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test(assemblers): add DOF-based mass assembly tests
This commit is contained in:
Jukka Aho
@@ -0,0 +1,381 @@
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# 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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Mass-matrix microkernel tests through the DOF-based assembler.
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What the test file proves:
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1. **Default kernel produces zero `M`.** A `ContinuumKernel` /
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`HeatKernel` constructed without `density` / `heat_capacity` returns
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`evaluate_mass_entry == 0` so both `apply_M!` and `assemble_M!`
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produce a structural-zero `M`. Existing static-only tests stay valid.
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2. **Consistent mass matrix is correct.** With unit density on a unit
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cube, the row-sum of `M` (which equals `sum(M*1) = ∫ ρ dV = ρ·V`)
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matches `density * volume` to round-off — for elasticity it sums
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each component independently, for heat it sums the scalar field.
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3. **`M` is symmetric, SPD on the active DOFs, and `apply_M!` matches
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`M * x`** to round-off for several random `x`.
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4. **Density scaling is linear.** Doubling `density` doubles every
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entry of `M` exactly.
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5. **Block-diagonal in components.** The elasticity mass matrix has
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no `(α, β)` cross terms — `M[i_x, j_y] == 0` for any node pair.
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6. **Zero allocations.** Both `apply_M!` and `assemble_M!` allocate
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0 bytes per call after warmup, same hard contract as `apply_K!` /
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`assemble!`.
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7. **Cache reuse.** Calling `assemble!` then `assemble_M!` on the
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same cache produces an independent `K` and `M`, both correct.
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The combination of (2) and (4) verifies the `evaluate_mass_entry`
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microkernel is *the* place to extend mass behaviour — variable density
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materials drop in by overriding `evaluate_mass_entry` for a new kernel
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type without touching the assembler.
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"""
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using Test
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using JuliaFEM
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using JuliaFEM: ContinuumFormulation, FullThreeD, Temperature, Vertex
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using JuliaFEM: @DOFSet, DOF
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using JuliaFEM: LinearElastic, Displacement, ContinuumKernel
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using JuliaFEM: HeatConductivity, HeatKernel
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using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache
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using JuliaFEM: apply_K!, apply_M!, assemble_M!, extract_system
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using JuliaFEM: create_elements!
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using LinearAlgebra
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using SparseArrays
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using Tensors
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using Random
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# ----------------------------------------------------------------------------
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# Mesh helpers (mirror the other DOF-based test files; kept local so this
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# file stays independent and the WARNINGS about helper redefinitions are
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# expected when the suites run together).
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# ----------------------------------------------------------------------------
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function _build_hex8_box(nx::Int, ny::Int, nz::Int)
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nodes = Vec{3,Float64}[]
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nidx(i, j, k) = (i - 1) + (j - 1) * (nx + 1) + (k - 1) * (nx + 1) * (ny + 1) + 1
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for k in 1:(nz + 1), j in 1:(ny + 1), i in 1:(nx + 1)
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push!(nodes, Vec{3}((Float64(i - 1) / nx,
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Float64(j - 1) / ny,
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Float64(k - 1) / nz)))
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end
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conns = NTuple{8,UInt32}[]
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for k in 1:nz, j in 1:ny, i in 1:nx
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n1 = nidx(i, j, k)
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n2 = nidx(i + 1, j, k)
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n3 = nidx(i + 1, j + 1, k)
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n4 = nidx(i, j + 1, k)
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n5 = nidx(i, j, k + 1)
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n6 = nidx(i + 1, j, k + 1)
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n7 = nidx(i + 1, j + 1, k + 1)
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n8 = nidx(i, j + 1, k + 1)
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push!(conns, (UInt32(n1), UInt32(n2), UInt32(n3), UInt32(n4),
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UInt32(n5), UInt32(n6), UInt32(n7), UInt32(n8)))
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end
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return Mesh{8,Hexahedron{8}}(nodes, conns)
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end
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"Set up DOF-based elasticity assembly with optional density."
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function _setup_elasticity(mesh; density::Float64 = 0.0)
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material = LinearElastic(E = 210e9, ν = 0.3)
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kernel = ContinuumKernel(ContinuumFormulation{FullThreeD}(),
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material, Displacement{3}();
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density = density)
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S = @DOFSet{u::DOF{Displacement{3}, Vertex}}
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elements, dof_mgr = create_elements!(mesh, Element{Hexahedron{8}, Lagrange{1}, S})
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asm = DOFBasedCOOAssembler()
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cache = DOFBasedCOOCache(elements, dof_mgr, mesh, kernel)
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return cache, asm, kernel, mesh
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end
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"Set up DOF-based heat assembly with optional heat capacity."
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function _setup_heat(mesh; heat_capacity::Float64 = 0.0)
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material = HeatConductivity(k = 50.2)
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kernel = HeatKernel(ContinuumFormulation{FullThreeD}(),
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material, Temperature();
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heat_capacity = heat_capacity)
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S = @DOFSet{T::DOF{Temperature, Vertex}}
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elements, dof_mgr = create_elements!(mesh, Element{Hexahedron{8}, Lagrange{1}, S})
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asm = DOFBasedCOOAssembler()
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cache = DOFBasedCOOCache(elements, dof_mgr, mesh, kernel)
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return cache, asm, kernel, mesh
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end
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# ----------------------------------------------------------------------------
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# 1. Default kernels (no density) → structurally-zero M
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# ----------------------------------------------------------------------------
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@testset "evaluate_mass_entry: default kernels return structural-zero M" begin
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println("\n" * "=" ^ 70)
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println("MASS MATRIX — defaults (no density / heat_capacity)")
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println("=" ^ 70)
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@testset "ContinuumKernel default density" begin
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mesh = _build_hex8_box(2, 1, 1)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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@test kernel.density == 0.0
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assemble_M!(cache, asm, kernel, m)
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M, _ = extract_system(cache)
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@test maximum(abs, M) == 0.0
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x = randn(cache.ndofs); y = zeros(cache.ndofs)
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apply_M!(y, cache, asm, kernel, m, x)
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@test all(iszero, y)
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println(" ContinuumKernel density=0 M structural zero ✓")
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end
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@testset "HeatKernel default heat_capacity" begin
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mesh = _build_hex8_box(2, 1, 1)
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cache, asm, kernel, m = _setup_heat(mesh)
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@test kernel.heat_capacity == 0.0
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assemble_M!(cache, asm, kernel, m)
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M, _ = extract_system(cache)
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@test maximum(abs, M) == 0.0
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x = randn(cache.ndofs); y = zeros(cache.ndofs)
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apply_M!(y, cache, asm, kernel, m, x)
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@test all(iszero, y)
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println(" HeatKernel heat_capacity=0 M structural zero ✓")
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end
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end
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# ----------------------------------------------------------------------------
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# 2. Correctness: row-sum = ρ·V, symmetry, SPD, apply_M! matches M*x.
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# ----------------------------------------------------------------------------
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@testset "evaluate_mass_entry: correctness (row-sum, symmetry, SPD, apply_M!)" begin
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println("\n" * "=" ^ 70)
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println("MASS MATRIX — CORRECTNESS (consistent M)")
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println("=" ^ 70)
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Random.seed!(20260508)
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@testset "Heat: ρcp = 1, unit cube" begin
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ρcp = 1.0
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mesh = _build_hex8_box(2, 2, 2)
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cache, asm, kernel, m = _setup_heat(mesh; heat_capacity = ρcp)
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n = cache.ndofs
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assemble_M!(cache, asm, kernel, m)
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M, _ = extract_system(cache)
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# Symmetric to round-off
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@test maximum(abs, M - M') < 1e-12 * maximum(abs, M)
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# Row-sum: sum(M*1) = ρcp · ∫ dV = ρcp · 1.0 (unit cube)
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rowsum_total = sum(M * ones(n))
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@test isapprox(rowsum_total, ρcp * 1.0; rtol = 1e-12)
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# SPD: every diagonal positive, x' M x > 0 for several random x
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@test all(>(0.0), diag(M))
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for _ in 1:5
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x = randn(n)
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@test x' * M * x > 0.0
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end
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# apply_M! ≡ M * x to round-off
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max_rel = 0.0
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for _ in 1:5
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x = randn(n)
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y_ref = M * x
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y_mf = zeros(n); apply_M!(y_mf, cache, asm, kernel, m, x)
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rel = norm(y_mf - y_ref) / max(norm(y_ref), 1.0)
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@test rel < 1e-12
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max_rel = max(max_rel, rel)
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end
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println(" Heat ndof=$n rowsum=$(round(rowsum_total; sigdigits = 5)) " *
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"(expected $(ρcp)) max(apply_M! vs M*x)=$(round(max_rel; sigdigits = 3))")
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end
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@testset "Elasticity: ρ = 1, unit cube" begin
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ρ = 1.0
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mesh = _build_hex8_box(2, 2, 2)
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cache, asm, kernel, m = _setup_elasticity(mesh; density = ρ)
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n = cache.ndofs
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assemble_M!(cache, asm, kernel, m)
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M, _ = extract_system(cache)
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# Symmetric to round-off
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@test maximum(abs, M - M') < 1e-12 * maximum(abs, M)
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# Row-sum per component: each of the 3 displacement components
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# independently has sum = ρ · V. Total row-sum is 3 · ρ · V.
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rowsum_total = sum(M * ones(n))
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@test isapprox(rowsum_total, 3 * ρ * 1.0; rtol = 1e-12)
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@test all(>(0.0), diag(M))
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max_rel = 0.0
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for _ in 1:5
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x = randn(n)
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y_ref = M * x
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y_mf = zeros(n); apply_M!(y_mf, cache, asm, kernel, m, x)
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rel = norm(y_mf - y_ref) / max(norm(y_ref), 1.0)
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@test rel < 1e-12
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max_rel = max(max_rel, rel)
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end
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println(" Elast ndof=$n rowsum=$(round(rowsum_total; sigdigits = 5)) " *
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"(expected $(3 * ρ)) max(apply_M! vs M*x)=$(round(max_rel; sigdigits = 3))")
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end
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end
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# ----------------------------------------------------------------------------
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# 3. Density scaling is linear.
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# ----------------------------------------------------------------------------
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@testset "evaluate_mass_entry: density scaling is linear" begin
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mesh = _build_hex8_box(2, 1, 1)
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cache_a, asm_a, kernel_a, m_a = _setup_elasticity(mesh; density = 1.0)
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cache_b, asm_b, kernel_b, m_b = _setup_elasticity(mesh; density = 2.5)
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assemble_M!(cache_a, asm_a, kernel_a, m_a); M_a, _ = extract_system(cache_a)
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assemble_M!(cache_b, asm_b, kernel_b, m_b); M_b, _ = extract_system(cache_b)
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@test maximum(abs, M_b - 2.5 * M_a) < 1e-12 * maximum(abs, M_a)
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end
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# ----------------------------------------------------------------------------
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# 4. Block-diagonal structure of the elasticity mass matrix.
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# ----------------------------------------------------------------------------
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@testset "evaluate_mass_entry: elasticity mass is block-diagonal in components" begin
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mesh = _build_hex8_box(1, 1, 1)
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cache, asm, kernel, m = _setup_elasticity(mesh; density = 1.0)
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n = cache.ndofs
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assemble_M!(cache, asm, kernel, m)
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M, _ = extract_system(cache)
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Md = Matrix(M)
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# DOF layout for displacement is (node, x), (node, y), (node, z) per node.
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# `local_dof_layout(Element{Hex8, ...})` orders them this way, and
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# `create_elements!` produces a global numbering matching that order.
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# So DOF index `3*(node-1) + α` for component α ∈ {1,2,3}.
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nnodes = length(m.nodes)
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@test n == 3 * nnodes
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# Cross-component blocks must be zero — pick a random pair of nodes
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# and verify M[i_x, j_y], M[i_x, j_z], M[i_y, j_z] are all zero.
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Random.seed!(20260508)
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for _ in 1:5
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i = rand(1:nnodes); j = rand(1:nnodes)
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for (αi, αj) in ((1, 2), (1, 3), (2, 3), (2, 1), (3, 1), (3, 2))
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row = 3 * (i - 1) + αi
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col = 3 * (j - 1) + αj
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@test Md[row, col] == 0.0
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end
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end
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end
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# ----------------------------------------------------------------------------
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# 5. Zero-alloc + KA-untouched contract.
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# ----------------------------------------------------------------------------
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@testset "evaluate_mass_entry: zero allocations (apply_M! + assemble_M!)" begin
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println("\n" * "=" ^ 70)
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println("MASS MATRIX — ZERO-ALLOC")
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println("=" ^ 70)
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@testset "Elast cube $(nx)×$(ny)×$(nz)" for (nx, ny, nz) in
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[(1, 1, 1), (2, 1, 1), (3, 2, 2)]
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mesh = _build_hex8_box(nx, ny, nz)
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cache, asm, kernel, m = _setup_elasticity(mesh; density = 7850.0)
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n = cache.ndofs
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x = ones(n); y = zeros(n)
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# warmup
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assemble_M!(cache, asm, kernel, m)
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apply_M!(y, cache, asm, kernel, m, x)
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GC.gc()
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a_asm = @allocated assemble_M!(cache, asm, kernel, m)
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@test a_asm == 0
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GC.gc()
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a_mf = @allocated apply_M!(y, cache, asm, kernel, m, x)
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@test a_mf == 0
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nelems = length(m.connectivity)
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println(" Elast $(nx)×$(ny)×$(nz) $(lpad(nelems,3)) elem " *
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"$(lpad(n,4)) dof assemble_M!=$a_asm apply_M!=$a_mf")
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end
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@testset "Heat cube $(nx)×$(ny)×$(nz)" for (nx, ny, nz) in
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[(1, 1, 1), (2, 1, 1), (3, 2, 2)]
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mesh = _build_hex8_box(nx, ny, nz)
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cache, asm, kernel, m = _setup_heat(mesh; heat_capacity = 3500.0)
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n = cache.ndofs
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x = ones(n); y = zeros(n)
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assemble_M!(cache, asm, kernel, m)
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apply_M!(y, cache, asm, kernel, m, x)
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GC.gc()
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a_asm = @allocated assemble_M!(cache, asm, kernel, m)
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@test a_asm == 0
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GC.gc()
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a_mf = @allocated apply_M!(y, cache, asm, kernel, m, x)
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@test a_mf == 0
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nelems = length(m.connectivity)
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println(" Heat $(nx)×$(ny)×$(nz) $(lpad(nelems,3)) elem " *
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"$(lpad(n,4)) dof assemble_M!=$a_asm apply_M!=$a_mf")
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end
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end
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# ----------------------------------------------------------------------------
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# 6. Cache reuse: assemble! then assemble_M! produces correct K and M.
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# ----------------------------------------------------------------------------
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@testset "evaluate_mass_entry: cache reuse (K then M)" begin
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println("\n" * "=" ^ 70)
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println("MASS MATRIX — CACHE REUSE (assemble! then assemble_M!)")
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println("=" ^ 70)
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mesh = _build_hex8_box(2, 2, 2)
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cache, asm, kernel, m = _setup_elasticity(mesh; density = 7850.0)
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n = cache.ndofs
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# 1. Assemble K, extract.
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assemble!(cache, asm, kernel, m)
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K, _ = extract_system(cache)
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# 2. Then assemble M into the *same* cache, extract.
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assemble_M!(cache, asm, kernel, m)
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M, _ = extract_system(cache)
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# K and M are independent SparseMatrixCSC instances now.
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# K must be SPD on free DOFs; M must be SPD outright (positive
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# diagonal, x' M x > 0).
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@test maximum(abs, K - K') < 1e-9 * maximum(abs, K)
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@test maximum(abs, M - M') < 1e-12 * maximum(abs, M)
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# M's row-sum must still equal 3 ρ V (unaffected by the prior K assembly).
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rowsum_total = sum(M * ones(n))
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@test isapprox(rowsum_total, 3 * 7850.0 * 1.0; rtol = 1e-12)
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# Quick sanity: K is *not* M (would imply the cache wasn't reset
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# between the two assemblies).
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@test maximum(abs, K - M) > 0.5 * maximum(abs, K)
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println(" Hex8 2×2×2 ndof=$n K SPD ✓ M SPD ✓ rowsum(M)=" *
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"$(round(rowsum_total; sigdigits = 5)) (expected $(3 * 7850.0))")
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end
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