test(domains): add Hellinger–Reissner kernel regression

2026-08-06 04:21:33 +00:00 · 2026-05-09 18:38:25 +03:00
parent 29403d1948
commit 360fd26b21
1 changed files with 84 additions and 0 deletions
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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+`HellingerReissnerKernel`: displacement + piecewise-constant symmetric stress
+on the DOF-based assembler.
+
+1. Global `K` is numerically symmetric.
+2. `K_uu` is zero (no displacement Laplace term in classical HR).
+3. `K_σσ` equals `-vol · (G M⁻¹ G)` on the stress block.
+4. `assemble!` allocates 0 bytes after warmup.
+"""
+
+using Test
+using JuliaFEM
+using JuliaFEM: HellingerReissnerKernel, ContinuumFormulation, FullThreeD
+using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache, assemble!, extract_system
+using JuliaFEM: create_unit_cube_mesh, create_elements!, @DOFSet, DOF, Displacement, Vertex
+using LinearAlgebra
+using Tensors
+
+function _hex8_unit_cube_single_element()
+    return create_unit_cube_mesh(Hex8; nx = 1, ny = 1, nz = 1)
+end
+
+@testset "HellingerReissnerKernel symmetry + empty displacement block" begin
+    mesh = _hex8_unit_cube_single_element()
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
+    elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elem, handler, mesh, k)
+    assemble!(cache, asm, k, mesh)
+    K, _ = extract_system(cache)
+
+    R = K - transpose(K)
+    @test norm(R) <= 1e-8 * max(1.0, norm(K))
+
+    n_u = 3 * length(mesh.nodes)
+    Kuu = K[1:n_u, 1:n_u]
+    @test norm(Kuu) <= 1e-10 * max(1.0, norm(K))
+end
+
+@testset "HellingerReissnerKernel K_σσ vs −vol·(G M⁻¹ G)" begin
+    mesh = _hex8_unit_cube_single_element()
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
+    elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elem, handler, mesh, k)
+    assemble!(cache, asm, k, mesh)
+    K, _ = extract_system(cache)
+
+    n_u = 3 * length(mesh.nodes)
+    Kss = K[(n_u + 1):end, (n_u + 1):end]
+    vol = 1.0  # unit cube
+    ref = -vol * k.σσ
+    @test size(Kss) == (6, 6)
+    @test norm(Kss - ref) / max(norm(ref), 1.0) < 1e-12
+end
+
+@testset "HellingerReissnerKernel assemble! zero allocations" begin
+    mesh = _hex8_unit_cube_single_element()
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    S = @DOFSet{u::DOF{Displacement{3}, Vertex}, sig::DOF{SymmetricTensor{2,3}, Cell}}
+    elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elem, handler, mesh, k)
+    for _ in 1:3
+        assemble!(cache, asm, k, mesh)
+    end
+    GC.gc()
+    @test (@allocated assemble!(cache, asm, k, mesh)) == 0
+end
+
+@testset "HellingerReissnerKernel API guards" begin
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    k = HellingerReissnerKernel(ContinuumFormulation{FullThreeD}(), mat)
+    @test dofs_per_node(k) == 5
+    @test_throws ErrorException get_field(k)
+end