mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
Jukka Aho
382 lines
14 KiB
Julia
382 lines
14 KiB
Julia
# This file is a part of JuliaFEM.
|
||
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
||
|
||
"""
|
||
Mass-matrix microkernel tests through the DOF-based assembler.
|
||
|
||
What the test file proves:
|
||
|
||
1. **Default kernel produces zero `M`.** A `ContinuumKernel` /
|
||
`HeatKernel` constructed without `density` / `heat_capacity` returns
|
||
`evaluate_mass_entry == 0` so both `apply_M!` and `assemble_M!`
|
||
produce a structural-zero `M`. Existing static-only tests stay valid.
|
||
|
||
2. **Consistent mass matrix is correct.** With unit density on a unit
|
||
cube, the row-sum of `M` (which equals `sum(M*1) = ∫ ρ dV = ρ·V`)
|
||
matches `density * volume` to round-off — for elasticity it sums
|
||
each component independently, for heat it sums the scalar field.
|
||
|
||
3. **`M` is symmetric, SPD on the active DOFs, and `apply_M!` matches
|
||
`M * x`** to round-off for several random `x`.
|
||
|
||
4. **Density scaling is linear.** Doubling `density` doubles every
|
||
entry of `M` exactly.
|
||
|
||
5. **Block-diagonal in components.** The elasticity mass matrix has
|
||
no `(α, β)` cross terms — `M[i_x, j_y] == 0` for any node pair.
|
||
|
||
6. **Zero allocations.** Both `apply_M!` and `assemble_M!` allocate
|
||
0 bytes per call after warmup, same hard contract as `apply_K!` /
|
||
`assemble!`.
|
||
|
||
7. **Cache reuse.** Calling `assemble!` then `assemble_M!` on the
|
||
same cache produces an independent `K` and `M`, both correct.
|
||
|
||
The combination of (2) and (4) verifies the `evaluate_mass_entry`
|
||
microkernel is *the* place to extend mass behaviour — variable density
|
||
materials drop in by overriding `evaluate_mass_entry` for a new kernel
|
||
type without touching the assembler.
|
||
"""
|
||
|
||
using Test
|
||
using JuliaFEM
|
||
using JuliaFEM: ContinuumFormulation, FullThreeD, Temperature, Vertex
|
||
using JuliaFEM: @DOFSet, DOF
|
||
using JuliaFEM: LinearElastic, Displacement, ContinuumKernel
|
||
using JuliaFEM: HeatConductivity, HeatKernel
|
||
using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache
|
||
using JuliaFEM: apply_K!, apply_M!, assemble_M!, extract_system
|
||
using JuliaFEM: create_elements!
|
||
using LinearAlgebra
|
||
using SparseArrays
|
||
using Tensors
|
||
using Random
|
||
|
||
# ----------------------------------------------------------------------------
|
||
# Mesh helpers (mirror the other DOF-based test files; kept local so this
|
||
# file stays independent and the WARNINGS about helper redefinitions are
|
||
# expected when the suites run together).
|
||
# ----------------------------------------------------------------------------
|
||
|
||
function _build_hex8_box(nx::Int, ny::Int, nz::Int)
|
||
nodes = Vec{3,Float64}[]
|
||
nidx(i, j, k) = (i - 1) + (j - 1) * (nx + 1) + (k - 1) * (nx + 1) * (ny + 1) + 1
|
||
for k in 1:(nz + 1), j in 1:(ny + 1), i in 1:(nx + 1)
|
||
push!(nodes, Vec{3}((Float64(i - 1) / nx,
|
||
Float64(j - 1) / ny,
|
||
Float64(k - 1) / nz)))
|
||
end
|
||
conns = NTuple{8,UInt32}[]
|
||
for k in 1:nz, j in 1:ny, i in 1:nx
|
||
n1 = nidx(i, j, k)
|
||
n2 = nidx(i + 1, j, k)
|
||
n3 = nidx(i + 1, j + 1, k)
|
||
n4 = nidx(i, j + 1, k)
|
||
n5 = nidx(i, j, k + 1)
|
||
n6 = nidx(i + 1, j, k + 1)
|
||
n7 = nidx(i + 1, j + 1, k + 1)
|
||
n8 = nidx(i, j + 1, k + 1)
|
||
push!(conns, (UInt32(n1), UInt32(n2), UInt32(n3), UInt32(n4),
|
||
UInt32(n5), UInt32(n6), UInt32(n7), UInt32(n8)))
|
||
end
|
||
return Mesh{8,Hexahedron{8}}(nodes, conns)
|
||
end
|
||
|
||
"Set up DOF-based elasticity assembly with optional density."
|
||
function _setup_elasticity(mesh; density::Float64 = 0.0)
|
||
material = LinearElastic(E = 210e9, ν = 0.3)
|
||
kernel = ContinuumKernel(ContinuumFormulation{FullThreeD}(),
|
||
material, Displacement{3}();
|
||
density = density)
|
||
S = @DOFSet{u::DOF{Displacement{3}, Vertex}}
|
||
elements, dof_mgr = create_elements!(mesh, Element{Hexahedron{8}, Lagrange{1}, S})
|
||
asm = DOFBasedCOOAssembler()
|
||
cache = DOFBasedCOOCache(elements, dof_mgr, mesh, kernel)
|
||
return cache, asm, kernel, mesh
|
||
end
|
||
|
||
"Set up DOF-based heat assembly with optional heat capacity."
|
||
function _setup_heat(mesh; heat_capacity::Float64 = 0.0)
|
||
material = HeatConductivity(k = 50.2)
|
||
kernel = HeatKernel(ContinuumFormulation{FullThreeD}(),
|
||
material, Temperature();
|
||
heat_capacity = heat_capacity)
|
||
S = @DOFSet{T::DOF{Temperature, Vertex}}
|
||
elements, dof_mgr = create_elements!(mesh, Element{Hexahedron{8}, Lagrange{1}, S})
|
||
asm = DOFBasedCOOAssembler()
|
||
cache = DOFBasedCOOCache(elements, dof_mgr, mesh, kernel)
|
||
return cache, asm, kernel, mesh
|
||
end
|
||
|
||
# ----------------------------------------------------------------------------
|
||
# 1. Default kernels (no density) → structurally-zero M
|
||
# ----------------------------------------------------------------------------
|
||
|
||
@testset "evaluate_mass_entry: default kernels return structural-zero M" begin
|
||
println("\n" * "=" ^ 70)
|
||
println("MASS MATRIX — defaults (no density / heat_capacity)")
|
||
println("=" ^ 70)
|
||
|
||
@testset "ContinuumKernel default density" begin
|
||
mesh = _build_hex8_box(2, 1, 1)
|
||
cache, asm, kernel, m = _setup_elasticity(mesh)
|
||
@test kernel.density == 0.0
|
||
|
||
assemble_M!(cache, asm, kernel, m)
|
||
M, _ = extract_system(cache)
|
||
@test maximum(abs, M) == 0.0
|
||
|
||
x = randn(cache.ndofs); y = zeros(cache.ndofs)
|
||
apply_M!(y, cache, asm, kernel, m, x)
|
||
@test all(iszero, y)
|
||
|
||
println(" ContinuumKernel density=0 M structural zero ✓")
|
||
end
|
||
|
||
@testset "HeatKernel default heat_capacity" begin
|
||
mesh = _build_hex8_box(2, 1, 1)
|
||
cache, asm, kernel, m = _setup_heat(mesh)
|
||
@test kernel.heat_capacity == 0.0
|
||
|
||
assemble_M!(cache, asm, kernel, m)
|
||
M, _ = extract_system(cache)
|
||
@test maximum(abs, M) == 0.0
|
||
|
||
x = randn(cache.ndofs); y = zeros(cache.ndofs)
|
||
apply_M!(y, cache, asm, kernel, m, x)
|
||
@test all(iszero, y)
|
||
|
||
println(" HeatKernel heat_capacity=0 M structural zero ✓")
|
||
end
|
||
end
|
||
|
||
# ----------------------------------------------------------------------------
|
||
# 2. Correctness: row-sum = ρ·V, symmetry, SPD, apply_M! matches M*x.
|
||
# ----------------------------------------------------------------------------
|
||
|
||
@testset "evaluate_mass_entry: correctness (row-sum, symmetry, SPD, apply_M!)" begin
|
||
println("\n" * "=" ^ 70)
|
||
println("MASS MATRIX — CORRECTNESS (consistent M)")
|
||
println("=" ^ 70)
|
||
|
||
Random.seed!(20260508)
|
||
|
||
@testset "Heat: ρcp = 1, unit cube" begin
|
||
ρcp = 1.0
|
||
mesh = _build_hex8_box(2, 2, 2)
|
||
cache, asm, kernel, m = _setup_heat(mesh; heat_capacity = ρcp)
|
||
n = cache.ndofs
|
||
|
||
assemble_M!(cache, asm, kernel, m)
|
||
M, _ = extract_system(cache)
|
||
|
||
# Symmetric to round-off
|
||
@test maximum(abs, M - M') < 1e-12 * maximum(abs, M)
|
||
|
||
# Row-sum: sum(M*1) = ρcp · ∫ dV = ρcp · 1.0 (unit cube)
|
||
rowsum_total = sum(M * ones(n))
|
||
@test isapprox(rowsum_total, ρcp * 1.0; rtol = 1e-12)
|
||
|
||
# SPD: every diagonal positive, x' M x > 0 for several random x
|
||
@test all(>(0.0), diag(M))
|
||
for _ in 1:5
|
||
x = randn(n)
|
||
@test x' * M * x > 0.0
|
||
end
|
||
|
||
# apply_M! ≡ M * x to round-off
|
||
max_rel = 0.0
|
||
for _ in 1:5
|
||
x = randn(n)
|
||
y_ref = M * x
|
||
y_mf = zeros(n); apply_M!(y_mf, cache, asm, kernel, m, x)
|
||
rel = norm(y_mf - y_ref) / max(norm(y_ref), 1.0)
|
||
@test rel < 1e-12
|
||
max_rel = max(max_rel, rel)
|
||
end
|
||
|
||
println(" Heat ndof=$n rowsum=$(round(rowsum_total; sigdigits = 5)) " *
|
||
"(expected $(ρcp)) max(apply_M! vs M*x)=$(round(max_rel; sigdigits = 3))")
|
||
end
|
||
|
||
@testset "Elasticity: ρ = 1, unit cube" begin
|
||
ρ = 1.0
|
||
mesh = _build_hex8_box(2, 2, 2)
|
||
cache, asm, kernel, m = _setup_elasticity(mesh; density = ρ)
|
||
n = cache.ndofs
|
||
|
||
assemble_M!(cache, asm, kernel, m)
|
||
M, _ = extract_system(cache)
|
||
|
||
# Symmetric to round-off
|
||
@test maximum(abs, M - M') < 1e-12 * maximum(abs, M)
|
||
|
||
# Row-sum per component: each of the 3 displacement components
|
||
# independently has sum = ρ · V. Total row-sum is 3 · ρ · V.
|
||
rowsum_total = sum(M * ones(n))
|
||
@test isapprox(rowsum_total, 3 * ρ * 1.0; rtol = 1e-12)
|
||
|
||
@test all(>(0.0), diag(M))
|
||
|
||
max_rel = 0.0
|
||
for _ in 1:5
|
||
x = randn(n)
|
||
y_ref = M * x
|
||
y_mf = zeros(n); apply_M!(y_mf, cache, asm, kernel, m, x)
|
||
rel = norm(y_mf - y_ref) / max(norm(y_ref), 1.0)
|
||
@test rel < 1e-12
|
||
max_rel = max(max_rel, rel)
|
||
end
|
||
|
||
println(" Elast ndof=$n rowsum=$(round(rowsum_total; sigdigits = 5)) " *
|
||
"(expected $(3 * ρ)) max(apply_M! vs M*x)=$(round(max_rel; sigdigits = 3))")
|
||
end
|
||
end
|
||
|
||
# ----------------------------------------------------------------------------
|
||
# 3. Density scaling is linear.
|
||
# ----------------------------------------------------------------------------
|
||
|
||
@testset "evaluate_mass_entry: density scaling is linear" begin
|
||
mesh = _build_hex8_box(2, 1, 1)
|
||
|
||
cache_a, asm_a, kernel_a, m_a = _setup_elasticity(mesh; density = 1.0)
|
||
cache_b, asm_b, kernel_b, m_b = _setup_elasticity(mesh; density = 2.5)
|
||
|
||
assemble_M!(cache_a, asm_a, kernel_a, m_a); M_a, _ = extract_system(cache_a)
|
||
assemble_M!(cache_b, asm_b, kernel_b, m_b); M_b, _ = extract_system(cache_b)
|
||
|
||
@test maximum(abs, M_b - 2.5 * M_a) < 1e-12 * maximum(abs, M_a)
|
||
end
|
||
|
||
# ----------------------------------------------------------------------------
|
||
# 4. Block-diagonal structure of the elasticity mass matrix.
|
||
# ----------------------------------------------------------------------------
|
||
|
||
@testset "evaluate_mass_entry: elasticity mass is block-diagonal in components" begin
|
||
mesh = _build_hex8_box(1, 1, 1)
|
||
cache, asm, kernel, m = _setup_elasticity(mesh; density = 1.0)
|
||
n = cache.ndofs
|
||
|
||
assemble_M!(cache, asm, kernel, m)
|
||
M, _ = extract_system(cache)
|
||
Md = Matrix(M)
|
||
|
||
# DOF layout for displacement is (node, x), (node, y), (node, z) per node.
|
||
# `local_dof_layout(Element{Hex8, ...})` orders them this way, and
|
||
# `create_elements!` produces a global numbering matching that order.
|
||
# So DOF index `3*(node-1) + α` for component α ∈ {1,2,3}.
|
||
nnodes = length(m.nodes)
|
||
@test n == 3 * nnodes
|
||
|
||
# Cross-component blocks must be zero — pick a random pair of nodes
|
||
# and verify M[i_x, j_y], M[i_x, j_z], M[i_y, j_z] are all zero.
|
||
Random.seed!(20260508)
|
||
for _ in 1:5
|
||
i = rand(1:nnodes); j = rand(1:nnodes)
|
||
for (αi, αj) in ((1, 2), (1, 3), (2, 3), (2, 1), (3, 1), (3, 2))
|
||
row = 3 * (i - 1) + αi
|
||
col = 3 * (j - 1) + αj
|
||
@test Md[row, col] == 0.0
|
||
end
|
||
end
|
||
end
|
||
|
||
# ----------------------------------------------------------------------------
|
||
# 5. Zero-alloc + KA-untouched contract.
|
||
# ----------------------------------------------------------------------------
|
||
|
||
@testset "evaluate_mass_entry: zero allocations (apply_M! + assemble_M!)" begin
|
||
println("\n" * "=" ^ 70)
|
||
println("MASS MATRIX — ZERO-ALLOC")
|
||
println("=" ^ 70)
|
||
|
||
@testset "Elast cube $(nx)×$(ny)×$(nz)" for (nx, ny, nz) in
|
||
[(1, 1, 1), (2, 1, 1), (3, 2, 2)]
|
||
|
||
mesh = _build_hex8_box(nx, ny, nz)
|
||
cache, asm, kernel, m = _setup_elasticity(mesh; density = 7850.0)
|
||
n = cache.ndofs
|
||
x = ones(n); y = zeros(n)
|
||
|
||
# warmup
|
||
assemble_M!(cache, asm, kernel, m)
|
||
apply_M!(y, cache, asm, kernel, m, x)
|
||
|
||
GC.gc()
|
||
a_asm = @allocated assemble_M!(cache, asm, kernel, m)
|
||
@test a_asm == 0
|
||
|
||
GC.gc()
|
||
a_mf = @allocated apply_M!(y, cache, asm, kernel, m, x)
|
||
@test a_mf == 0
|
||
|
||
nelems = length(m.connectivity)
|
||
println(" Elast $(nx)×$(ny)×$(nz) $(lpad(nelems,3)) elem " *
|
||
"$(lpad(n,4)) dof assemble_M!=$a_asm apply_M!=$a_mf")
|
||
end
|
||
|
||
@testset "Heat cube $(nx)×$(ny)×$(nz)" for (nx, ny, nz) in
|
||
[(1, 1, 1), (2, 1, 1), (3, 2, 2)]
|
||
|
||
mesh = _build_hex8_box(nx, ny, nz)
|
||
cache, asm, kernel, m = _setup_heat(mesh; heat_capacity = 3500.0)
|
||
n = cache.ndofs
|
||
x = ones(n); y = zeros(n)
|
||
|
||
assemble_M!(cache, asm, kernel, m)
|
||
apply_M!(y, cache, asm, kernel, m, x)
|
||
|
||
GC.gc()
|
||
a_asm = @allocated assemble_M!(cache, asm, kernel, m)
|
||
@test a_asm == 0
|
||
|
||
GC.gc()
|
||
a_mf = @allocated apply_M!(y, cache, asm, kernel, m, x)
|
||
@test a_mf == 0
|
||
|
||
nelems = length(m.connectivity)
|
||
println(" Heat $(nx)×$(ny)×$(nz) $(lpad(nelems,3)) elem " *
|
||
"$(lpad(n,4)) dof assemble_M!=$a_asm apply_M!=$a_mf")
|
||
end
|
||
end
|
||
|
||
# ----------------------------------------------------------------------------
|
||
# 6. Cache reuse: assemble! then assemble_M! produces correct K and M.
|
||
# ----------------------------------------------------------------------------
|
||
|
||
@testset "evaluate_mass_entry: cache reuse (K then M)" begin
|
||
println("\n" * "=" ^ 70)
|
||
println("MASS MATRIX — CACHE REUSE (assemble! then assemble_M!)")
|
||
println("=" ^ 70)
|
||
|
||
mesh = _build_hex8_box(2, 2, 2)
|
||
cache, asm, kernel, m = _setup_elasticity(mesh; density = 7850.0)
|
||
n = cache.ndofs
|
||
|
||
# 1. Assemble K, extract.
|
||
assemble!(cache, asm, kernel, m)
|
||
K, _ = extract_system(cache)
|
||
|
||
# 2. Then assemble M into the *same* cache, extract.
|
||
assemble_M!(cache, asm, kernel, m)
|
||
M, _ = extract_system(cache)
|
||
|
||
# K and M are independent SparseMatrixCSC instances now.
|
||
# K must be SPD on free DOFs; M must be SPD outright (positive
|
||
# diagonal, x' M x > 0).
|
||
@test maximum(abs, K - K') < 1e-9 * maximum(abs, K)
|
||
@test maximum(abs, M - M') < 1e-12 * maximum(abs, M)
|
||
|
||
# M's row-sum must still equal 3 ρ V (unaffected by the prior K assembly).
|
||
rowsum_total = sum(M * ones(n))
|
||
@test isapprox(rowsum_total, 3 * 7850.0 * 1.0; rtol = 1e-12)
|
||
|
||
# Quick sanity: K is *not* M (would imply the cache wasn't reset
|
||
# between the two assemblies).
|
||
@test maximum(abs, K - M) > 0.5 * maximum(abs, K)
|
||
|
||
println(" Hex8 2×2×2 ndof=$n K SPD ✓ M SPD ✓ rowsum(M)=" *
|
||
"$(round(rowsum_total; sigdigits = 5)) (expected $(3 * 7850.0))")
|
||
end
|