mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-10-02 22:31:31 +00:00
Jukka Aho
85 lines
3.2 KiB
Julia
85 lines
3.2 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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"""
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`HellingerReissnerKernel`: displacement + piecewise-constant symmetric stress
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on the DOF-based assembler.
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1. Global `K` is numerically symmetric.
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2. `K_uu` is zero (no displacement Laplace term in classical HR).
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3. `K_σσ` equals `-vol · (G M⁻¹ G)` on the stress block.
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4. `assemble!` allocates 0 bytes after warmup.
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"""
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using Test
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using JuliaFEM
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using JuliaFEM: HellingerReissnerKernel, ContinuumFormulation, FullThreeD
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using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache, assemble!, extract_system
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using JuliaFEM: create_unit_cube_mesh, create_elements!, @DOFSet, DOF, Displacement, Vertex
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using LinearAlgebra
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using Tensors
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function _hex8_unit_cube_single_element()
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return create_unit_cube_mesh(Hex8; nx = 1, ny = 1, nz = 1)
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end
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@testset "HellingerReissnerKernel symmetry + empty displacement block" begin
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mesh = _hex8_unit_cube_single_element()
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mat = LinearElastic(E = 210e9, ν = 0.3)
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S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
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elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
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k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
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asm = DOFBasedCOOAssembler()
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cache = DOFBasedCOOCache(elem, handler, mesh, k)
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assemble!(cache, asm, k, mesh)
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K, _ = extract_system(cache)
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R = K - transpose(K)
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@test norm(R) <= 1e-8 * max(1.0, norm(K))
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n_u = 3 * length(mesh.nodes)
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Kuu = K[1:n_u, 1:n_u]
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@test norm(Kuu) <= 1e-10 * max(1.0, norm(K))
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end
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@testset "HellingerReissnerKernel K_σσ vs −vol·(G M⁻¹ G)" begin
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mesh = _hex8_unit_cube_single_element()
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mat = LinearElastic(E = 210e9, ν = 0.3)
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S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
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elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
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k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
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asm = DOFBasedCOOAssembler()
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cache = DOFBasedCOOCache(elem, handler, mesh, k)
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assemble!(cache, asm, k, mesh)
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K, _ = extract_system(cache)
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n_u = 3 * length(mesh.nodes)
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Kss = K[(n_u + 1):end, (n_u + 1):end]
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vol = 1.0 # unit cube
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ref = -vol * k.σσ
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@test size(Kss) == (6, 6)
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@test norm(Kss - ref) / max(norm(ref), 1.0) < 1e-12
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end
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@testset "HellingerReissnerKernel assemble! zero allocations" begin
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mesh = _hex8_unit_cube_single_element()
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mat = LinearElastic(E = 210e9, ν = 0.3)
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S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
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elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
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k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
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asm = DOFBasedCOOAssembler()
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cache = DOFBasedCOOCache(elem, handler, mesh, k)
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for _ in 1:3
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assemble!(cache, asm, k, mesh)
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end
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GC.gc()
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@test (@allocated assemble!(cache, asm, k, mesh)) == 0
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end
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@testset "HellingerReissnerKernel API guards" begin
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mat = LinearElastic(E = 210e9, ν = 0.3)
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k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
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@test dofs_per_node(k) == 5
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@test_throws ErrorException get_field(k)
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end
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