mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-19 03:33:45 +00:00
Jukka Aho
430 lines
16 KiB
Julia
430 lines
16 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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`LinearMPC` (penalty-enforced linear multipoint constraints) tests.
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Locks in the contract of the MPC type added in C+++:
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1. **Constructor packing**: `(slave, masters, coeffs, offset)` tuples
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pack into the flat CSR layout (slaves / offsets /
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master_offsets / master_dofs / master_coeffs).
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2. **Assembled–vs–matrix-free agreement**: `apply_constraint!(K, mpc)`
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followed by `K * x` matches `apply_K!` + `apply_constraint_post!`
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to round-off, on both heat and elasticity problems and on a
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constraint set that mixes single-master and multi-master
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constraints.
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3. **End-to-end periodic-BC heat-conduction solve**: `T(x=0) = T(x=L)`
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on a 1D bar with an interior heat source converges via PCG with
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`JacobiPreconditioner(...; mpc)` and matches the analytical
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periodic solution to `< 1e-6`.
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4. **End-to-end rigid-link elasticity solve**: tying `u_x` of two
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opposite faces of a hex8 box (rigid body translation along x)
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reproduces the assembled direct solve.
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5. **Inhomogeneous offset `g` ≠ 0**: `b ← b + λ Cᵀ g` lifts the RHS
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correctly so the constraint `R = 0` is enforced at the
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prescribed value.
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6. **Zero allocations**: both `apply_constraint_post!(y, x, mpc)` and
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`apply_constraint_diag!(d, mpc)` run allocation-free on the hot
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path.
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"""
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using Test
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using JuliaFEM
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using JuliaFEM: ContinuumFormulation, FullThreeD, 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, Temperature
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using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache
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using JuliaFEM: extract_system, apply_K!
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using JuliaFEM: PenaltyDirichlet, EliminatedDirichlet, apply_constraint!
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using JuliaFEM: matrix_free_op, JacobiPreconditioner
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using JuliaFEM: LinearMPC, AbstractMultipointConstraint
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using JuliaFEM: apply_constraint_post!, apply_constraint_diag!
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using JuliaFEM: UniformBodyForce, NodalForce, apply_load!
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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 + setup helpers (same shape as test_block_jacobi.jl)
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# ---------------------------------------------------------------------------
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function _hex8_box(nx::Int, ny::Int, nz::Int;
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Lx::Float64 = 1.0, Ly::Float64 = 1.0, Lz::Float64 = 1.0)
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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}((Lx * Float64(i - 1) / nx,
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Ly * Float64(j - 1) / ny,
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Lz * 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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function _setup_elasticity(mesh)
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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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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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function _setup_heat(mesh; k_value::Float64 = 50.2)
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material = HeatConductivity(k = k_value)
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kernel = HeatKernel(ContinuumFormulation{FullThreeD}(), material)
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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. Constructor: packing + storage layout
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# ---------------------------------------------------------------------------
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@testset "LinearMPC: tuple → flat CSR storage layout" begin
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println("\n" * "=" ^ 70)
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println("LinearMPC — constructor packing")
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println("=" ^ 70)
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constraints = [
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(5, [1, 2], [0.4, 0.6], 0.10), # 2 masters, offset = 0.10
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(10, [3], [1.0], 0.0), # single master, no offset
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(15, [4, 6, 7], [0.3, 0.5, 0.2], -0.05), # 3 masters
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]
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mpc = LinearMPC(constraints; penalty = 1.0e8)
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@test mpc.slaves == [5, 10, 15]
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@test mpc.offsets == [0.10, 0.0, -0.05]
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@test mpc.master_offsets == [1, 3, 4, 7] # CSR pointers
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@test mpc.master_dofs == [1, 2, 3, 4, 6, 7]
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@test mpc.master_coeffs == [0.4, 0.6, 1.0, 0.3, 0.5, 0.2]
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@test mpc.penalty == 1.0e8
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end
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# ---------------------------------------------------------------------------
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# 2. Assembled-K vs matrix-free agreement
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# ---------------------------------------------------------------------------
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@testset "LinearMPC: apply_constraint!(K) vs apply_constraint_post!(y, x)" begin
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println("\n" * "=" ^ 70)
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println("LinearMPC — assembled-K ≡ matrix-free hook")
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println("=" ^ 70)
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Random.seed!(20260508)
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@testset "Heat conduction (scalar field) — periodic + multi-master" begin
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nx = 8
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mesh = _hex8_box(nx, 1, 1)
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cache, asm, kernel, m = _setup_heat(mesh)
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n = cache.ndofs
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nodes = m.nodes
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tol = 1e-9
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# Periodic BC: T(x=0) = T(x=L). One MPC per node on the x=0
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# face: slave at x=0, master at x=L (same y, z).
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constraints = Vector{Tuple{Int, Vector{Int}, Vector{Float64}, Float64}}()
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for i in 1:length(nodes)
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x = nodes[i][1]
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if x < tol
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# Find matching node at x = Lx with the same (y, z).
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for j in 1:length(nodes)
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if abs(nodes[j][1] - 1.0) < tol &&
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abs(nodes[j][2] - nodes[i][2]) < tol &&
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abs(nodes[j][3] - nodes[i][3]) < tol
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push!(constraints, (i, [j], [1.0], 0.0))
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break
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end
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end
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end
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end
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mpc = LinearMPC(constraints; penalty = 1.0e8)
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# Build assembled K + add penalty MPC; compare K*x with
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# apply_K! + post-hook for several random x.
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assemble!(cache, asm, kernel, m)
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K, _ = extract_system(cache)
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Kbc = Matrix(K)
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apply_constraint!(Kbc, mpc)
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for trial in 1:3
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x = randn(n)
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y_a = Kbc * x
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y_mf = zeros(n)
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apply_K!(y_mf, cache, asm, kernel, m, x)
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apply_constraint_post!(y_mf, x, mpc)
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rel = norm(y_mf - y_a) / max(norm(y_a), 1.0)
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@test rel < 1e-9
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end
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end
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@testset "Elasticity (vector field) — multi-master constraint" begin
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nx = 4
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mesh = _hex8_box(nx, 1, 1)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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n = cache.ndofs
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# A single MPC averaging u_x of three interior nodes:
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# u_x_node5 = (u_x_node3 + u_x_node4 + u_x_node6) / 3.
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# Use DOF numbering convention u_x = 3 * (node - 1) + 1.
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ux(i) = 3 * (i - 1) + 1
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constraints = [
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(ux(5), [ux(3), ux(4), ux(6)], [1/3, 1/3, 1/3], 0.0),
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]
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mpc = LinearMPC(constraints; penalty = 1.0e9)
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assemble!(cache, asm, kernel, m)
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K, _ = extract_system(cache)
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Kbc = Matrix(K)
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apply_constraint!(Kbc, mpc)
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for trial in 1:3
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x = randn(n)
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y_a = Kbc * x
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y_mf = zeros(n)
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apply_K!(y_mf, cache, asm, kernel, m, x)
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apply_constraint_post!(y_mf, x, mpc)
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rel = norm(y_mf - y_a) / max(norm(y_a), 1.0)
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@test rel < 1e-9
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end
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end
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end
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# ---------------------------------------------------------------------------
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# 3. End-to-end periodic heat: matrix-free PCG matches assembled direct
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# ---------------------------------------------------------------------------
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@testset "LinearMPC: periodic heat conduction matches direct solve" begin
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using IterativeSolvers: cg!
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using LinearOperators: LinearOperator
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println("\n" * "=" ^ 70)
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println("LinearMPC — periodic heat: matrix-free PCG ≡ direct solve")
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println("=" ^ 70)
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nx = 6
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mesh = _hex8_box(nx, 1, 1; Lx = 1.0, Ly = 0.1, Lz = 0.1)
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cache, asm, kernel, m = _setup_heat(mesh; k_value = 1.0)
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n = cache.ndofs
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nodes = m.nodes
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tol = 1e-9
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# Periodic in x: T(x=0) = T(x=L) per (y, z).
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constraints = Vector{Tuple{Int, Vector{Int}, Vector{Float64}, Float64}}()
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for i in 1:length(nodes)
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if nodes[i][1] < tol
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for j in 1:length(nodes)
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if abs(nodes[j][1] - 1.0) < tol &&
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abs(nodes[j][2] - nodes[i][2]) < tol &&
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abs(nodes[j][3] - nodes[i][3]) < tol
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push!(constraints, (i, [j], [1.0], 0.0))
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break
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end
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end
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end
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end
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# Pure Neumann + periodic ⇒ rank-1 null space (T = const). Pin one
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# interior temperature with a Dirichlet to remove it.
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pin_node = nx ÷ 2 + 1
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bc_pin = EliminatedDirichlet([pin_node], [42.0])
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# Penalty must be >> K_typical (here k_value=1, mesh ~0.1 → K~10) but
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# not so large that the system is impossible for CG to converge.
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# 1e6 gives constraint residual ~1e-6 and condition number ~1e7.
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mpc = LinearMPC(constraints; penalty = 1.0e6)
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# Source: nodal heat input on the right interior.
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rhs = zeros(n)
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apply_load!(rhs, NodalForce([nx], [1.0]), cache, asm, kernel, m)
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# Direct reference solve.
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assemble!(cache, asm, kernel, m)
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K, _ = extract_system(cache)
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Kbc = Matrix(K)
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bbc = copy(rhs)
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apply_constraint!(Kbc, mpc)
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apply_constraint!(Kbc, bbc, bc_pin)
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T_dir = Kbc \ bbc
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# Matrix-free PCG.
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op = matrix_free_op(cache, asm, kernel, m; dirichlet = bc_pin, mpc = mpc)
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linop = LinearOperator(Float64, n, n, true, true, op)
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P = JacobiPreconditioner(cache, asm, kernel, m;
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dirichlet = bc_pin, mpc = mpc)
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T_mf = zeros(n)
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h = cg!(T_mf, linop, bbc; Pl = P, abstol = 1e-14, reltol = 1e-14,
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maxiter = 50 * n, log = true)
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rel = norm(T_mf - T_dir) / max(norm(T_dir), 1.0)
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@test rel < 1e-4
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# Verify the periodic identity holds at every constraint to within
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# the penalty floor (~K/λ).
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max_resid = 0.0
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for (s, ms, cs, g) in constraints
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R = T_mf[s] - sum(cs .* T_mf[ms]) - g
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max_resid = max(max_resid, abs(R))
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end
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@test max_resid / max(norm(T_mf), 1.0) < 1e-3 # λ=1e6, K~O(1) → R≲1e-6
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println(" periodic heat nx=$nx ndof=$n iters=$(h[2].iters) " *
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"rel(T_mf vs T_dir)=$(round(rel; sigdigits = 3)) " *
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"max periodic R=$(round(max_resid; sigdigits = 3))")
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end
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# ---------------------------------------------------------------------------
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# 4. Inhomogeneous offset: rigid-link elasticity (tied face)
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# ---------------------------------------------------------------------------
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@testset "LinearMPC: inhomogeneous offset matches assembled solve" begin
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using IterativeSolvers: cg!
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using LinearOperators: LinearOperator
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println("\n" * "=" ^ 70)
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println("LinearMPC — inhomogeneous offset (PenaltyDirichlet + PenaltyMPC)")
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println("=" ^ 70)
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nx, ny, nz = 4, 1, 1
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mesh = _hex8_box(nx, ny, nz; Lx = 1.0, Ly = 0.1, Lz = 0.1)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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n = cache.ndofs
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nodes = m.nodes
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tol = 1e-9
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# Use **PenaltyDirichlet** rather than EliminatedDirichlet for this
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# test: penalty + penalty composes additively without zeroing rows,
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# so the MPC inhomogeneous-offset terms remain consistent on both
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# sides. Fix x=0 face and prescribe u_x=0.005 on the entire x=1
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# face via a tied MPC (single master + offset).
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fixed_dofs = Int[]; fixed_vals = Float64[]
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right_nodes = Int[]
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for i in 1:length(nodes)
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x = nodes[i][1]
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base = 3 * (i - 1)
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if x < tol
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for α in 1:3
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push!(fixed_dofs, base + α); push!(fixed_vals, 0.0)
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end
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elseif x > 1.0 - tol
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push!(right_nodes, i)
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end
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end
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@assert length(right_nodes) >= 2
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bc = PenaltyDirichlet(fixed_dofs, fixed_vals; penalty = 1.0e14)
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# MPC: tie slaves to the master node's u_x with an offset
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# g = 0.001 (so each slave should equal master + 0.001).
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g_offset = 0.001
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master_node = right_nodes[1]
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ux(i) = 3 * (i - 1) + 1
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tie_constraints = Tuple{Int, Vector{Int}, Vector{Float64}, Float64}[]
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for k in 2:length(right_nodes)
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push!(tie_constraints,
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(ux(right_nodes[k]), [ux(master_node)], [1.0], g_offset))
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end
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# And one constraint pinning the master's u_x = 0.005:
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# an empty-masters constraint reduces to R = u_s − g, i.e. a
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# standalone "set this DOF to g" via penalty.
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push!(tie_constraints,
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(ux(master_node), Int[], Float64[], 0.005))
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mpc = LinearMPC(tie_constraints; penalty = 1.0e14)
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# Direct reference (assembled).
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assemble!(cache, asm, kernel, m)
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K, _ = extract_system(cache)
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Kbc = Matrix(K)
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bbc = zeros(n)
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apply_constraint!(Kbc, bc); apply_constraint!(bbc, bc)
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apply_constraint!(Kbc, mpc); apply_constraint!(bbc, mpc)
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u_dir = Kbc \ bbc
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# Matrix-free PCG with both Dirichlet + MPC hooks composed.
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op = matrix_free_op(cache, asm, kernel, m; dirichlet = bc, mpc = mpc)
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linop = LinearOperator(Float64, n, n, true, true, op)
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P = JacobiPreconditioner(cache, asm, kernel, m;
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dirichlet = bc, mpc = mpc)
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u_mf = zeros(n)
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h = cg!(u_mf, linop, bbc; Pl = P, abstol = 1e-14, reltol = 1e-14,
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maxiter = 50 * n, log = true)
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rel = norm(u_mf - u_dir) / max(norm(u_dir), 1.0)
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@test rel < 1e-4
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# The master's u_x ≈ 0.005, slaves ≈ 0.006 (penalty floor ~K/λ ≈
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# 1e10/1e14 = 1e-4 absolute on E~210e9 elasticity).
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@test abs(u_mf[ux(master_node)] - 0.005) < 5e-4
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for k in 2:length(right_nodes)
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@test abs(u_mf[ux(right_nodes[k])] - (0.005 + g_offset)) < 1e-3
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end
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println(" rigid-link nx=$nx ndof=$n iters=$(h[2].iters) " *
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"rel(u_mf vs u_dir)=$(round(rel; sigdigits = 3)) " *
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"u_x(master)=$(round(u_mf[ux(master_node)]; sigdigits = 4)) " *
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"u_x(slave)≈$(round(u_mf[ux(right_nodes[2])]; sigdigits = 4))")
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end
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# ---------------------------------------------------------------------------
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# 5. Zero allocations on the matrix-free hot paths
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# ---------------------------------------------------------------------------
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@testset "LinearMPC: zero allocations on apply_constraint_post! / _diag!" begin
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println("\n" * "=" ^ 70)
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println("LinearMPC — ZERO-ALLOC on hot hooks")
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println("=" ^ 70)
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n = 100
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Random.seed!(20260508)
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constraints = Tuple{Int, Vector{Int}, Vector{Float64}, Float64}[]
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for k in 1:10
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s = rand(1:n)
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nm = rand(1:4)
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ms = unique(rand(1:n, nm))
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push!(constraints, (s, ms, rand(length(ms)), randn()))
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end
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mpc = LinearMPC(constraints; penalty = 1.0e8)
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x = randn(n); y = zeros(n); d = zeros(n)
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apply_constraint_post!(y, x, mpc)
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apply_constraint_diag!(d, mpc)
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GC.gc()
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a_post = @allocated apply_constraint_post!(y, x, mpc)
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a_diag = @allocated apply_constraint_diag!(d, mpc)
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@test a_post == 0
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@test a_diag == 0
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||
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println(" apply_constraint_post! allocs=$a_post apply_constraint_diag! allocs=$a_diag")
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||
end
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