From 269fa9a4ada23e5fb0ea7dcffbc3f004629aeb57 Mon Sep 17 00:00:00 2001
From: Jukka Aho <ahojukka5@gmail.com>
Date: Mon, 10 Nov 2025 22:26:23 +0200
Subject: [PATCH] feat(basis): Add dual-API basis function support (modern +
 legacy)

- New API: get_basis_functions() returns tuple of functions
- New API: get_basis_derivatives() returns tuple of gradient functions
- basis_api.jl: 210 lines implementing modern functional API
- Re-generated lagrange_generated.jl with 242 new lines
- abstract.jl: Add nnodes() method for Lagrange type
- Backward compatible: old eval_basis! API unchanged
- See ADR-003 for design rationale
---
 src/basis/abstract.jl           |   9 +-
 src/basis/basis_api.jl          | 210 +++++++++++++++++++++++++++
 src/basis/lagrange_generated.jl | 242 +++++++++++++++++++++++++++++++-
 src/basis/lagrange_generator.jl |  31 ++++
 4 files changed, 490 insertions(+), 2 deletions(-)
 create mode 100644 src/basis/basis_api.jl

diff --git a/src/basis/abstract.jl b/src/basis/abstract.jl
index 5a2aebc..116f71b 100644
--- a/src/basis/abstract.jl
+++ b/src/basis/abstract.jl
@@ -48,9 +48,16 @@ nnodes(B::T) where {T<:AbstractBasis} = nnodes(T)
 function eval_basis! end
 function eval_dbasis! end
 
+# New API functions (declared here, implemented in basis_api.jl)
+function get_basis_functions end
+function get_basis_derivatives end
+
 # ============================================================================
-# Parametric Lagrange Basis Type
+# Parametric Lagrange Basis Type (OLD - with topology parameter)
 # ============================================================================
+# NOTE: This is the OLD API with topology in the type parameter.
+# New code should use LagrangeP{P} below (topology passed separately).
+# This is kept for backward compatibility during migration.
 
 """
     Lagrange{T<:AbstractTopology, P} <: AbstractBasis
diff --git a/src/basis/basis_api.jl b/src/basis/basis_api.jl
new file mode 100644
index 0000000..7811190
--- /dev/null
+++ b/src/basis/basis_api.jl
@@ -0,0 +1,210 @@
+# Basis Function API - New Design (Nov 2025)
+#
+# This file implements the new basis function API based on comprehensive
+# benchmarking results (see docs/book/adr-003-basis-function-api.md).
+#
+# Key design decisions:
+# 1. Topology passed separately: get_basis_functions(topology, basis, xi)
+# 2. Return tuples (zero allocation, type-stable)
+# 3. Use simple runtime indexing for single access (fastest!)
+# 4. Clear naming: get_basis_functions, get_basis_derivatives
+#
+# Performance: 6.5 ns for Tet10 derivatives, zero allocations
+
+"""
+    get_basis_functions(topology::AbstractTopology, basis::AbstractBasis, xi::Vec)
+
+Evaluate all basis functions at parametric point `xi`.
+
+Returns `NTuple{N, Float64}` where N is the number of nodes/DOFs for the given
+topology and basis combination.
+
+# Arguments
+- `topology`: Element topology (e.g., `Tetrahedron()`, `Triangle()`)
+- `basis`: Interpolation scheme (e.g., `Lagrange{1}()`, `Lagrange{2}()`)
+- `xi`: Parametric coordinates as `Vec{D, T}` where D is spatial dimension
+
+# Returns
+- `NTuple{N, Float64}`: All N basis function values
+
+# Examples
+
+```julia
+# Tet10: 10-node quadratic tetrahedron
+topology = Tetrahedron()
+basis = Lagrange{2}()
+xi = Vec(0.25, 0.25, 0.2)
+
+N_all = get_basis_functions(topology, basis, xi)
+# Returns: (N1, N2, ..., N10) as NTuple{10, Float64}
+
+# Access single basis function (simple runtime indexing)
+N_5 = N_all[5]
+
+# Verify partition of unity
+@assert abs(sum(N_all) - 1.0) < 1e-10
+```
+
+# Performance
+- Tet10 (10 nodes): ~3.6 ns, zero allocations
+- Triangle P1 (3 nodes): ~2.5 ns, zero allocations
+
+See also: [`get_basis_derivatives`](@ref), [`get_basis_function`](@ref)
+"""
+function get_basis_functions end
+
+"""
+    get_basis_derivatives(topology::AbstractTopology, basis::AbstractBasis, xi::Vec)
+
+Evaluate all basis function derivatives at parametric point `xi`.
+
+Returns `NTuple{N, Vec{D, Float64}}` where:
+- N is the number of nodes/DOFs
+- D is the spatial dimension
+
+Each derivative is ∇N_i = (∂N_i/∂ξ₁, ∂N_i/∂ξ₂, ..., ∂N_i/∂ξ_D)
+
+# Arguments
+- `topology`: Element topology (e.g., `Tetrahedron()`, `Triangle()`)
+- `basis`: Interpolation scheme (e.g., `Lagrange{1}()`, `Lagrange{2}()`)
+- `xi`: Parametric coordinates as `Vec{D, T}` where D is spatial dimension
+
+# Returns
+- `NTuple{N, Vec{D, Float64}}`: All N basis function gradients
+
+# Examples
+
+```julia
+# Tet10: 10-node quadratic tetrahedron
+topology = Tetrahedron()
+basis = Lagrange{2}()
+xi = Vec(0.25, 0.25, 0.2)
+
+dN_all = get_basis_derivatives(topology, basis, xi)
+# Returns: (∇N1, ∇N2, ..., ∇N10) as NTuple{10, Vec{3, Float64}}
+
+# Access single derivative (simple runtime indexing)
+dN_5 = dN_all[5]  # Vec{3, Float64} gradient for node 5
+
+# Use in assembly (typical pattern)
+for i in 1:10
+    for j in 1:10
+        dNi = dN_all[i]
+        dNj = dN_all[j]
+        K_local[i,j] += dot(dNi, dNj) * detJ  # Simplified
+    end
+end
+```
+
+# Performance
+- Tet10 (10 nodes, 3D): ~6.5 ns, zero allocations ← HOT PATH!
+- Triangle P2 (6 nodes, 2D): ~4.0 ns, zero allocations
+
+This is the critical path for stiffness matrix assembly!
+
+See also: [`get_basis_functions`](@ref), [`get_basis_derivative`](@ref)
+"""
+function get_basis_derivatives end
+
+"""
+    get_basis_function(topology, basis, xi, i::Int)
+
+Convenience function to get a single basis function value.
+
+Equivalent to `get_basis_functions(topology, basis, xi)[i]`.
+
+# Note
+Simple runtime tuple indexing is fastest (~1 ns overhead). No need for
+Val dispatch or @generated functions (benchmarks showed those are 25-300× slower!).
+
+# Examples
+
+```julia
+N_5 = get_basis_function(Tetrahedron(), Lagrange{2}(), xi, 5)
+# Equivalent to:
+N_5 = get_basis_functions(Tetrahedron(), Lagrange{2}(), xi)[5]
+```
+"""
+@inline function get_basis_function(topology::AbstractTopology,
+    basis::AbstractBasis,
+    xi::Vec,
+    i::Int)
+    return get_basis_functions(topology, basis, xi)[i]
+end
+
+"""
+    get_basis_derivative(topology, basis, xi, i::Int)
+
+Convenience function to get a single basis function derivative.
+
+Equivalent to `get_basis_derivatives(topology, basis, xi)[i]`.
+
+# Note
+Simple runtime tuple indexing is fastest (~1 ns overhead).
+
+# Examples
+
+```julia
+dN_5 = get_basis_derivative(Tetrahedron(), Lagrange{2}(), xi, 5)
+# Equivalent to:
+dN_5 = get_basis_derivatives(Tetrahedron(), Lagrange{2}(), xi)[5]
+```
+"""
+@inline function get_basis_derivative(topology::AbstractTopology,
+    basis::AbstractBasis,
+    xi::Vec,
+    i::Int)
+    return get_basis_derivatives(topology, basis, xi)[i]
+end
+
+# ============================================================================
+# Implementation for Lagrange Basis
+# ============================================================================
+# 
+# These implementations are auto-generated for all topology/degree combinations.
+# See src/basis/lagrange_generator.jl for the code generation.
+#
+# Pattern for each topology:
+#
+# @inline function get_basis_functions(::Topology, ::Lagrange{P}, xi::Vec{D,T}) where T
+#     # Compute basis functions
+#     return (N1, N2, ..., Nn)  # NTuple{N, Float64}
+# end
+#
+# @inline function get_basis_derivatives(::Topology, ::Lagrange{P}, xi::Vec{D,T}) where T
+#     # Compute derivatives
+#     return (dN1, dN2, ..., dNn)  # NTuple{N, Vec{D, Float64}}
+# end
+
+# Include auto-generated implementations
+# TODO: Update lagrange_generator.jl to generate get_basis_* functions
+# For now, implementations will be added to lagrange_generated.jl
+
+# ============================================================================
+# Backward Compatibility Bridge (Temporary)
+# ============================================================================
+#
+# These functions bridge to the new API from old API.
+# Will be deprecated after full migration.
+
+"""
+    eval_basis!(basis_type, xi) (DEPRECATED)
+
+**DEPRECATED**: Use `get_basis_functions(topology, basis, xi)` instead.
+
+This function is provided for backward compatibility during migration.
+"""
+function eval_basis! end
+
+"""
+    eval_dbasis!(basis_type, xi) (DEPRECATED)
+
+**DEPRECATED**: Use `get_basis_derivatives(topology, basis, xi)` instead.
+
+This function is provided for backward compatibility during migration.
+"""
+function eval_dbasis! end
+
+# TODO: Add deprecation warnings after new API is implemented
+# @deprecate eval_basis!(args...) get_basis_functions(args...)
+# @deprecate eval_dbasis!(args...) get_basis_derivatives(args...)
diff --git a/src/basis/lagrange_generated.jl b/src/basis/lagrange_generated.jl
index 85ddcbe..c107df1 100644
--- a/src/basis/lagrange_generated.jl
+++ b/src/basis/lagrange_generated.jl
@@ -20,7 +20,7 @@
 # Generator:
 #   src/basis/lagrange_generator.jl (symbolic engine)
 #
-# Generated: 2025-11-09 17:25:56
+# Generated: 2025-11-10 11:31:12
 # ============================================================================
 
 # This file generates methods for Lagrange{T,P} where:
@@ -56,6 +56,22 @@
                                     (u,) = xi
                          @inbounds return (Vec(float.(tuple(-0.5))), Vec(float.(tuple(0.5))))
         end
+         @inline function get_basis_functions(::Type{Segment}, ::Type{Lagrange{Segment, 1}}, xi::Vec)
+                                    (u,) = xi
+                         @inbounds return (0.5 + -0.5u, 0.5 + 0.5u)
+        end
+         @inline function get_basis_functions(::Segment, ::Lagrange{Segment, 1}, xi::Vec)
+                                    (u,) = xi
+                         @inbounds return (0.5 + -0.5u, 0.5 + 0.5u)
+        end
+         @inline function get_basis_derivatives(::Type{Segment}, ::Type{Lagrange{Segment, 1}}, xi::Vec)
+                                    (u,) = xi
+                         @inbounds return (Vec(float.(tuple(-0.5))), Vec(float.(tuple(0.5))))
+        end
+         @inline function get_basis_derivatives(::Segment, ::Lagrange{Segment, 1}, xi::Vec)
+                                    (u,) = xi
+                         @inbounds return (Vec(float.(tuple(-0.5))), Vec(float.(tuple(0.5))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Segment, 2}: 3-node quadratic segment element
@@ -84,6 +100,22 @@
                                     (u,) = xi
                          @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))))))
         end
+         @inline function get_basis_functions(::Type{Segment}, ::Type{Lagrange{Segment, 2}}, xi::Vec)
+                                    (u,) = xi
+                         @inbounds return (-0.5u + 0.5 * u ^ 2, 0.5u + 0.5 * u ^ 2, 1 + -1.0 * u ^ 2)
+        end
+         @inline function get_basis_functions(::Segment, ::Lagrange{Segment, 2}, xi::Vec)
+                                    (u,) = xi
+                         @inbounds return (-0.5u + 0.5 * u ^ 2, 0.5u + 0.5 * u ^ 2, 1 + -1.0 * u ^ 2)
+        end
+         @inline function get_basis_derivatives(::Type{Segment}, ::Type{Lagrange{Segment, 2}}, xi::Vec)
+                                    (u,) = xi
+                         @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))))))
+        end
+         @inline function get_basis_derivatives(::Segment, ::Lagrange{Segment, 2}, xi::Vec)
+                                    (u,) = xi
+                         @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))))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Triangle, 1}: 3-node linear triangular element
@@ -112,6 +144,22 @@
                                     (u, v) = xi
                          @inbounds return (Vec(float.(tuple(-1.0, -1.0))), Vec(float.(tuple(1, 0))), Vec(float.(tuple(0, 1))))
         end
+         @inline function get_basis_functions(::Type{Triangle}, ::Type{Lagrange{Triangle, 1}}, xi::Vec)
+                                    (u, v) = xi
+                         @inbounds return (1 + -1.0u + -1.0v, +u, +v)
+        end
+         @inline function get_basis_functions(::Triangle, ::Lagrange{Triangle, 1}, xi::Vec)
+                                    (u, v) = xi
+                         @inbounds return (1 + -1.0u + -1.0v, +u, +v)
+        end
+         @inline function get_basis_derivatives(::Type{Triangle}, ::Type{Lagrange{Triangle, 1}}, xi::Vec)
+                                    (u, v) = xi
+                         @inbounds return (Vec(float.(tuple(-1.0, -1.0))), Vec(float.(tuple(1, 0))), Vec(float.(tuple(0, 1))))
+        end
+         @inline function get_basis_derivatives(::Triangle, ::Lagrange{Triangle, 1}, xi::Vec)
+                                    (u, v) = xi
+                         @inbounds return (Vec(float.(tuple(-1.0, -1.0))), Vec(float.(tuple(1, 0))), Vec(float.(tuple(0, 1))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Triangle, 2}: 6-node quadratic triangular element
@@ -140,6 +188,22 @@
                                     (u, v) = xi
                          @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))))))
         end
+         @inline function get_basis_functions(::Type{Triangle}, ::Type{Lagrange{Triangle, 2}}, xi::Vec)
+                                    (u, v) = xi
+                         @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)
+        end
+         @inline function get_basis_functions(::Triangle, ::Lagrange{Triangle, 2}, xi::Vec)
+                                    (u, v) = xi
+                         @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)
+        end
+         @inline function get_basis_derivatives(::Type{Triangle}, ::Type{Lagrange{Triangle, 2}}, xi::Vec)
+                                    (u, v) = xi
+                         @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))))))
+        end
+         @inline function get_basis_derivatives(::Triangle, ::Lagrange{Triangle, 2}, xi::Vec)
+                                    (u, v) = xi
+                         @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))))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Quadrilateral, 1}: 4-node bilinear quadrilateral element
@@ -168,6 +232,22 @@
                                     (u, v) = xi
                          @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))))
         end
+         @inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 1}}, xi::Vec)
+                                    (u, v) = xi
+                         @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))
+        end
+         @inline function get_basis_functions(::Quadrilateral, ::Lagrange{Quadrilateral, 1}, xi::Vec)
+                                    (u, v) = xi
+                         @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))
+        end
+         @inline function get_basis_derivatives(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 1}}, xi::Vec)
+                                    (u, v) = xi
+                         @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))))
+        end
+         @inline function get_basis_derivatives(::Quadrilateral, ::Lagrange{Quadrilateral, 1}, xi::Vec)
+                                    (u, v) = xi
+                         @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))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Quadrilateral, 2}: 8-node serendipity quadrilateral element
@@ -196,6 +276,22 @@
                                     (u, v) = xi
                          @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)))))))
         end
+         @inline function get_basis_functions(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
+                                    (u, v) = xi
+                         @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))
+        end
+         @inline function get_basis_functions(::Quadrilateral, ::Lagrange{Quadrilateral, 2}, xi::Vec)
+                                    (u, v) = xi
+                         @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))
+        end
+         @inline function get_basis_derivatives(::Type{Quadrilateral}, ::Type{Lagrange{Quadrilateral, 2}}, xi::Vec)
+                                    (u, v) = xi
+                         @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)))))))
+        end
+         @inline function get_basis_derivatives(::Quadrilateral, ::Lagrange{Quadrilateral, 2}, xi::Vec)
+                                    (u, v) = xi
+                         @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)))))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Quadrilateral, 2}: 9-node biquadratic quadrilateral element
@@ -224,6 +320,22 @@
                                     (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_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, 1}: 4-node linear tetrahedral element
@@ -252,6 +364,22 @@
                                     (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_functions(::Type{Tetrahedron}, ::Type{Lagrange{Tetrahedron, 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, ::Lagrange{Tetrahedron, 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}, ::Type{Lagrange{Tetrahedron, 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, ::Lagrange{Tetrahedron, 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, 2}: 10-node quadratic tetrahedral element
@@ -280,6 +408,22 @@
                                     (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_functions(::Type{Tetrahedron}, ::Type{Lagrange{Tetrahedron, 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, ::Lagrange{Tetrahedron, 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}, ::Type{Lagrange{Tetrahedron, 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, ::Lagrange{Tetrahedron, 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, 1}: 8-node trilinear hexahedral element
@@ -308,6 +452,22 @@
                                     (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)))))
         end
+         @inline function get_basis_functions(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 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, ::Lagrange{Hexahedron, 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}, ::Type{Lagrange{Hexahedron, 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)))))
+        end
+         @inline function get_basis_derivatives(::Hexahedron, ::Lagrange{Hexahedron, 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)))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Hexahedron, 2}: 20-node serendipity hexahedral element
@@ -336,6 +496,22 @@
                                     (u, v, w) = xi
                          @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)))))
         end
+         @inline function get_basis_functions(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
+                                    (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))
+        end
+         @inline function get_basis_functions(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
+                                    (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))
+        end
+         @inline function get_basis_derivatives(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
+                                    (u, v, w) = xi
+                         @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)))))
+        end
+         @inline function get_basis_derivatives(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
+                                    (u, v, w) = xi
+                         @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)))))
+        end
 
 # ──────────────────────────────────────────────────────────────────────────────
 # Lagrange{Hexahedron, 2}: 27-node triquadratic hexahedral element
@@ -364,6 +540,22 @@
                                     (u, v, w) = xi
                          @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
+         @inline function get_basis_functions(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
+                                    (u, v, w) = xi
+                         @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))
+        end
+         @inline function get_basis_functions(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
+                                    (u, v, w) = xi
+                         @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))
+        end
+         @inline function get_basis_derivatives(::Type{Hexahedron}, ::Type{Lagrange{Hexahedron, 2}}, xi::Vec)
+                                    (u, v, w) = xi
+                         @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
+         @inline function get_basis_derivatives(::Hexahedron, ::Lagrange{Hexahedron, 2}, xi::Vec)
+                                    (u, v, w) = xi
+                         @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
@@ -392,6 +584,22 @@
                                     (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
+         @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
+         @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)
@@ -420,6 +628,22 @@
                                     (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_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
@@ -448,4 +672,20 @@
                                     (u, v, w) = xi
                          @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)))))
         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
+                         @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)))))
+        end
+         @inline function get_basis_derivatives(::Wedge, ::Lagrange{Wedge, 2}, xi::Vec)
+                                    (u, v, w) = xi
+                         @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)))))
+        end
 
diff --git a/src/basis/lagrange_generator.jl b/src/basis/lagrange_generator.jl
index 89cfb9c..64c4692 100644
--- a/src/basis/lagrange_generator.jl
+++ b/src/basis/lagrange_generator.jl
@@ -271,6 +271,10 @@ function create_basis(topology_type::Symbol, polynomial_degree::Int, description
             return $coord_tuple
         end
 
+        # ──────────────────────────────────────────────────────────────────────
+        # OLD API (for compatibility during transition)
+        # ──────────────────────────────────────────────────────────────────────
+
         # Return tuple directly - zero allocations!
         @inline function eval_basis!(::Type{Lagrange{$topology_type,$polynomial_degree}}, ::Type{T}, xi::Vec) where T
             $unpack
@@ -292,6 +296,33 @@ function create_basis(topology_type::Symbol, polynomial_degree::Int, description
             $unpack
             @inbounds return $dbasis_tuple
         end
+
+        # ──────────────────────────────────────────────────────────────────────
+        # NEW API (separation of concerns: topology + basis)
+        # See: docs/book/adr-003-basis-function-api.md
+        # ──────────────────────────────────────────────────────────────────────
+
+        # Basis functions at a point in reference element
+        @inline function get_basis_functions(::Type{$topology_type}, ::Type{Lagrange{$topology_type,$polynomial_degree}}, xi::Vec)
+            $unpack
+            @inbounds return $basis_tuple
+        end
+
+        @inline function get_basis_functions(::$topology_type, ::Lagrange{$topology_type,$polynomial_degree}, xi::Vec)
+            $unpack
+            @inbounds return $basis_tuple
+        end
+
+        # Basis function derivatives (gradients) at a point in reference element
+        @inline function get_basis_derivatives(::Type{$topology_type}, ::Type{Lagrange{$topology_type,$polynomial_degree}}, xi::Vec)
+            $unpack
+            @inbounds return $dbasis_tuple
+        end
+
+        @inline function get_basis_derivatives(::$topology_type, ::Lagrange{$topology_type,$polynomial_degree}, xi::Vec)
+            $unpack
+            @inbounds return $dbasis_tuple
+        end
     end
     return code
 end