mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
Jukka Aho
fb3056e513
Ensure gradient identities run against the same API users import, not a bespoke subset of source files. - Replace relative includes with `using JuliaFEM`.
82 lines
2.8 KiB
Julia
82 lines
2.8 KiB
Julia
# Test gradient properties for all elements
|
|
using Test
|
|
using StaticArrays, Tensors
|
|
|
|
using JuliaFEM
|
|
|
|
@testset "Gradient Properties" begin
|
|
@testset "Linear elements - constant gradients" begin
|
|
# Tri3 gradients should be constant everywhere
|
|
dN1 = get_basis_derivatives(Tri3(), Lagrange{1}(), Vec{2}((0.2, 0.3)))
|
|
dN2 = get_basis_derivatives(Tri3(), Lagrange{1}(), Vec{2}((0.5, 0.4)))
|
|
|
|
for i in 1:3
|
|
@test dN1[i] ≈ dN2[i] atol = 1e-14
|
|
end
|
|
|
|
# Tet4 gradients should be constant everywhere
|
|
dN1 = get_basis_derivatives(Tet4(), Lagrange{1}(), Vec{3}((0.1, 0.2, 0.3)))
|
|
dN2 = get_basis_derivatives(Tet4(), Lagrange{1}(), Vec{3}((0.2, 0.1, 0.4)))
|
|
|
|
for i in 1:4
|
|
@test dN1[i] ≈ dN2[i] atol = 1e-14
|
|
end
|
|
end
|
|
|
|
@testset "Sum of gradients = 0 (rigid body motion)" begin
|
|
# For any basis, sum of all gradients should be zero vector
|
|
# (ensures constant field has zero gradient)
|
|
|
|
# 1D
|
|
dN = get_basis_derivatives(Seg2(), Lagrange{1}(), Vec{1}((0.3,)))
|
|
@test sum(dN)[1] ≈ 0.0 atol = 1e-14
|
|
|
|
# 2D
|
|
dN = get_basis_derivatives(Tri6(), Lagrange{2}(), Vec{2}((0.3, 0.4)))
|
|
sum_grad = sum(dN)
|
|
@test sum_grad[1] ≈ 0.0 atol = 1e-14
|
|
@test sum_grad[2] ≈ 0.0 atol = 1e-14
|
|
|
|
dN = get_basis_derivatives(Quad9(), Lagrange{2}(), Vec{2}((0.5, -0.5)))
|
|
sum_grad = sum(dN)
|
|
@test sum_grad[1] ≈ 0.0 atol = 1e-14
|
|
@test sum_grad[2] ≈ 0.0 atol = 1e-14
|
|
|
|
# 3D
|
|
dN = get_basis_derivatives(Hex27(), Lagrange{2}(), Vec{3}((0.2, 0.3, -0.1)))
|
|
sum_grad = sum(dN)
|
|
@test sum_grad[1] ≈ 0.0 atol = 1e-14
|
|
@test sum_grad[2] ≈ 0.0 atol = 1e-14
|
|
@test sum_grad[3] ≈ 0.0 atol = 1e-14
|
|
end
|
|
|
|
@testset "Gradient return types" begin
|
|
# Test that gradients have correct Vec type
|
|
dN = get_basis_derivatives(Tri3(), Lagrange{1}(), Vec{2}((0.5, 0.25)))
|
|
@test dN isa SVector{3,Vec{2,Float64}}
|
|
@test dN[1] isa Vec{2,Float64}
|
|
|
|
dN = get_basis_derivatives(Hex8(), Lagrange{1}(), Vec{3}((0.0, 0.0, 0.0)))
|
|
@test dN isa SVector{8,Vec{3,Float64}}
|
|
@test dN[1] isa Vec{3,Float64}
|
|
end
|
|
|
|
@testset "Numerical gradient check (finite differences)" begin
|
|
# Simple finite difference check for Quad4
|
|
h = 1e-8
|
|
xi = Vec{2}((0.3, 0.4))
|
|
|
|
# Analytical gradient
|
|
dN = get_basis_derivatives(Quad4(), Lagrange{1}(), xi)
|
|
|
|
# Finite difference in u-direction
|
|
N_plus = get_basis_functions(Quad4(), Lagrange{1}(), Vec{2}((xi[1] + h, xi[2])))
|
|
N_minus = get_basis_functions(Quad4(), Lagrange{1}(), Vec{2}((xi[1] - h, xi[2])))
|
|
dN_u_fd = (N_plus - N_minus) / (2h)
|
|
|
|
for i in 1:4
|
|
@test dN[i][1] ≈ dN_u_fd[i] atol = 1e-6
|
|
end
|
|
end
|
|
end
|