mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-19 17:58:53 +00:00
Jukka Aho
91 lines
3.2 KiB
Julia
91 lines
3.2 KiB
Julia
# Test basis functions at element nodes
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# At a node, the corresponding basis function should be 1, all others 0 (Kronecker delta property)
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using Test
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using StaticArrays, Tensors
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include("../../src/topology/api.jl")
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include("../../src/topology/segments.jl")
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include("../../src/topology/triangles.jl")
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include("../../src/topology/quadrilaterals.jl")
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include("../../src/topology/tetrahedra.jl")
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include("../../src/topology/hexahedra.jl")
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include("../../src/topology/pyramids.jl")
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include("../../src/topology/wedges.jl")
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include("../../src/basis/api.jl")
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include("../../src/basis/basis_generated.jl")
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@testset "Kronecker Delta Property at Nodes" begin
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@testset "Seg2 at nodes" begin
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# Node 1: xi = -1
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N = get_basis_functions(Seg2(), Lagrange{1}(), Vec{1}((-1.0,)))
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@test N[1] ≈ 1.0 atol = 1e-14
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@test N[2] ≈ 0.0 atol = 1e-14
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# Node 2: xi = 1
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N = get_basis_functions(Seg2(), Lagrange{1}(), Vec{1}((1.0,)))
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@test N[1] ≈ 0.0 atol = 1e-14
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@test N[2] ≈ 1.0 atol = 1e-14
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end
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@testset "Tri3 at nodes" begin
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# Node 1: (0, 0)
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N = get_basis_functions(Tri3(), Lagrange{1}(), Vec{2}((0.0, 0.0)))
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@test N[1] ≈ 1.0 atol = 1e-14
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@test N[2] ≈ 0.0 atol = 1e-14
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@test N[3] ≈ 0.0 atol = 1e-14
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# Node 2: (1, 0)
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N = get_basis_functions(Tri3(), Lagrange{1}(), Vec{2}((1.0, 0.0)))
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@test N[1] ≈ 0.0 atol = 1e-14
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@test N[2] ≈ 1.0 atol = 1e-14
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@test N[3] ≈ 0.0 atol = 1e-14
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# Node 3: (0, 1)
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N = get_basis_functions(Tri3(), Lagrange{1}(), Vec{2}((0.0, 1.0)))
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@test N[1] ≈ 0.0 atol = 1e-14
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@test N[2] ≈ 0.0 atol = 1e-14
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@test N[3] ≈ 1.0 atol = 1e-14
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end
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@testset "Quad4 at nodes" begin
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# Node 1: (-1, -1)
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N = get_basis_functions(Quad4(), Lagrange{1}(), Vec{2}((-1.0, -1.0)))
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@test N[1] ≈ 1.0 atol = 1e-14
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@test N[2] ≈ 0.0 atol = 1e-14
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@test N[3] ≈ 0.0 atol = 1e-14
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@test N[4] ≈ 0.0 atol = 1e-14
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# Node 3: (1, 1)
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N = get_basis_functions(Quad4(), Lagrange{1}(), Vec{2}((1.0, 1.0)))
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@test N[1] ≈ 0.0 atol = 1e-14
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@test N[2] ≈ 0.0 atol = 1e-14
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@test N[3] ≈ 1.0 atol = 1e-14
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@test N[4] ≈ 0.0 atol = 1e-14
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end
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@testset "Tet4 at nodes" begin
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# Node 1: (0, 0, 0)
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N = get_basis_functions(Tet4(), Lagrange{1}(), Vec{3}((0.0, 0.0, 0.0)))
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@test N[1] ≈ 1.0 atol = 1e-14
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@test all(N[2:4] .≈ 0.0)
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# Node 2: (1, 0, 0)
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N = get_basis_functions(Tet4(), Lagrange{1}(), Vec{3}((1.0, 0.0, 0.0)))
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@test N[2] ≈ 1.0 atol = 1e-14
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@test N[1] ≈ 0.0 atol = 1e-14
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@test N[3] ≈ 0.0 atol = 1e-14
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@test N[4] ≈ 0.0 atol = 1e-14
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end
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@testset "Hex8 at nodes" begin
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# Node 1: (-1, -1, -1)
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N = get_basis_functions(Hex8(), Lagrange{1}(), Vec{3}((-1.0, -1.0, -1.0)))
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@test N[1] ≈ 1.0 atol=1e-14
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@test all(N[2:8] .≈ 0.0)
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# Check interior point for partition of unity
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N = get_basis_functions(Hex8(), Lagrange{1}(), Vec{3}((0.5, 0.3, -0.2)))
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@test sum(N) ≈ 1.0 atol=1e-14
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end
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end
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