diff --git a/test/quadrature/test_accuracy.jl b/test/quadrature/test_accuracy.jl deleted file mode 100644 index b0ca443..0000000 --- a/test/quadrature/test_accuracy.jl +++ /dev/null @@ -1,151 +0,0 @@ -# This file is a part of JuliaFEM. -# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md - -@testset "Quadrature Accuracy Verification" begin - - @testset "1D Segment - Polynomial Integration" begin - # Test that N-point rule integrates polynomials of degree 2N-1 exactly - - @testset "Order 1: Integrate constant (degree 0)" begin - points = get_quadrature_points(Segment, GaussLegendre{1}()) - # ∫₋₁¹ 1 dx = 2 - result = sum(p.weight * 1.0 for p in points) - @test result ≈ 2.0 - end - - @testset "Order 2: Integrate x³ (degree 3)" begin - points = get_quadrature_points(Segment, GaussLegendre{2}()) - # ∫₋₁¹ x³ dx = 0 (odd function) - result = sum(p.weight * p.coords[1]^3 for p in points) - @test result ≈ 0.0 atol=1e-15 - - # ∫₋₁¹ x² dx = 2/3 - result = sum(p.weight * p.coords[1]^2 for p in points) - @test result ≈ 2/3 rtol=1e-10 - end - - @testset "Order 3: Integrate x⁵ (degree 5)" begin - points = get_quadrature_points(Segment, GaussLegendre{3}()) - # ∫₋₁¹ x⁵ dx = 0 (odd function) - result = sum(p.weight * p.coords[1]^5 for p in points) - @test result ≈ 0.0 atol=1e-15 - - # ∫₋₁¹ x⁴ dx = 2/5 - result = sum(p.weight * p.coords[1]^4 for p in points) - @test result ≈ 2/5 rtol=1e-10 - end - end - - @testset "2D Triangle - Polynomial Integration" begin - # Reference triangle: vertices at (0,0), (1,0), (0,1) - # Area = 0.5 - - @testset "Order 1: Integrate constant" begin - points = get_quadrature_points(Triangle, GaussLegendre{1}()) - # ∫∫ 1 dA = 0.5 - result = sum(p.weight * 1.0 for p in points) - @test result ≈ 0.5 - end - - @testset "Order 2: Integrate linear functions" begin - points = get_quadrature_points(Triangle, GaussLegendre{2}()) - - # ∫∫ x dA = ∫₀¹ ∫₀^(1-x) x dy dx = 1/6 - result = sum(p.weight * p.coords[1] for p in points) - @test result ≈ 1/6 rtol=1e-10 - - # ∫∫ y dA = 1/6 (by symmetry) - result = sum(p.weight * p.coords[2] for p in points) - @test result ≈ 1/6 rtol=1e-10 - - # ∫∫ (x+y) dA = 1/3 - result = sum(p.weight * (p.coords[1] + p.coords[2]) for p in points) - @test result ≈ 1/3 rtol=1e-10 - end - - @testset "Order 3: Integrate quadratic functions" begin - points = get_quadrature_points(Triangle, GaussLegendre{3}()) - - # ∫∫ x² dA = ∫₀¹ ∫₀^(1-x) x² dy dx = 1/12 - result = sum(p.weight * p.coords[1]^2 for p in points) - @test result ≈ 1/12 rtol=1e-10 - - # ∫∫ xy dA = 1/24 - result = sum(p.weight * p.coords[1] * p.coords[2] for p in points) - @test result ≈ 1/24 rtol=1e-10 - end - end - - @testset "2D Quadrilateral - Polynomial Integration" begin - # Reference quad: [-1,1]², Area = 4 - - @testset "Order 2: Integrate x²" begin - points = get_quadrature_points(Quadrilateral, GaussLegendre{2}()) - # ∫₋₁¹ ∫₋₁¹ x² dy dx = 2 * (2/3) * 2 = 8/3 - result = sum(p.weight * p.coords[1]^2 for p in points) - @test result ≈ 8/3 rtol=1e-10 - end - - @testset "Order 3: Integrate x²y²" begin - points = get_quadrature_points(Quadrilateral, GaussLegendre{3}()) - # ∫₋₁¹ ∫₋₁¹ x²y² dy dx = (2/3) * (2/3) = 4/9 - result = sum(p.weight * p.coords[1]^2 * p.coords[2]^2 for p in points) - @test result ≈ 4/9 rtol=1e-10 - end - end - - @testset "3D Tetrahedron - Polynomial Integration" begin - # Reference tetrahedron: vertices at (0,0,0), (1,0,0), (0,1,0), (0,0,1) - # Volume = 1/6 - - @testset "Order 1: Integrate constant" begin - points = get_quadrature_points(Tetrahedron, GaussLegendre{1}()) - # ∫∫∫ 1 dV = 1/6 - result = sum(p.weight * 1.0 for p in points) - @test result ≈ 1/6 - end - - @testset "Order 2: Integrate linear functions" begin - points = get_quadrature_points(Tetrahedron, GaussLegendre{2}()) - - # ∫∫∫ x dV = 1/24 (by symmetry and integration) - result = sum(p.weight * p.coords[1] for p in points) - @test result ≈ 1/24 rtol=1e-10 - - # ∫∫∫ (x+y+z) dV = 3/24 = 1/8 - result = sum(p.weight * (p.coords[1] + p.coords[2] + p.coords[3]) for p in points) - @test result ≈ 1/8 rtol=1e-10 - end - end - - @testset "3D Hexahedron - Polynomial Integration" begin - # Reference hex: [-1,1]³, Volume = 8 - - @testset "Order 2: Integrate x²" begin - points = get_quadrature_points(Hexahedron, GaussLegendre{2}()) - # ∫₋₁¹ ∫₋₁¹ ∫₋₁¹ x² dz dy dx = 2 * 2 * (2/3) = 8/3 - result = sum(p.weight * p.coords[1]^2 for p in points) - @test result ≈ 8/3 rtol=1e-10 - end - - @testset "Order 3: Integrate x²y²z²" begin - points = get_quadrature_points(Hexahedron, GaussLegendre{3}()) - # ∫₋₁¹ ∫₋₁¹ ∫₋₁¹ x²y²z² dz dy dx = (2/3)³ = 8/27 - result = sum(p.weight * p.coords[1]^2 * p.coords[2]^2 * p.coords[3]^2 for p in points) - @test result ≈ 8/27 rtol=1e-10 - end - end - - @testset "Verify exactness limits" begin - # GaussLegendre{N} should NOT be exact for degree 2N or higher - - @testset "Segment: Order 2 fails for degree 4" begin - points = get_quadrature_points(Segment, GaussLegendre{2}()) - # ∫₋₁¹ x⁴ dx = 2/5, but 2-point rule gives different answer - result = sum(p.weight * p.coords[1]^4 for p in points) - exact = 2/5 - # Should have some error (not exact) - @test abs(result - exact) > 1e-10 - end - end -end