
|
|
@inline function get_basis_derivatives(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
|
|
(u, v) = xi
|
|
@inbounds return (Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2, -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1))))))
|
|
end
|
|
@inline function get_basis_derivatives(::Quadrilateral, ::Lagrange{Quadrilateral, 2}, xi::Vec)
|
|
(u, v) = xi
|
|
@inbounds return (Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * (u * (2 * v ^ (2 - 1))) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), -0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2), 0.5 * (u * (2 * v ^ (2 - 1))) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2, -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1))))))
|
|
end
|
|
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
# Lagrange{Tetrahedron{4}, 1}: 4-node linear tetrahedral element
|
|
# (Old name: Tet4, 4 nodes)
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
|
|
function get_reference_element_coordinates(::Type{Lagrange{Tetrahedron{4}, 1}})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)))
|
|
end
|
|
function get_reference_element_coordinates(::Lagrange{Tetrahedron{4}, 1})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)))
|
|
end
|
|
@inline function get_basis_functions(::Type{Tetrahedron{4}}, ::Type{Lagrange{Tetrahedron{4}, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (1 + -1.0u + -1.0v + -1.0w, +u, +v, +w)
|
|
end
|
|
@inline function get_basis_functions(::Tetrahedron{4}, ::Lagrange{Tetrahedron{4}, 1}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (1 + -1.0u + -1.0v + -1.0w, +u, +v, +w)
|
|
end
|
|
@inline function get_basis_derivatives(::Type{Tetrahedron{4}}, ::Type{Lagrange{Tetrahedron{4}, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-1.0, -1.0, -1.0))), Vec(float.(tuple(1, 0, 0))), Vec(float.(tuple(0, 1, 0))), Vec(float.(tuple(0, 0, 1))))
|
|
end
|
|
@inline function get_basis_derivatives(::Tetrahedron{4}, ::Lagrange{Tetrahedron{4}, 1}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-1.0, -1.0, -1.0))), Vec(float.(tuple(1, 0, 0))), Vec(float.(tuple(0, 1, 0))), Vec(float.(tuple(0, 0, 1))))
|
|
end
|
|
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
# Lagrange{Tetrahedron{10}, 2}: 10-node quadratic tetrahedral element
|
|
# (Old name: Tet10, 10 nodes)
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
|
|
function get_reference_element_coordinates(::Type{Lagrange{Tetrahedron{10}, 2}})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.0, 0.0)), Vec{3, Float64}(tuple(0.5, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.5)), Vec{3, Float64}(tuple(0.5, 0.0, 0.5)), Vec{3, Float64}(tuple(0.0, 0.5, 0.5)))
|
|
end
|
|
function get_reference_element_coordinates(::Lagrange{Tetrahedron{10}, 2})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.0, 0.0)), Vec{3, Float64}(tuple(0.5, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.5, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.5)), Vec{3, Float64}(tuple(0.5, 0.0, 0.5)), Vec{3, Float64}(tuple(0.0, 0.5, 0.5)))
|
|
end
|
|
@inline function get_basis_functions(::Type{Tetrahedron{10}}, ::Type{Lagrange{Tetrahedron{10}, 2}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (1 + -3.0u + -3.0v + -3.0w + 2.0 * u ^ 2 + 2.0 * v ^ 2 + 2.0 * w ^ 2 + 4.0 * (u * v) + 4.0 * (u * w) + 4.0 * (v * w), -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, -1.0w + 2.0 * w ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v) + -4.0 * (u * w), +(4.0 * (u * v)), 4.0v + -4.0 * v ^ 2 + -4.0 * (u * v) + -4.0 * (v * w), 4.0w + -4.0 * w ^ 2 + -4.0 * (u * w) + -4.0 * (v * w), +(4.0 * (u * w)), +(4.0 * (v * w)))
|
|
end
|
|
@inline function get_basis_functions(::Tetrahedron{10}, ::Lagrange{Tetrahedron{10}, 2}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (1 + -3.0u + -3.0v + -3.0w + 2.0 * u ^ 2 + 2.0 * v ^ 2 + 2.0 * w ^ 2 + 4.0 * (u * v) + 4.0 * (u * w) + 4.0 * (v * w), -1.0u + 2.0 * u ^ 2, -1.0v + 2.0 * v ^ 2, -1.0w + 2.0 * w ^ 2, 4.0u + -4.0 * u ^ 2 + -4.0 * (u * v) + -4.0 * (u * w), +(4.0 * (u * v)), 4.0v + -4.0 * v ^ 2 + -4.0 * (u * v) + -4.0 * (v * w), 4.0w + -4.0 * w ^ 2 + -4.0 * (u * w) + -4.0 * (v * w), +(4.0 * (u * w)), +(4.0 * (v * w)))
|
|
end
|
|
@inline function get_basis_derivatives(::Type{Tetrahedron{10}}, ::Type{Lagrange{Tetrahedron{10}, 2}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v + 4.0w, -3.0 + 2.0 * (2 * v ^ (2 - 1)) + 4.0u + 4.0w, -3.0 + 2.0 * (2 * w ^ (2 - 1)) + 4.0u + 4.0v))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0, 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1)), 0))), Vec(float.(tuple(0, 0, -1.0 + 2.0 * (2 * w ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v + -4.0w, -4.0u, -4.0u))), Vec(float.(tuple(4.0v, 4.0u, 0))), Vec(float.(tuple(-4.0v, 4.0 + -4.0 * (2 * v ^ (2 - 1)) + -4.0u + -4.0w, -4.0v))), Vec(float.(tuple(-4.0w, -4.0w, 4.0 + -4.0 * (2 * w ^ (2 - 1)) + -4.0u + -4.0v))), Vec(float.(tuple(4.0w, 0, 4.0u))), Vec(float.(tuple(0, 4.0w, 4.0v))))
|
|
end
|
|
@inline function get_basis_derivatives(::Tetrahedron{10}, ::Lagrange{Tetrahedron{10}, 2}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-3.0 + 2.0 * (2 * u ^ (2 - 1)) + 4.0v + 4.0w, -3.0 + 2.0 * (2 * v ^ (2 - 1)) + 4.0u + 4.0w, -3.0 + 2.0 * (2 * w ^ (2 - 1)) + 4.0u + 4.0v))), Vec(float.(tuple(-1.0 + 2.0 * (2 * u ^ (2 - 1)), 0, 0))), Vec(float.(tuple(0, -1.0 + 2.0 * (2 * v ^ (2 - 1)), 0))), Vec(float.(tuple(0, 0, -1.0 + 2.0 * (2 * w ^ (2 - 1))))), Vec(float.(tuple(4.0 + -4.0 * (2 * u ^ (2 - 1)) + -4.0v + -4.0w, -4.0u, -4.0u))), Vec(float.(tuple(4.0v, 4.0u, 0))), Vec(float.(tuple(-4.0v, 4.0 + -4.0 * (2 * v ^ (2 - 1)) + -4.0u + -4.0w, -4.0v))), Vec(float.(tuple(-4.0w, -4.0w, 4.0 + -4.0 * (2 * w ^ (2 - 1)) + -4.0u + -4.0v))), Vec(float.(tuple(4.0w, 0, 4.0u))), Vec(float.(tuple(0, 4.0w, 4.0v))))
|
|
end
|
|
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
# Lagrange{Hexahedron{8}, 1}: 8-node trilinear hexahedral element
|
|
# (Old name: Hex8, 8 nodes)
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
|
|
function get_reference_element_coordinates(::Type{Lagrange{Hexahedron{8}, 1}})
|
|
return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)))
|
|
end
|
|
function get_reference_element_coordinates(::Lagrange{Hexahedron{8}, 1})
|
|
return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)))
|
|
end
|
|
@inline function get_basis_functions(::Type{Hexahedron{8}}, ::Type{Lagrange{Hexahedron{8}, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (0.125 + -0.125u + -0.125v + -0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + -0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + -0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + -0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + -0.125v + 0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + 0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + 0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + 0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w))
|
|
end
|
|
@inline function get_basis_functions(::Hexahedron{8}, ::Lagrange{Hexahedron{8}, 1}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (0.125 + -0.125u + -0.125v + -0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + -0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + -0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + -0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + -0.125v + 0.125w + 0.125 * (u * v) + -0.125 * (u * w) + -0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + 0.125u + -0.125v + 0.125w + -0.125 * (u * v) + 0.125 * (u * w) + -0.125 * (v * w) + -0.125 * (u * v * w), 0.125 + 0.125u + 0.125v + 0.125w + 0.125 * (u * v) + 0.125 * (u * w) + 0.125 * (v * w) + 0.125 * (u * v * w), 0.125 + -0.125u + 0.125v + 0.125w + -0.125 * (u * v) + -0.125 * (u * w) + 0.125 * (v * w) + -0.125 * (u * v * w))
|
|
end
|
|
@inline function get_basis_derivatives(::Type{Hexahedron{8}}, ::Type{Lagrange{Hexahedron{8}, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-0.125 + 0.125v + 0.125w + -0.125 * (v * w), -0.125 + 0.125u + 0.125w + -0.125 * (u * w), -0.125 + 0.125u + 0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + -0.125w + 0.125 * (v * w), -0.125 + -0.125u + 0.125w + 0.125 * (u * w), -0.125 + -0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + -0.125w + -0.125 * (v * w), 0.125 + 0.125u + -0.125w + -0.125 * (u * w), -0.125 + -0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + 0.125w + 0.125 * (v * w), 0.125 + -0.125u + -0.125w + 0.125 * (u * w), -0.125 + 0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + 0.125v + -0.125w + 0.125 * (v * w), -0.125 + 0.125u + -0.125w + 0.125 * (u * w), 0.125 + -0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + 0.125w + -0.125 * (v * w), -0.125 + -0.125u + -0.125w + -0.125 * (u * w), 0.125 + 0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + 0.125w + 0.125 * (v * w), 0.125 + 0.125u + 0.125w + 0.125 * (u * w), 0.125 + 0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + -0.125w + -0.125 * (v * w), 0.125 + -0.125u + 0.125w + -0.125 * (u * w), 0.125 + -0.125u + 0.125v + -0.125 * (u * v)))))
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end
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@inline function get_basis_derivatives(::Hexahedron{8}, ::Lagrange{Hexahedron{8}, 1}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (Vec(float.(tuple(-0.125 + 0.125v + 0.125w + -0.125 * (v * w), -0.125 + 0.125u + 0.125w + -0.125 * (u * w), -0.125 + 0.125u + 0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + -0.125w + 0.125 * (v * w), -0.125 + -0.125u + 0.125w + 0.125 * (u * w), -0.125 + -0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + -0.125w + -0.125 * (v * w), 0.125 + 0.125u + -0.125w + -0.125 * (u * w), -0.125 + -0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + 0.125w + 0.125 * (v * w), 0.125 + -0.125u + -0.125w + 0.125 * (u * w), -0.125 + 0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + 0.125v + -0.125w + 0.125 * (v * w), -0.125 + 0.125u + -0.125w + 0.125 * (u * w), 0.125 + -0.125u + -0.125v + 0.125 * (u * v)))), Vec(float.(tuple(0.125 + -0.125v + 0.125w + -0.125 * (v * w), -0.125 + -0.125u + -0.125w + -0.125 * (u * w), 0.125 + 0.125u + -0.125v + -0.125 * (u * v)))), Vec(float.(tuple(0.125 + 0.125v + 0.125w + 0.125 * (v * w), 0.125 + 0.125u + 0.125w + 0.125 * (u * w), 0.125 + 0.125u + 0.125v + 0.125 * (u * v)))), Vec(float.(tuple(-0.125 + -0.125v + -0.125w + -0.125 * (v * w), 0.125 + -0.125u + 0.125w + -0.125 * (u * w), 0.125 + -0.125u + 0.125v + -0.125 * (u * v)))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Hexahedron{20}, 2}: 20-node serendipity hexahedral element
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# (Old name: Hex20, 20 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Hexahedron{20}, 2}})
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return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)))
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end
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function get_reference_element_coordinates(::Lagrange{Hexahedron{20}, 2})
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return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)))
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end
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@inline function get_basis_functions(::Type{Hexahedron{20}}, ::Type{Lagrange{Hexahedron{20}, 2}}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (-0.25 + 0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + 0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), 0.25 + -0.25v + -0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + -0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + -0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + -0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + -0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + 0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + -0.25u + -0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + 0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + 0.25u + -0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + -0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + 0.25u + 0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + -0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + -0.25u + 0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + 0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + -0.25v + 0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + 0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + -0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + 0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + 0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + 0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w))
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end
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@inline function get_basis_functions(::Hexahedron{20}, ::Lagrange{Hexahedron{20}, 2}, xi::Vec)
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|
(u, v, w) = xi
|
|
@inbounds return (-0.25 + 0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + 0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + -0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + -0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + 0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + -0.125u + 0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + -0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), -0.25 + -0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + 0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + 0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2), -0.25 + 0.125u + -0.125v + -0.125w + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (u ^ 2 * v) + 0.125 * (u ^ 2 * w) + -0.125 * (v ^ 2 * u) + 0.125 * (v ^ 2 * w) + -0.125 * (w ^ 2 * u) + 0.125 * (w ^ 2 * v) + -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2), 0.25 + -0.25v + -0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + -0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + -0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + -0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + -0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + 0.25 * (v ^ 2 * u) + 0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + -0.25u + -0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + 0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + 0.25u + -0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + -0.25 * (w ^ 2 * u) + 0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + 0.25u + 0.25v + -0.25 * w ^ 2 + 0.25 * (u * v) + -0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + -0.25 * (u * v * w ^ 2), 0.25 + -0.25u + 0.25v + -0.25 * w ^ 2 + -0.25 * (u * v) + 0.25 * (w ^ 2 * u) + -0.25 * (w ^ 2 * v) + 0.25 * (u * v * w ^ 2), 0.25 + -0.25v + 0.25w + -0.25 * u ^ 2 + -0.25 * (v * w) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * v * w), 0.25 + 0.25u + 0.25w + -0.25 * v ^ 2 + 0.25 * (u * w) + -0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + -0.25 * (u * v ^ 2 * w), 0.25 + 0.25v + 0.25w + -0.25 * u ^ 2 + 0.25 * (v * w) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * v * w), 0.25 + -0.25u + 0.25w + -0.25 * v ^ 2 + -0.25 * (u * w) + 0.25 * (v ^ 2 * u) + -0.25 * (v ^ 2 * w) + 0.25 * (u * v ^ 2 * w))
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end
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@inline function get_basis_derivatives(::Type{Hexahedron{20}}, ::Type{Lagrange{Hexahedron{20}, 2}}, xi::Vec)
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|
(u, v, w) = xi
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@inbounds return (Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + 0.25w + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), -0.25 + 0.25v + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + -0.25w + -0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + -0.25u + 0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + -0.25w + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), -0.25 + -0.25v + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + 0.25w + 0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + 0.25u + 0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 + 0.25v + 0.25 * w ^ 2 + -0.25 * (v * w ^ 2), -0.25 + 0.25u + 0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + -0.25v + -0.25 * w ^ 2 + 0.25 * (v * w ^ 2), -0.25 + -0.25u + 0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + 0.25v + -0.25 * w ^ 2 + -0.25 * (v * w ^ 2), 0.25 + 0.25u + -0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 + -0.25v + 0.25 * w ^ 2 + 0.25 * (v * w ^ 2), 0.25 + -0.25u + -0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + -0.25w + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), 0.25 + -0.25v + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + 0.25w + -0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + 0.25u + -0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + 0.25w + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), 0.25 + 0.25v + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + -0.25w + 0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + -0.25u + -0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))))
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end
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@inline function get_basis_derivatives(::Hexahedron{20}, ::Lagrange{Hexahedron{20}, 2}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + -0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + -0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), 0.125 + 0.125 * (2 * w ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + 0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + -0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + -0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), 0.125 + 0.125 * (2 * v ^ (2 - 1)) + -0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + -0.125 * w ^ 2 + -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + -0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + 0.125 * v ^ 2 + 0.125 * w ^ 2 + 0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + 0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 + 0.125 * (2 * u ^ (2 - 1)) + 0.125 * ((2 * u ^ (2 - 1)) * v) + 0.125 * ((2 * u ^ (2 - 1)) * w) + -0.125 * v ^ 2 + -0.125 * w ^ 2 + -0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2), -0.125 + 0.125 * (2 * v ^ (2 - 1)) + 0.125 * u ^ 2 + -0.125 * ((2 * v ^ (2 - 1)) * u) + 0.125 * ((2 * v ^ (2 - 1)) * w) + 0.125 * w ^ 2 + -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2), -0.125 + 0.125 * (2 * w ^ (2 - 1)) + 0.125 * u ^ 2 + 0.125 * v ^ 2 + -0.125 * ((2 * w ^ (2 - 1)) * u) + 0.125 * ((2 * w ^ (2 - 1)) * v) + -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + 0.25w + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), -0.25 + 0.25v + 0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + -0.25w + -0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + -0.25u + 0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + -0.25w + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), -0.25 + -0.25v + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + 0.25w + 0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), -0.25 + 0.25u + 0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 + 0.25v + 0.25 * w ^ 2 + -0.25 * (v * w ^ 2), -0.25 + 0.25u + 0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + -0.25v + -0.25 * w ^ 2 + 0.25 * (v * w ^ 2), -0.25 + -0.25u + 0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 + 0.25v + -0.25 * w ^ 2 + -0.25 * (v * w ^ 2), 0.25 + 0.25u + -0.25 * w ^ 2 + -0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + -0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + -0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 + -0.25v + 0.25 * w ^ 2 + 0.25 * (v * w ^ 2), 0.25 + -0.25u + -0.25 * w ^ 2 + 0.25 * (u * w ^ 2), -0.25 * (2 * w ^ (2 - 1)) + 0.25 * ((2 * w ^ (2 - 1)) * u) + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (u * v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w), -0.25 + -0.25w + 0.25 * u ^ 2 + 0.25 * (u ^ 2 * w), 0.25 + -0.25v + -0.25 * u ^ 2 + 0.25 * (u ^ 2 * v)))), Vec(float.(tuple(0.25 + 0.25w + -0.25 * v ^ 2 + -0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + -0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + 0.25u + -0.25 * v ^ 2 + -0.25 * (u * v ^ 2)))), Vec(float.(tuple(-0.25 * (2 * u ^ (2 - 1)) + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w), 0.25 + 0.25w + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * w), 0.25 + 0.25v + -0.25 * u ^ 2 + -0.25 * (u ^ 2 * v)))), Vec(float.(tuple(-0.25 + -0.25w + 0.25 * v ^ 2 + 0.25 * (v ^ 2 * w), -0.25 * (2 * v ^ (2 - 1)) + 0.25 * ((2 * v ^ (2 - 1)) * u) + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w), 0.25 + -0.25u + -0.25 * v ^ 2 + 0.25 * (u * v ^ 2)))))
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end
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# ──────────────────────────────────────────────────────────────────────────────
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# Lagrange{Hexahedron{27}, 2}: 27-node triquadratic hexahedral element
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# (Old name: Hex27, 27 nodes)
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# ──────────────────────────────────────────────────────────────────────────────
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function get_reference_element_coordinates(::Type{Lagrange{Hexahedron{27}, 2}})
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return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.0)))
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end
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function get_reference_element_coordinates(::Lagrange{Hexahedron{27}, 2})
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return (Vec{3, Float64}(tuple(-1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, -1.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.0)))
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end
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@inline function get_basis_functions(::Type{Hexahedron{27}}, ::Type{Lagrange{Hexahedron{27}, 2}}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (-0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + -0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + -0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + -0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + -0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + 0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + 0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + 0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + 0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5w + 0.5 * w ^ 2 + 0.5 * (u ^ 2 * w) + 0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5w + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * w) + -0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + 0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (v ^ 2 * u) + -0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (v ^ 2 * u) + 0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -1.0 * w ^ 2 + u ^ 2 * v ^ 2 + u ^ 2 * w ^ 2 + v ^ 2 * w ^ 2 + -1.0 * (u ^ 2 * v ^ 2 * w ^ 2))
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end
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@inline function get_basis_functions(::Hexahedron{27}, ::Lagrange{Hexahedron{27}, 2}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (-0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + -0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + -0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + -0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + 0.125 * (u * v ^ 2 * w) + 0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + 0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), -0.125 * (u * v * w) + 0.125 * (u ^ 2 * v * w) + -0.125 * (u * v ^ 2 * w) + -0.125 * (u * v * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w) + 0.125 * (u ^ 2 * v * w ^ 2) + -0.125 * (u * v ^ 2 * w ^ 2) + 0.125 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + -0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + -0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + -0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + -0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + 0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + -0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + -0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * v) + 0.25 * (u ^ 2 * v) + 0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * v) + 0.25 * (u ^ 2 * v) + -0.25 * (v ^ 2 * u) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v * w ^ 2) + -0.25 * (u ^ 2 * v * w ^ 2) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (v * w) + 0.25 * (v ^ 2 * w) + -0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + 0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (u * w) + 0.25 * (u ^ 2 * w) + 0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), 0.25 * (v * w) + 0.25 * (v ^ 2 * w) + 0.25 * (w ^ 2 * v) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + -0.25 * (u ^ 2 * v * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.25 * (u * w) + 0.25 * (u ^ 2 * w) + -0.25 * (w ^ 2 * u) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * v ^ 2 * w) + -0.25 * (u ^ 2 * v ^ 2 * w) + 0.25 * (u * v ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5w + 0.5 * w ^ 2 + 0.5 * (u ^ 2 * w) + 0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5w + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * w) + -0.5 * (v ^ 2 * w) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5v + 0.5 * v ^ 2 + 0.5 * (u ^ 2 * v) + 0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + -0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5u + 0.5 * u ^ 2 + -0.5 * (v ^ 2 * u) + -0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 0.5v + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * v) + -0.5 * (w ^ 2 * v) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), -0.5u + 0.5 * u ^ 2 + 0.5 * (v ^ 2 * u) + 0.5 * (w ^ 2 * u) + -0.5 * (u ^ 2 * v ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + -0.5 * (u * v ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * w ^ 2), 1 + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -1.0 * w ^ 2 + u ^ 2 * v ^ 2 + u ^ 2 * w ^ 2 + v ^ 2 * w ^ 2 + -1.0 * (u ^ 2 * v ^ 2 * w ^ 2))
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end
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@inline function get_basis_derivatives(::Type{Hexahedron{27}}, ::Type{Lagrange{Hexahedron{27}, 2}}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + -0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + -0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + 0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + 0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + 0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2 + (2 * u ^ (2 - 1)) * w ^ 2 + -1.0 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1)) + (2 * v ^ (2 - 1)) * w ^ 2 + -1.0 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -1.0 * (2 * w ^ (2 - 1)) + u ^ 2 * (2 * w ^ (2 - 1)) + v ^ 2 * (2 * w ^ (2 - 1)) + -1.0 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))))
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end
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@inline function get_basis_derivatives(::Hexahedron{27}, ::Lagrange{Hexahedron{27}, 2}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + -0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + -0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + -0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + -0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + -0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + -0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + -0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + -0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + 0.125 * (v ^ 2 * w) + 0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.125 * (u * w) + 0.125 * (u ^ 2 * w) + 0.125 * (u * (2 * v ^ (2 - 1)) * w) + 0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + 0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.125 * (u * v) + 0.125 * (u ^ 2 * v) + 0.125 * (u * v ^ 2) + 0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.125 * (v * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w) + -0.125 * (v ^ 2 * w) + -0.125 * (v * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.125 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.125 * (v ^ 2 * w ^ 2) + 0.125 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.125 * (u * w) + 0.125 * (u ^ 2 * w) + -0.125 * (u * (2 * v ^ (2 - 1)) * w) + -0.125 * (u * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.125 * (u ^ 2 * w ^ 2) + -0.125 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.125 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.125 * (u * v) + 0.125 * (u ^ 2 * v) + -0.125 * (u * v ^ 2) + -0.125 * (u * v * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2) + 0.125 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.125 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.125 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + -0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + -0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + -0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + 0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + -0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + 0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + -0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + -0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + -0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + 0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25v + 0.25 * ((2 * u ^ (2 - 1)) * v) + -0.25 * v ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.25 * (v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * v ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.25 * (u * w ^ 2) + -0.25 * (u ^ 2 * w ^ 2) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25 * (u * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25v + 0.25 * v ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25u + 0.25 * u ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25 * ((2 * u ^ (2 - 1)) * v * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25w + 0.25 * ((2 * v ^ (2 - 1)) * w) + 0.25 * w ^ 2 + 0.25 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.25v + 0.25 * v ^ 2 + 0.25 * ((2 * w ^ (2 - 1)) * v) + 0.25 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v) + -0.25 * (u ^ 2 * v ^ 2) + -0.25 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.25w + 0.25 * ((2 * u ^ (2 - 1)) * w) + -0.25 * w ^ 2 + 0.25 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.25 * (v ^ 2 * w) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.25 * (v ^ 2 * w ^ 2) + -0.25 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.25 * (u * (2 * v ^ (2 - 1)) * w) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.25 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + -0.25 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.25u + 0.25 * u ^ 2 + -0.25 * ((2 * w ^ (2 - 1)) * u) + 0.25 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.25 * (u * v ^ 2) + -0.25 * (u ^ 2 * v ^ 2) + 0.25 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + -0.25 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * w) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * w) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * v ^ 2 + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 + 0.5 * (2 * v ^ (2 - 1)) + 0.5 * u ^ 2 + 0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + -0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0.5 + 0.5 * (2 * u ^ (2 - 1)) + -0.5 * v ^ 2 + -0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + 0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + 0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 * ((2 * u ^ (2 - 1)) * v) + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 + 0.5 * (2 * v ^ (2 - 1)) + -0.5 * u ^ 2 + -0.5 * w ^ 2 + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * ((2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -0.5 * ((2 * w ^ (2 - 1)) * v) + -0.5 * (v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-0.5 + 0.5 * (2 * u ^ (2 - 1)) + 0.5 * v ^ 2 + 0.5 * w ^ 2 + -0.5 * ((2 * u ^ (2 - 1)) * v ^ 2) + -0.5 * ((2 * u ^ (2 - 1)) * w ^ 2) + -0.5 * (v ^ 2 * w ^ 2) + 0.5 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), 0.5 * ((2 * v ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * v ^ (2 - 1))) + -0.5 * (u * (2 * v ^ (2 - 1)) * w ^ 2) + 0.5 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), 0.5 * ((2 * w ^ (2 - 1)) * u) + -0.5 * (u ^ 2 * (2 * w ^ (2 - 1))) + -0.5 * (u * v ^ 2 * (2 * w ^ (2 - 1))) + 0.5 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 * (2 * u ^ (2 - 1)) + (2 * u ^ (2 - 1)) * v ^ 2 + (2 * u ^ (2 - 1)) * w ^ 2 + -1.0 * ((2 * u ^ (2 - 1)) * v ^ 2 * w ^ 2), -1.0 * (2 * v ^ (2 - 1)) + u ^ 2 * (2 * v ^ (2 - 1)) + (2 * v ^ (2 - 1)) * w ^ 2 + -1.0 * (u ^ 2 * (2 * v ^ (2 - 1)) * w ^ 2), -1.0 * (2 * w ^ (2 - 1)) + u ^ 2 * (2 * w ^ (2 - 1)) + v ^ 2 * (2 * w ^ (2 - 1)) + -1.0 * (u ^ 2 * v ^ 2 * (2 * w ^ (2 - 1)))))))
|
|
end
|
|
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
# Lagrange{Pyramid, 1}: 5-node linear pyramid element
|
|
# (Old name: Pyr5, 5 nodes)
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
|
|
function get_reference_element_coordinates(::Type{Lagrange{Pyramid, 1}})
|
|
return (Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)))
|
|
end
|
|
function get_reference_element_coordinates(::Lagrange{Pyramid, 1})
|
|
return (Vec{3, Float64}(tuple(-1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, -1.0, 0.0)), Vec{3, Float64}(tuple(1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(-1.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)))
|
|
end
|
|
@inline function get_basis_functions(::Type{Pyramid}, ::Type{Lagrange{Pyramid, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (0.25 + -0.25u + -0.25v + -0.25w + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25w + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + -0.25w + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25w + -0.25 * (u * v), +w)
|
|
end
|
|
@inline function get_basis_functions(::Pyramid, ::Lagrange{Pyramid, 1}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (0.25 + -0.25u + -0.25v + -0.25w + 0.25 * (u * v), 0.25 + 0.25u + -0.25v + -0.25w + -0.25 * (u * v), 0.25 + 0.25u + 0.25v + -0.25w + 0.25 * (u * v), 0.25 + -0.25u + 0.25v + -0.25w + -0.25 * (u * v), +w)
|
|
end
|
|
@inline function get_basis_derivatives(::Type{Pyramid}, ::Type{Lagrange{Pyramid, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u, -0.25))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u, -0.25))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u, -0.25))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u, -0.25))), Vec(float.(tuple(0, 0, 1))))
|
|
end
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|
@inline function get_basis_derivatives(::Pyramid, ::Lagrange{Pyramid, 1}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-0.25 + 0.25v, -0.25 + 0.25u, -0.25))), Vec(float.(tuple(0.25 + -0.25v, -0.25 + -0.25u, -0.25))), Vec(float.(tuple(0.25 + 0.25v, 0.25 + 0.25u, -0.25))), Vec(float.(tuple(-0.25 + -0.25v, 0.25 + -0.25u, -0.25))), Vec(float.(tuple(0, 0, 1))))
|
|
end
|
|
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
# Lagrange{Wedge, 1}: 6-node linear wedge element (triangular prism)
|
|
# (Old name: Wedge6, 6 nodes)
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
|
|
function get_reference_element_coordinates(::Type{Lagrange{Wedge, 1}})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)))
|
|
end
|
|
function get_reference_element_coordinates(::Lagrange{Wedge, 1})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)))
|
|
end
|
|
@inline function get_basis_functions(::Type{Wedge}, ::Type{Lagrange{Wedge, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (0.5 + -0.5u + -0.5v + -0.5w + 0.5 * (u * w) + 0.5 * (v * w), 0.5u + -0.5 * (u * w), 0.5v + -0.5 * (v * w), 0.5 + -0.5u + -0.5v + 0.5w + -0.5 * (u * w) + -0.5 * (v * w), 0.5u + 0.5 * (u * w), 0.5v + 0.5 * (v * w))
|
|
end
|
|
@inline function get_basis_functions(::Wedge, ::Lagrange{Wedge, 1}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (0.5 + -0.5u + -0.5v + -0.5w + 0.5 * (u * w) + 0.5 * (v * w), 0.5u + -0.5 * (u * w), 0.5v + -0.5 * (v * w), 0.5 + -0.5u + -0.5v + 0.5w + -0.5 * (u * w) + -0.5 * (v * w), 0.5u + 0.5 * (u * w), 0.5v + 0.5 * (v * w))
|
|
end
|
|
@inline function get_basis_derivatives(::Type{Wedge}, ::Type{Lagrange{Wedge, 1}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-0.5 + 0.5w, -0.5 + 0.5w, -0.5 + 0.5u + 0.5v))), Vec(float.(tuple(0.5 + -0.5w, 0, -0.5u))), Vec(float.(tuple(0, 0.5 + -0.5w, -0.5v))), Vec(float.(tuple(-0.5 + -0.5w, -0.5 + -0.5w, 0.5 + -0.5u + -0.5v))), Vec(float.(tuple(0.5 + 0.5w, 0, 0.5u))), Vec(float.(tuple(0, 0.5 + 0.5w, 0.5v))))
|
|
end
|
|
@inline function get_basis_derivatives(::Wedge, ::Lagrange{Wedge, 1}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (Vec(float.(tuple(-0.5 + 0.5w, -0.5 + 0.5w, -0.5 + 0.5u + 0.5v))), Vec(float.(tuple(0.5 + -0.5w, 0, -0.5u))), Vec(float.(tuple(0, 0.5 + -0.5w, -0.5v))), Vec(float.(tuple(-0.5 + -0.5w, -0.5 + -0.5w, 0.5 + -0.5u + -0.5v))), Vec(float.(tuple(0.5 + 0.5w, 0, 0.5u))), Vec(float.(tuple(0, 0.5 + 0.5w, 0.5v))))
|
|
end
|
|
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
# Lagrange{Wedge, 2}: 15-node quadratic wedge element
|
|
# (Old name: Wedge15, 15 nodes)
|
|
# ──────────────────────────────────────────────────────────────────────────────
|
|
|
|
function get_reference_element_coordinates(::Type{Lagrange{Wedge, 2}})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.0, -1.0)), Vec{3, Float64}(tuple(0.5, 0.5, -1.0)), Vec{3, Float64}(tuple(0.0, 0.5, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.5, 0.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.5, 1.0)), Vec{3, Float64}(tuple(0.0, 0.5, 1.0)))
|
|
end
|
|
function get_reference_element_coordinates(::Lagrange{Wedge, 2})
|
|
return (Vec{3, Float64}(tuple(0.0, 0.0, -1.0)), Vec{3, Float64}(tuple(1.0, 0.0, -1.0)), Vec{3, Float64}(tuple(0.0, 1.0, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 1.0)), Vec{3, Float64}(tuple(1.0, 0.0, 1.0)), Vec{3, Float64}(tuple(0.0, 1.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.0, -1.0)), Vec{3, Float64}(tuple(0.5, 0.5, -1.0)), Vec{3, Float64}(tuple(0.0, 0.5, -1.0)), Vec{3, Float64}(tuple(0.0, 0.0, 0.0)), Vec{3, Float64}(tuple(1.0, 0.0, 0.0)), Vec{3, Float64}(tuple(0.0, 1.0, 0.0)), Vec{3, Float64}(tuple(0.5, 0.0, 1.0)), Vec{3, Float64}(tuple(0.5, 0.5, 1.0)), Vec{3, Float64}(tuple(0.0, 0.5, 1.0)))
|
|
end
|
|
@inline function get_basis_functions(::Type{Wedge}, ::Type{Lagrange{Wedge, 2}}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (-1.0u + -1.0v + -0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + 1.5 * (u * w) + 1.5 * (v * w) + -1.0 * (u ^ 2 * w) + -1.0 * (v ^ 2 * w) + -2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + 0.5 * (u * w) + -1.0 * (u ^ 2 * w) + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + 0.5 * (v * w) + -1.0 * (v ^ 2 * w) + 0.5 * (v * w ^ 2), -1.0u + -1.0v + 0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + -1.5 * (u * w) + -1.5 * (v * w) + u ^ 2 * w + v ^ 2 * w + 2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + -0.5 * (u * w) + u ^ 2 * w + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + -0.5 * (v * w) + v ^ 2 * w + 0.5 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + -2.0 * (u * w) + 2.0 * (u ^ 2 * w) + 2.0 * (u * v * w), 2.0 * (u * v) + -2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + -2.0 * (v * w) + 2.0 * (v ^ 2 * w) + 2.0 * (u * v * w), 1 + -1.0u + -1.0v + -1.0 * w ^ 2 + u * w ^ 2 + v * w ^ 2, u + -1.0 * (u * w ^ 2), v + -1.0 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + 2.0 * (u * w) + -2.0 * (u ^ 2 * w) + -2.0 * (u * v * w), 2.0 * (u * v) + 2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + 2.0 * (v * w) + -2.0 * (v ^ 2 * w) + -2.0 * (u * v * w))
|
|
end
|
|
@inline function get_basis_functions(::Wedge, ::Lagrange{Wedge, 2}, xi::Vec)
|
|
(u, v, w) = xi
|
|
@inbounds return (-1.0u + -1.0v + -0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + 1.5 * (u * w) + 1.5 * (v * w) + -1.0 * (u ^ 2 * w) + -1.0 * (v ^ 2 * w) + -2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + 0.5 * (u * w) + -1.0 * (u ^ 2 * w) + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + 0.5 * (v * w) + -1.0 * (v ^ 2 * w) + 0.5 * (v * w ^ 2), -1.0u + -1.0v + 0.5w + u ^ 2 + v ^ 2 + 0.5 * w ^ 2 + 2.0 * (u * v) + -1.5 * (u * w) + -1.5 * (v * w) + u ^ 2 * w + v ^ 2 * w + 2.0 * (u * v * w) + -0.5 * (u * w ^ 2) + -0.5 * (v * w ^ 2), -1.0u + u ^ 2 + -0.5 * (u * w) + u ^ 2 * w + 0.5 * (u * w ^ 2), -1.0v + v ^ 2 + -0.5 * (v * w) + v ^ 2 * w + 0.5 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + -2.0 * (u * w) + 2.0 * (u ^ 2 * w) + 2.0 * (u * v * w), 2.0 * (u * v) + -2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + -2.0 * (v * w) + 2.0 * (v ^ 2 * w) + 2.0 * (u * v * w), 1 + -1.0u + -1.0v + -1.0 * w ^ 2 + u * w ^ 2 + v * w ^ 2, u + -1.0 * (u * w ^ 2), v + -1.0 * (v * w ^ 2), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v) + 2.0 * (u * w) + -2.0 * (u ^ 2 * w) + -2.0 * (u * v * w), 2.0 * (u * v) + 2.0 * (u * v * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v) + 2.0 * (v * w) + -2.0 * (v ^ 2 * w) + -2.0 * (u * v * w))
|
|
end
|
|
@inline function get_basis_derivatives(::Type{Wedge}, ::Type{Lagrange{Wedge, 2}}, xi::Vec)
|
|
(u, v, w) = xi
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@inbounds return (Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + 1.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + 1.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w) + -0.5 * w ^ 2, -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 1.5u + 1.5v + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 0.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0, 0.5u + -1.0 * u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + 0.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0.5v + -1.0 * v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + -1.5w + (2 * u ^ (2 - 1)) * w + 2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + -1.5w + (2 * v ^ (2 - 1)) * w + 2.0 * (u * w) + -0.5 * w ^ 2, 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -1.5u + -1.5v + u ^ 2 + v ^ 2 + 2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + -0.5w + (2 * u ^ (2 - 1)) * w + 0.5 * w ^ 2, 0, -0.5u + u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + -0.5w + (2 * v ^ (2 - 1)) * w + 0.5 * w ^ 2, -0.5v + v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + -2.0w + 2.0 * ((2 * u ^ (2 - 1)) * w) + 2.0 * (v * w), -2.0u + 2.0 * (u * w), -2.0u + 2.0 * u ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(2.0v + -2.0 * (v * w), 2.0u + -2.0 * (u * w), -2.0 * (u * v)))), Vec(float.(tuple(-2.0v + 2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + -2.0w + 2.0 * ((2 * v ^ (2 - 1)) * w) + 2.0 * (u * w), -2.0v + 2.0 * v ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(-1.0 + w ^ 2, -1.0 + w ^ 2, -1.0 * (2 * w ^ (2 - 1)) + u * (2 * w ^ (2 - 1)) + v * (2 * w ^ (2 - 1))))), Vec(float.(tuple(1 + -1.0 * w ^ 2, 0, -1.0 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, 1 + -1.0 * w ^ 2, -1.0 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + 2.0w + -2.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w), -2.0u + -2.0 * (u * w), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v)))), Vec(float.(tuple(2.0v + 2.0 * (v * w), 2.0u + 2.0 * (u * w), 2.0 * (u * v)))), Vec(float.(tuple(-2.0v + -2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + 2.0w + -2.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v)))))
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end
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@inline function get_basis_derivatives(::Wedge, ::Lagrange{Wedge, 2}, xi::Vec)
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(u, v, w) = xi
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@inbounds return (Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + 1.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + 1.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w) + -0.5 * w ^ 2, -0.5 + 0.5 * (2 * w ^ (2 - 1)) + 1.5u + 1.5v + -1.0 * u ^ 2 + -1.0 * v ^ 2 + -2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 0.5w + -1.0 * ((2 * u ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0, 0.5u + -1.0 * u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + 0.5w + -1.0 * ((2 * v ^ (2 - 1)) * w) + 0.5 * w ^ 2, 0.5v + -1.0 * v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + 2.0v + -1.5w + (2 * u ^ (2 - 1)) * w + 2.0 * (v * w) + -0.5 * w ^ 2, -1.0 + 2 * v ^ (2 - 1) + 2.0u + -1.5w + (2 * v ^ (2 - 1)) * w + 2.0 * (u * w) + -0.5 * w ^ 2, 0.5 + 0.5 * (2 * w ^ (2 - 1)) + -1.5u + -1.5v + u ^ 2 + v ^ 2 + 2.0 * (u * v) + -0.5 * (u * (2 * w ^ (2 - 1))) + -0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(-1.0 + 2 * u ^ (2 - 1) + -0.5w + (2 * u ^ (2 - 1)) * w + 0.5 * w ^ 2, 0, -0.5u + u ^ 2 + 0.5 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, -1.0 + 2 * v ^ (2 - 1) + -0.5w + (2 * v ^ (2 - 1)) * w + 0.5 * w ^ 2, -0.5v + v ^ 2 + 0.5 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + -2.0w + 2.0 * ((2 * u ^ (2 - 1)) * w) + 2.0 * (v * w), -2.0u + 2.0 * (u * w), -2.0u + 2.0 * u ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(2.0v + -2.0 * (v * w), 2.0u + -2.0 * (u * w), -2.0 * (u * v)))), Vec(float.(tuple(-2.0v + 2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + -2.0w + 2.0 * ((2 * v ^ (2 - 1)) * w) + 2.0 * (u * w), -2.0v + 2.0 * v ^ 2 + 2.0 * (u * v)))), Vec(float.(tuple(-1.0 + w ^ 2, -1.0 + w ^ 2, -1.0 * (2 * w ^ (2 - 1)) + u * (2 * w ^ (2 - 1)) + v * (2 * w ^ (2 - 1))))), Vec(float.(tuple(1 + -1.0 * w ^ 2, 0, -1.0 * (u * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(0, 1 + -1.0 * w ^ 2, -1.0 * (v * (2 * w ^ (2 - 1)))))), Vec(float.(tuple(2.0 + -2.0 * (2 * u ^ (2 - 1)) + -2.0v + 2.0w + -2.0 * ((2 * u ^ (2 - 1)) * w) + -2.0 * (v * w), -2.0u + -2.0 * (u * w), 2.0u + -2.0 * u ^ 2 + -2.0 * (u * v)))), Vec(float.(tuple(2.0v + 2.0 * (v * w), 2.0u + 2.0 * (u * w), 2.0 * (u * v)))), Vec(float.(tuple(-2.0v + -2.0 * (v * w), 2.0 + -2.0 * (2 * v ^ (2 - 1)) + -2.0u + 2.0w + -2.0 * ((2 * v ^ (2 - 1)) * w) + -2.0 * (u * w), 2.0v + -2.0 * v ^ 2 + -2.0 * (u * v)))))
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end
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