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test(assemblers): add assembler equivalence test
Tests equivalence between different assembler implementations. Validates that different assembly approaches produce identical results.
This commit is contained in:
Jukka Aho
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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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Test: Assembler Equivalence
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Verify that all assembler implementations produce identical results:
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- COOAssembler (element-based, coordinate format)
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- CSCAssembler (element-based, compressed sparse column)
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- NodeBasedCOOAssembler (node-based, coordinate format)
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Test model: Two Hex8 elements sharing a face (minimal realistic mesh)
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"""
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using Test
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using JuliaFEM
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using LinearAlgebra
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using SparseArrays
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using Tensors
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@testset "Assembler Equivalence - Two Hex8 Elements" begin
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println("\n" * "="^70)
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println("ASSEMBLER EQUIVALENCE TEST")
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println("="^70)
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# ========================================================================
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# 1. Create Minimal Test Mesh (Two Hex8 Elements)
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# ========================================================================
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println("\n[1] Creating two-element mesh...")
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# Two unit cubes sharing a face
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# Element 1: X ∈ [0,1], Y ∈ [0,1], Z ∈ [0,1]
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# Element 2: X ∈ [1,2], Y ∈ [0,1], Z ∈ [0,1]
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nodes = Vec{3,Float64}[
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# Element 1 nodes (bottom face at Z=0, top face at Z=1)
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Vec{3}((0.0, 0.0, 0.0)), # 1
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Vec{3}((1.0, 0.0, 0.0)), # 2
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Vec{3}((1.0, 1.0, 0.0)), # 3
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Vec{3}((0.0, 1.0, 0.0)), # 4
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Vec{3}((0.0, 0.0, 1.0)), # 5
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Vec{3}((1.0, 0.0, 1.0)), # 6
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Vec{3}((1.0, 1.0, 1.0)), # 7
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Vec{3}((0.0, 1.0, 1.0)), # 8
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# Element 2 additional nodes (shares face with element 1)
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Vec{3}((2.0, 0.0, 0.0)), # 9
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Vec{3}((2.0, 1.0, 0.0)), # 10
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Vec{3}((2.0, 0.0, 1.0)), # 11
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Vec{3}((2.0, 1.0, 1.0)), # 12
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]
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# Connectivity (Hex8 standard ordering)
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connectivity = [
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(1, 2, 3, 4, 5, 6, 7, 8), # Element 1
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(2, 9, 10, 3, 6, 11, 12, 7), # Element 2 (shares face 2-3-7-6 with element 1)
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]
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nnodes = length(nodes)
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nelems = length(connectivity)
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ndofs = 3 * nnodes
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println(" Nodes: $nnodes")
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println(" Elements: $nelems")
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println(" DOFs: $ndofs")
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# Create mesh
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connectivity_uint32 = [NTuple{8,UInt32}(c) for c in connectivity]
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element_sets = Dict{Symbol,Set{UInt32}}(:all => Set(UInt32(1):UInt32(nelems)))
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mesh = Mesh{8,Hexahedron{8}}(nodes, connectivity_uint32, element_sets)
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# ========================================================================
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# 2. Material and Kernel
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# ========================================================================
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println("\n[2] Setting up physics...")
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# Simple linear elastic material
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E = 210e9 # Pa
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ν = 0.3
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material = LinearElastic(E=E, ν=ν)
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# Create kernel
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kernel = ContinuumKernel(
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ContinuumFormulation{FullThreeD}(),
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material,
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Displacement{3}()
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)
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println(" Material: LinearElastic (E=$(E/1e9) GPa, ν=$ν)")
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println(" Kernel: ContinuumKernel (FullThreeD, Displacement{3})")
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# ========================================================================
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# 3. Boundary Conditions
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# ========================================================================
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println("\n[3] Setting up boundary conditions...")
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# Fix left face (X=0): nodes 1,4,5,8
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fixed_nodes = [1, 4, 5, 8]
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# Load right face (X=2): nodes 9,10,11,12
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loaded_nodes = [9, 10, 11, 12]
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# Apply unit load in X-direction
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force_per_node = Vec{3}((1000.0, 0.0, 0.0)) # 1 kN per node
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# Create boundary conditions
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bc_dirichlet = DirichletBC()
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for node in fixed_nodes
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push!(bc_dirichlet.node_ids, node)
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push!(bc_dirichlet.components, [1, 2, 3])
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push!(bc_dirichlet.values, 0.0)
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end
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bc_neumann = NeumannBC()
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for node in loaded_nodes
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push!(bc_neumann.surface_ids, node)
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push!(bc_neumann.values, force_per_node)
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end
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println(" Fixed nodes (X=0): $fixed_nodes")
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println(" Loaded nodes (X=2): $loaded_nodes")
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println(" Force per node: $(force_per_node[1]/1e3) kN")
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# ========================================================================
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# 4. Assemble with Each Assembler
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# ========================================================================
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println("\n[4] Assembling with all three assemblers...")
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# -------------------------------------------------------------------------
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# 4a. COOAssembler (Element-Based)
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# -------------------------------------------------------------------------
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println("\n [4a] COOAssembler (element-based)...")
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assembler_coo = COOAssembler()
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cache_coo = create_cache(assembler_coo, mesh, kernel)
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t_coo = @elapsed begin
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assemble!(cache_coo, assembler_coo, kernel, mesh)
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K_coo, f_coo = extract_system(cache_coo)
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apply_neumann_bcs!(f_coo, kernel, mesh, bc_neumann)
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K_coo_bc = copy(K_coo)
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f_coo_bc = copy(f_coo)
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apply_dirichlet_bcs!(K_coo_bc, f_coo_bc, kernel, mesh, bc_dirichlet)
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end
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println(" Assembly time: $(round(t_coo*1e6, digits=2)) μs")
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println(" Matrix nnz: $(nnz(K_coo))")
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println(" Force norm: $(round(norm(f_coo), digits=6))")
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# -------------------------------------------------------------------------
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# 4b. CSCAssembler (Element-Based, Optimized)
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# -------------------------------------------------------------------------
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println("\n [4b] CSCAssembler (element-based, optimized)...")
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assembler_csc = CSCAssembler()
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cache_csc = create_cache(assembler_csc, mesh, kernel)
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t_csc = @elapsed begin
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assemble!(cache_csc, assembler_csc, kernel, mesh)
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K_csc, f_csc = extract_system(cache_csc)
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apply_neumann_bcs!(f_csc, kernel, mesh, bc_neumann)
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K_csc_bc = copy(K_csc)
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f_csc_bc = copy(f_csc)
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apply_dirichlet_bcs!(K_csc_bc, f_csc_bc, kernel, mesh, bc_dirichlet)
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end
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println(" Assembly time: $(round(t_csc*1e6, digits=2)) μs")
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println(" Matrix nnz: $(nnz(K_csc))")
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println(" Force norm: $(round(norm(f_csc), digits=6))")
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# -------------------------------------------------------------------------
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# 4c. NodeBasedCOOAssembler (Node-Based)
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# -------------------------------------------------------------------------
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println("\n [4c] NodeBasedCOOAssembler (node-based)...")
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assembler_nodal = NodeBasedCOOAssembler()
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cache_nodal = create_cache(assembler_nodal, mesh, kernel)
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t_nodal = @elapsed begin
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assemble!(cache_nodal, assembler_nodal, kernel, mesh)
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K_nodal, f_nodal = extract_system(cache_nodal)
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apply_neumann_bcs!(f_nodal, kernel, mesh, bc_neumann)
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K_nodal_bc = copy(K_nodal)
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f_nodal_bc = copy(f_nodal)
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apply_dirichlet_bcs!(K_nodal_bc, f_nodal_bc, kernel, mesh, bc_dirichlet)
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end
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println(" Assembly time: $(round(t_nodal*1e6, digits=2)) μs")
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println(" Matrix nnz: $(nnz(K_nodal))")
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println(" Force norm: $(round(norm(f_nodal), digits=6))")
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# ========================================================================
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# 5. Compare Results (Before BC Application)
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# ========================================================================
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println("\n[5] Comparing assembled systems (before BC)...")
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# Compare stiffness matrices
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K_diff_coo_csc = norm(K_coo - K_csc)
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K_diff_coo_nodal = norm(K_coo - K_nodal)
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K_diff_csc_nodal = norm(K_csc - K_nodal)
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K_norm = norm(K_coo)
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println(" Stiffness matrix differences:")
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println(" ||K_coo - K_csc||: $(K_diff_coo_csc)")
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println(" ||K_coo - K_nodal||: $(K_diff_coo_nodal)")
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println(" ||K_csc - K_nodal||: $(K_diff_csc_nodal)")
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println(" ||K_coo|| (reference): $(K_norm)")
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# Compare force vectors
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f_diff_coo_csc = norm(f_coo - f_csc)
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f_diff_coo_nodal = norm(f_coo - f_nodal)
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f_diff_csc_nodal = norm(f_csc - f_nodal)
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f_norm = norm(f_coo)
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println(" Force vector differences:")
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println(" ||f_coo - f_csc||: $(f_diff_coo_csc)")
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println(" ||f_coo - f_nodal||: $(f_diff_coo_nodal)")
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println(" ||f_csc - f_nodal||: $(f_diff_csc_nodal)")
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println(" ||f_coo|| (reference): $(f_norm)")
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# ========================================================================
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# 6. Solve and Compare Solutions
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# ========================================================================
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println("\n[6] Solving systems and comparing solutions...")
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u_coo = K_coo_bc \ f_coo_bc
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u_csc = K_csc_bc \ f_csc_bc
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u_nodal = K_nodal_bc \ f_nodal_bc
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u_diff_coo_csc = norm(u_coo - u_csc)
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u_diff_coo_nodal = norm(u_coo - u_nodal)
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u_diff_csc_nodal = norm(u_csc - u_nodal)
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u_norm = norm(u_coo)
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println(" Solution differences:")
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println(" ||u_coo - u_csc||: $(u_diff_coo_csc)")
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println(" ||u_coo - u_nodal||: $(u_diff_coo_nodal)")
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println(" ||u_csc - u_nodal||: $(u_diff_csc_nodal)")
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println(" ||u_coo|| (reference): $(u_norm)")
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# ========================================================================
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# 7. Test Assertions
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# ========================================================================
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println("\n[7] Running test assertions...")
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# Tolerance for floating-point comparison
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rtol = 1e-10 # Relative tolerance
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atol = 1e-12 # Absolute tolerance
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# Test 1: Stiffness matrices are identical
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@test isapprox(K_coo, K_csc, rtol=rtol, atol=atol)
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@test isapprox(K_coo, K_nodal, rtol=rtol, atol=atol)
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@test isapprox(K_csc, K_nodal, rtol=rtol, atol=atol)
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println(" ✓ All stiffness matrices are identical (within tolerance)")
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# Test 2: Force vectors are identical (should be zero for internal forces)
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@test isapprox(f_coo, f_csc, rtol=rtol, atol=atol)
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@test isapprox(f_coo, f_nodal, rtol=rtol, atol=atol)
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@test isapprox(f_csc, f_nodal, rtol=rtol, atol=atol)
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println(" ✓ All force vectors are identical (within tolerance)")
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# Test 3: Solutions are identical
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@test isapprox(u_coo, u_csc, rtol=rtol, atol=atol)
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@test isapprox(u_coo, u_nodal, rtol=rtol, atol=atol)
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@test isapprox(u_csc, u_nodal, rtol=rtol, atol=atol)
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println(" ✓ All solutions are identical (within tolerance)")
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# Test 4: Solutions are physically reasonable
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@test !any(isnan, u_coo)
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@test !any(isinf, u_coo)
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@test norm(u_coo) > 0 # Solution should not be zero
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println(" ✓ Solutions are physically reasonable (finite, non-zero)")
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# ========================================================================
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# 8. Performance Comparison
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# ========================================================================
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println("\n[8] Performance comparison...")
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println(" Assembly times:")
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println(" COO: $(round(t_coo*1e6, digits=2)) μs (baseline)")
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println(" CSC: $(round(t_csc*1e6, digits=2)) μs ($(round(t_coo/t_csc, digits=2))×)")
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println(" Nodal: $(round(t_nodal*1e6, digits=2)) μs ($(round(t_coo/t_nodal, digits=2))×)")
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if t_csc < t_coo
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println(" → CSC is $(round(t_coo/t_csc, digits=2))× faster than COO")
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end
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# Note: For very small problems, nodal may be slower due to overhead
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# But it should scale better for large problems and GPU
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if t_nodal > t_coo
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println(" → Nodal is slower for this tiny problem (expected)")
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println(" (Nodal assembly excels on GPU and large problems)")
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end
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# ========================================================================
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# 9. Summary
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# ========================================================================
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println("\n" * "="^70)
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println("TEST SUMMARY - ASSEMBLER EQUIVALENCE")
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println("="^70)
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println("Problem:")
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println(" Elements: $nelems Hex8")
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println(" Nodes: $nnodes")
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println(" DOFs: $ndofs")
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println()
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println("Results:")
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println(" All assemblers produce IDENTICAL results:")
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println(" ✓ Stiffness matrices match (||K_i - K_j|| < $rtol)")
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println(" ✓ Force vectors match (||f_i - f_j|| < $rtol)")
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println(" ✓ Solutions match (||u_i - u_j|| < $rtol)")
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println()
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println("Performance (tiny problem, CPU overhead dominant):")
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println(" COO: $(round(t_coo*1e6, digits=2)) μs")
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println(" CSC: $(round(t_csc*1e6, digits=2)) μs")
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println(" Nodal: $(round(t_nodal*1e6, digits=2)) μs")
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println()
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println("Status: ✓ ALL TESTS PASSED")
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println("="^70)
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end
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