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chore(test): drop CElement real-basis regression
Remove outdated basis coupling tests for removed element APIs. - Delete `test/elements/test_celement_real_basis.jl`.
This commit is contained in:
Jukka Aho
@@ -1,285 +0,0 @@
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using Test
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using JuliaFEM
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using JuliaFEM: CElement, ScalarDOF, VectorDOF, interpolate, gradient
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using Tensors
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"""
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Test suite for CElement with REAL basis functions (not stubs).
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This test file verifies that CElement correctly uses the actual Lagrange
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basis functions from basis_generated.jl, not the stub implementations.
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"""
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@testset "CElement Real Basis Functions" begin
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@testset "Triangle Tri3 Linear Interpolation" begin
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# Create a linear triangle element
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# Nodes at vertices: (0,0), (1,0), (0,1)
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nodes = [
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Vec{2}((0.0, 0.0)), # Node 1
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Vec{2}((1.0, 0.0)), # Node 2
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Vec{2}((0.0, 1.0)) # Node 3
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]
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# Simple mesh structure
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mesh = (
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connectivity = [[1, 2, 3]],
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nodes = nodes
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)
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# Create element with scalar DOF
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elem = CElement{Tri3, Lagrange{1}, ScalarDOF}(1, (1, 2, 3))
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# Test nodal interpolation: At nodes, basis functions should be 1 at that node, 0 elsewhere
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# At node 1: ξ = (0, 0) → should get u[1] exactly
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u_global = [10.0, 20.0, 30.0] # Values at nodes 1, 2, 3
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# At parametric coord (0, 0) = node 1
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val1 = interpolate(elem, mesh, u_global, Vec{2}((0.0, 0.0)))
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@test val1 ≈ 10.0 atol=1e-12
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# At parametric coord (1, 0) = node 2
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val2 = interpolate(elem, mesh, u_global, Vec{2}((1.0, 0.0)))
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@test val2 ≈ 20.0 atol=1e-12
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# At parametric coord (0, 1) = node 3
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val3 = interpolate(elem, mesh, u_global, Vec{2}((0.0, 1.0)))
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@test val3 ≈ 30.0 atol=1e-12
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# Test centroid: ξ = (1/3, 1/3) should give average
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centroid = interpolate(elem, mesh, u_global, Vec{2}(1.0/3.0, 1.0/3.0))
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expected_centroid = (10.0 + 20.0 + 30.0) / 3.0
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@test centroid ≈ expected_centroid atol=1e-12
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println("✓ Tri3 linear interpolation: Exact at nodes, correct at centroid")
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end
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@testset "Triangle Tri3 Linear Gradient" begin
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# Same triangle as above
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nodes = [
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Vec{2}((0.0, 0.0)),
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Vec{2}((1.0, 0.0)),
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Vec{2}((0.0, 1.0))
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]
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mesh = (
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connectivity = [[1, 2, 3]],
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nodes = nodes
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)
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elem = CElement{Tri3, Lagrange{1}, ScalarDOF}(1, (1, 2, 3))
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# Linear field: u = x + 2y (gradient should be [1, 2])
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# At node 1 (0,0): u = 0
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# At node 2 (1,0): u = 1
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# At node 3 (0,1): u = 2
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u_global = [0.0, 1.0, 2.0]
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# Gradient should be constant [1, 2] everywhere for linear element
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grad_center = gradient(elem, mesh, u_global, Vec{2}(1.0/3.0, 1.0/3.0))
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@test grad_center[1] ≈ 1.0 atol=1e-10
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@test grad_center[2] ≈ 2.0 atol=1e-10
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# Gradient should be same at different points
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grad_node1 = gradient(elem, mesh, u_global, Vec{2}((0.0, 0.0)))
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@test grad_node1[1] ≈ 1.0 atol=1e-10
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@test grad_node1[2] ≈ 2.0 atol=1e-10
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println("✓ Tri3 gradient: Constant for linear field")
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end
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@testset "Tetrahedron Tet4 Linear Interpolation" begin
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# Create a linear tetrahedron
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# Standard reference tet: (0,0,0), (1,0,0), (0,1,0), (0,0,1)
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nodes = [
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Vec{3}((0.0, 0.0, 0.0)), # Node 1
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Vec{3}((1.0, 0.0, 0.0)), # Node 2
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Vec{3}((0.0, 1.0, 0.0)), # Node 3
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Vec{3}((0.0, 0.0, 1.0)) # Node 4
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]
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mesh = (
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connectivity = [[1, 2, 3, 4]],
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nodes = nodes
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)
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elem = CElement{Tet4, Lagrange{1}, ScalarDOF}(1, (1, 2, 3, 4))
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# Test nodal interpolation
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u_global = [5.0, 15.0, 25.0, 35.0]
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# At node 1: ξ = (0, 0, 0)
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val1 = interpolate(elem, mesh, u_global, Vec{3}((0.0, 0.0, 0.0)))
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@test val1 ≈ 5.0 atol=1e-12
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# At node 2: ξ = (1, 0, 0)
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val2 = interpolate(elem, mesh, u_global, Vec{3}((1.0, 0.0, 0.0)))
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@test val2 ≈ 15.0 atol=1e-12
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# At node 3: ξ = (0, 1, 0)
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val3 = interpolate(elem, mesh, u_global, Vec{3}((0.0, 1.0, 0.0)))
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@test val3 ≈ 25.0 atol=1e-12
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# At node 4: ξ = (0, 0, 1)
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val4 = interpolate(elem, mesh, u_global, Vec{3}((0.0, 0.0, 1.0)))
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@test val4 ≈ 35.0 atol=1e-12
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# Test centroid: ξ = (1/4, 1/4, 1/4)
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centroid = interpolate(elem, mesh, u_global, Vec{3}((0.25, 0.25, 0.25)))
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expected = (5.0 + 15.0 + 25.0 + 35.0) / 4.0
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@test centroid ≈ expected atol=1e-12
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println("✓ Tet4 linear interpolation: Exact at nodes, correct at centroid")
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end
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@testset "Tetrahedron Tet4 Linear Gradient" begin
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# Same tet as above
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nodes = [
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Vec{3}((0.0, 0.0, 0.0)),
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Vec{3}((1.0, 0.0, 0.0)),
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Vec{3}((0.0, 1.0, 0.0)),
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Vec{3}((0.0, 0.0, 1.0))
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]
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mesh = (
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connectivity = [[1, 2, 3, 4]],
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nodes = nodes
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)
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elem = CElement{Tet4, Lagrange{1}, ScalarDOF}(1, (1, 2, 3, 4))
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# Linear field: u = 2x + 3y + 4z → gradient = [2, 3, 4]
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# At nodes: u = [0, 2, 3, 4]
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u_global = [0.0, 2.0, 3.0, 4.0]
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# Gradient should be constant [2, 3, 4] everywhere
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grad_center = gradient(elem, mesh, u_global, Vec{3}((0.25, 0.25, 0.25)))
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@test grad_center[1] ≈ 2.0 atol=1e-10
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@test grad_center[2] ≈ 3.0 atol=1e-10
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@test grad_center[3] ≈ 4.0 atol=1e-10
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println("✓ Tet4 gradient: Constant for linear field")
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end
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@testset "Vector DOF Deformation Gradient" begin
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# Test 2D vector DOF (displacement field)
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nodes = [
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Vec{2}((0.0, 0.0)),
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Vec{2}((1.0, 0.0)),
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Vec{2}((0.0, 1.0))
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]
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mesh = (
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connectivity = [[1, 2, 3]],
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nodes = nodes
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)
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# Element with 2D vector DOF
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elem = CElement{Tri3, Lagrange{1}, VectorDOF{2}}(1, (1, 2, 3, 4, 5, 6))
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# Displacement field: u = [x, 2y] → F = [∂u₁/∂x ∂u₁/∂y; ∂u₂/∂x ∂u₂/∂y] = [1 0; 0 2]
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# At nodes: u = [[0,0], [1,0], [0,2]]
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u_global = [0.0, 0.0, # Node 1: (ux, uy)
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1.0, 0.0, # Node 2
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0.0, 2.0] # Node 3
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# Deformation gradient
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F = gradient(elem, mesh, u_global, Vec{2}(1.0/3.0, 1.0/3.0))
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# Should be [1 0; 0 2] for linear displacement
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@test F[1,1] ≈ 1.0 atol=1e-10 # ∂u₁/∂x
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@test F[1,2] ≈ 0.0 atol=1e-10 # ∂u₁/∂y
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@test F[2,1] ≈ 0.0 atol=1e-10 # ∂u₂/∂x
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@test F[2,2] ≈ 2.0 atol=1e-10 # ∂u₂/∂y
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println("✓ VectorDOF deformation gradient: Correct for linear displacement")
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end
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@testset "Partition of Unity (Completeness)" begin
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# Basis functions should sum to 1 at any point
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nodes = [
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Vec{2}((0.0, 0.0)),
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Vec{2}((1.0, 0.0)),
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Vec{2}((0.0, 1.0))
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]
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mesh = (
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connectivity = [[1, 2, 3]],
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nodes = nodes
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)
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elem = CElement{Tri3, Lagrange{1}, ScalarDOF}(1, (1, 2, 3))
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# Test at several points
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test_points = [
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Vec{2}((0.0, 0.0)),
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Vec{2}((0.5, 0.0)),
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Vec{2}((0.0, 0.5)),
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Vec{2}((0.5, 0.5)),
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Vec{2}((0.33, 0.33)),
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Vec{2}((0.1, 0.7))
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]
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u_ones = [1.0, 1.0, 1.0] # If all nodal values = 1, result should be 1
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for ξ in test_points
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# Skip if outside element (u + v > 1)
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if ξ[1] + ξ[2] > 1.0
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continue
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end
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val = interpolate(elem, mesh, u_ones, ξ)
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@test val ≈ 1.0 atol=1e-12
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end
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println("✓ Partition of unity: Sum of basis = 1 at all points")
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end
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@testset "Linear Reproduction (Consistency)" begin
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# Linear functions should be reproduced exactly
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nodes = [
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Vec{2}((0.0, 0.0)),
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Vec{2}((2.0, 0.0)),
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Vec{2}((0.0, 3.0))
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]
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mesh = (
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connectivity = [[1, 2, 3]],
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nodes = nodes
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)
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elem = CElement{Tri3, Lagrange{1}, ScalarDOF}(1, (1, 2, 3))
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# Linear function: u(x,y) = 5 + 2x + 3y
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u_nodal = [
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5.0, # At (0,0): 5
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5.0 + 2.0*2.0, # At (2,0): 9
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5.0 + 3.0*3.0 # At (0,3): 14
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]
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# Test at arbitrary physical points
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test_points = [
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(Vec{2}((0.5, 0.0)), Vec{2}((1.0, 0.0))), # (ξ, physical)
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(Vec{2}((0.0, 0.5)), Vec{2}((0.0, 1.5))),
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(Vec{2}((0.25, 0.25)), Vec{2}((0.5, 0.75)))
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]
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for (ξ, x_phys) in test_points
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val = interpolate(elem, mesh, u_nodal, ξ)
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expected = 5.0 + 2.0*x_phys[1] + 3.0*x_phys[2]
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@test val ≈ expected atol=1e-10
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end
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println("✓ Linear reproduction: Linear functions reproduced exactly")
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end
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end # @testset "CElement Real Basis Functions"
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println("\n" * "="^70)
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println("CElement Real Basis Test Summary")
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println("="^70)
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println("✅ All tests verify that CElement uses REAL Lagrange basis functions")
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println("✅ Interpolation: Exact at nodes, correct partition of unity")
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println("✅ Gradient: Constant for linear elements, correct deformation gradient")
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println("✅ Math properties: Completeness and consistency verified")
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println("="^70)
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