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test(assemblers): add surface traction assembly tests
This commit is contained in:
Jukka Aho
@@ -0,0 +1,400 @@
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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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`SurfaceLoad` — distributed traction (or heat flux) integrated as
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`∫_Γ N_i · t dS` over a list of mesh faces. The natural complement of
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`UniformBodyForce` (`∫_Ω N_i · b dV`). Added in D+++.
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Locks in the contract that:
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1. The face Gauss quadrature (2 × 2 for quad, 1-point for tri)
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reproduces the analytical integral `∫_Γ t dS = t · area` for
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constant traction on a flat face — exact to machine precision
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for both quadrilateral and triangular faces.
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2. Vector-valued traction (3D elasticity) and scalar-valued flux
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(heat conduction) both go through the same `apply_load!` path
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with no kernel-specific dispatch. The same `_integrate_face!`
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unrolls correctly for `_t_comp_count(t) ∈ {1, 3}`.
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3. `SurfaceLoad` and `UniformBodyForce` compose additively (apply
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both, get the sum) — the combined RHS still solves
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∫_Γ N · t dS + ∫_Ω N · b dV correctly.
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4. End-to-end pull test on a unit Hex8 cube (1 × 1 × 1 elements):
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fix the bottom face, apply unit traction in `+z` on the top
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face, recover the analytical extension `u_z(z) = σ_z / E · z`
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to within finite-element accuracy.
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5. End-to-end heat flux problem: insulated 5 of 6 faces of a Hex8
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cube, apply uniform inward flux on the remaining face,
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recover the linear conduction temperature profile.
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6. Per-face traction (different `t` per face) overlays correctly.
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7. `apply_load!(SurfaceLoad)` is allocation-free after warmup.
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This file deliberately uses the existing `cache.dof_handler` field
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(added in D+++) instead of any face-extraction machinery — the
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SurfaceLoad path is intentionally compositional and does not depend on
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`Mesh.extract_surface!` (which is incomplete).
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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, Temperature
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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: extract_system, create_elements!
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using JuliaFEM: SurfaceLoad, UniformBodyForce, NodalForce, apply_load!
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using JuliaFEM: PenaltyDirichlet, apply_constraint!
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using LinearAlgebra
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using SparseArrays
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using Tensors
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# ----------------------------------------------------------------------------
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# Mesh helpers
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# ----------------------------------------------------------------------------
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function _unit_hex8(nx::Int, ny::Int, nz::Int; Lx = 1.0, Ly = 1.0, Lz = 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 * (i - 1) / nx,
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Ly * (j - 1) / ny,
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Lz * (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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# Top-face quad nodes for every (i, j) column at the top of an
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# (nx × ny × nz) Hex8 box. Returns a Vector{NTuple{4,Int}}.
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function _top_face_quads(nx::Int, ny::Int, nz::Int)
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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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faces = NTuple{4,Int}[]
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k = nz + 1 # top z layer
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for 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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push!(faces, (n1, n2, n3, n4))
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end
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return faces
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end
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function _bottom_face_node_dofs(nx::Int, ny::Int, dof_per_node::Int)
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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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dofs = Int[]
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vals = Float64[]
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k = 1
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for j in 1:(ny + 1), i in 1:(nx + 1)
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node = nidx(i, j, k)
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for c in 1:dof_per_node
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push!(dofs, (node - 1) * dof_per_node + c)
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push!(vals, 0.0)
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end
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end
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return dofs, vals
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end
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function _setup_elasticity(mesh; E::Float64 = 210e9, ν::Float64 = 0.3)
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material = LinearElastic(E = E, ν = ν)
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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::Float64 = 50.0)
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material = HeatConductivity(k = k)
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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. Quadrature reproduces ∫_Γ t dS = t · area exactly
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# ----------------------------------------------------------------------------
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@testset "SurfaceLoad: row-sum identity = t · area" begin
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println("\n" * "=" ^ 70)
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println("D+++ SurfaceLoad — row-sum identity (analytical area)")
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println("=" ^ 70)
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@testset "Vector traction on Hex8 top face $(nx)×$(ny)" for (nx, ny) in
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[(1, 1), (3, 2), (4, 3)]
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nz = 1
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mesh = _unit_hex8(nx, ny, nz; Lx = 2.0, Ly = 1.5, Lz = 1.0)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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faces = _top_face_quads(nx, ny, nz)
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t = Vec{3}((10.0, -7.0, 3.0)) # arbitrary uniform traction
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load = SurfaceLoad(faces, t)
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f = zeros(cache.ndofs)
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apply_load!(f, load, cache, asm, kernel, m)
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# Sum of the assembled force vector, by component, must equal
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# `t · area_Γ` (here area = Lx · Ly = 3.0).
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area = 2.0 * 1.5
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f_sum_x = sum(f[1:3:end])
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f_sum_y = sum(f[2:3:end])
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f_sum_z = sum(f[3:3:end])
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@test isapprox(f_sum_x, t[1] * area; atol = 1e-10)
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@test isapprox(f_sum_y, t[2] * area; atol = 1e-10)
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@test isapprox(f_sum_z, t[3] * area; atol = 1e-10)
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println(" $(nx)×$(ny) area=$(round(area; digits=3)) " *
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"Σf_x=$(round(f_sum_x; digits=4)) (t·area=$(round(t[1]*area; digits=4))) " *
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"Σf_z=$(round(f_sum_z; digits=4)) (t·area=$(round(t[3]*area; digits=4)))")
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end
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@testset "Scalar flux on Hex8 top face $(nx)×$(ny)" for (nx, ny) in
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[(1, 1), (2, 3)]
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nz = 1
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mesh = _unit_hex8(nx, ny, nz; Lx = 1.5, Ly = 2.0, Lz = 1.0)
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cache, asm, kernel, m = _setup_heat(mesh)
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faces = _top_face_quads(nx, ny, nz)
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q = 25.0 # uniform flux
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load = SurfaceLoad(faces, q)
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f = zeros(cache.ndofs)
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apply_load!(f, load, cache, asm, kernel, m)
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area = 1.5 * 2.0
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@test isapprox(sum(f), q * area; atol = 1e-10)
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println(" $(nx)×$(ny) area=$(round(area; digits=3)) " *
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"Σf=$(round(sum(f); digits=4)) (q·area=$(round(q*area; digits=4)))")
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end
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end
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# ----------------------------------------------------------------------------
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# 2. Triangular face support (Tri3)
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# ----------------------------------------------------------------------------
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@testset "SurfaceLoad: triangular face row-sum" begin
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# Single tri: corners (0,0,0), (2,0,0), (0,3,0) — area = 3.0
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mesh = _unit_hex8(1, 1, 1)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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# Manual nodes/face — we'll re-purpose the cube's nodes 1, 2, 4 which
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# at (Lx, Ly, Lz) = (1, 1, 1) form a corner triangle of area 0.5.
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faces = NTuple{3,Int}[(1, 2, 4)]
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t = Vec{3}((4.0, 0.0, 0.0))
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load = SurfaceLoad(faces, t)
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f = zeros(cache.ndofs)
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apply_load!(f, load, cache, asm, kernel, m)
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expected_area = 0.5
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@test isapprox(sum(f[1:3:end]), t[1] * expected_area; atol = 1e-10)
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@test isapprox(sum(f[2:3:end]), t[2] * expected_area; atol = 1e-10)
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@test isapprox(sum(f[3:3:end]), t[3] * expected_area; atol = 1e-10)
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end
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# ----------------------------------------------------------------------------
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# 3. Per-face traction
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# ----------------------------------------------------------------------------
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@testset "SurfaceLoad: per-face traction overlays correctly" begin
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nx, ny, nz = 2, 2, 1
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mesh = _unit_hex8(nx, ny, nz)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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faces = _top_face_quads(nx, ny, nz)
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@test length(faces) == 4
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# Pull on faces 1 & 4 with +z, push on 2 & 3 with -z. The total
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# force resultant should equal Σᵢ (tᵢ · area_face) summed over
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# faces; with all face areas = 0.25 and tractions all in z, the
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# total z-force is (1 - 1 - 1 + 1) * 0.25 = 0.
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tractions = [Vec{3}((0.0, 0.0, 1.0)),
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Vec{3}((0.0, 0.0, -1.0)),
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Vec{3}((0.0, 0.0, -1.0)),
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Vec{3}((0.0, 0.0, 1.0))]
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load = SurfaceLoad(faces, tractions)
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f = zeros(cache.ndofs)
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apply_load!(f, load, cache, asm, kernel, m)
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f_sum_z = sum(f[3:3:end])
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@test isapprox(f_sum_z, 0.0; atol = 1e-10)
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end
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# ----------------------------------------------------------------------------
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# 4. End-to-end pull test (3D elasticity)
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# ----------------------------------------------------------------------------
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@testset "SurfaceLoad: 3D pull test on Hex8 column" begin
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println("\n" * "=" ^ 70)
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println("D+++ SurfaceLoad — end-to-end 3D elasticity pull")
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println("=" ^ 70)
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# Single Hex8 column 1×1×1 m with σ_zz applied on the top face,
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# bottom face fully fixed. Expect u_z(z) = σ_z · z / E.
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nx, ny, nz = 1, 1, 4
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Lx, Ly, Lz = 1.0, 1.0, 1.0
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Eyoung = 1.0e11
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σ_z = 1.0e6
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mesh = _unit_hex8(nx, ny, nz; Lx = Lx, Ly = Ly, Lz = Lz)
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cache, asm, kernel, m = _setup_elasticity(mesh; E = Eyoung, ν = 0.0)
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n = cache.ndofs
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# Assemble K, then add surface load to f.
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assemble!(cache, asm, kernel, m)
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K, f = extract_system(cache)
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faces = _top_face_quads(nx, ny, nz)
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apply_load!(f, SurfaceLoad(faces, Vec{3}((0.0, 0.0, σ_z))),
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cache, asm, kernel, m)
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# Fix bottom face (penalty Dirichlet, all 3 components).
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fixed_dofs, fixed_vals = _bottom_face_node_dofs(nx, ny, 3)
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bc = PenaltyDirichlet(fixed_dofs, fixed_vals; penalty = 1e10 * Eyoung)
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apply_constraint!(K, bc)
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apply_constraint!(f, bc)
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u = K \ Vector(f)
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# Top-layer node z-displacements: should all equal σ_z * Lz / E.
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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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u_top = Float64[]
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for j in 1:(ny + 1), i in 1:(nx + 1)
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node = nidx(i, j, nz + 1)
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push!(u_top, u[(node - 1) * 3 + 3])
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end
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u_z_exact = σ_z * Lz / Eyoung
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rel = maximum(abs.(u_top .- u_z_exact)) / abs(u_z_exact)
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@test rel < 1e-3
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println(" σ_z=$σ_z E=$(Eyoung) u_z_exact=$(round(u_z_exact; sigdigits = 4)) " *
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"u_z_FE=$(round(mean(u_top); sigdigits = 4)) rel=$(round(rel; sigdigits = 3))")
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end
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# ----------------------------------------------------------------------------
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# 5. End-to-end heat flux problem (1D conduction)
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# ----------------------------------------------------------------------------
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@testset "SurfaceLoad: 1D heat conduction with surface flux" begin
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println("\n" * "=" ^ 70)
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println("D+++ SurfaceLoad — heat flux + Dirichlet (1D)")
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println("=" ^ 70)
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# Hex8 column with T=0 on bottom, +q heat flux on top (entering),
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# all sides insulated. Expect linear T(z) = q · z / k.
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nx, ny, nz = 1, 1, 6
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Lx, Ly, Lz = 1.0, 1.0, 1.0
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k_cond = 50.0
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q_flux = 200.0
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mesh = _unit_hex8(nx, ny, nz; Lx = Lx, Ly = Ly, Lz = Lz)
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cache, asm, kernel, m = _setup_heat(mesh; k = k_cond)
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n = cache.ndofs
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assemble!(cache, asm, kernel, m)
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K, f = extract_system(cache)
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faces = _top_face_quads(nx, ny, nz)
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apply_load!(f, SurfaceLoad(faces, q_flux), cache, asm, kernel, m)
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fixed_dofs, fixed_vals = _bottom_face_node_dofs(nx, ny, 1)
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bc = PenaltyDirichlet(fixed_dofs, fixed_vals; penalty = 1e10 * k_cond)
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apply_constraint!(K, bc)
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apply_constraint!(f, bc)
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T = K \ Vector(f)
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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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T_top = Float64[]
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for j in 1:(ny + 1), i in 1:(nx + 1)
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node = nidx(i, j, nz + 1)
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push!(T_top, T[node])
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end
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T_top_exact = q_flux * Lz / k_cond
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rel = maximum(abs.(T_top .- T_top_exact)) / abs(T_top_exact)
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@test rel < 1e-3
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println(" q=$(q_flux) W/m² k=$k_cond T_top_exact=$(round(T_top_exact; sigdigits = 4)) " *
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"T_top_FE=$(round(mean(T_top); sigdigits = 4)) rel=$(round(rel; sigdigits = 3))")
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end
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# ----------------------------------------------------------------------------
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# 6. Composition with UniformBodyForce
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# ----------------------------------------------------------------------------
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@testset "SurfaceLoad + UniformBodyForce compose additively" begin
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nx, ny, nz = 2, 2, 1
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mesh = _unit_hex8(nx, ny, nz)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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body = UniformBodyForce(Vec{3}((0.0, 0.0, -10.0)))
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surf = SurfaceLoad(_top_face_quads(nx, ny, nz), Vec{3}((0.0, 0.0, 5.0)))
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f_combined = zeros(cache.ndofs)
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apply_load!(f_combined, body, cache, asm, kernel, m)
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apply_load!(f_combined, surf, cache, asm, kernel, m)
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f_body = zeros(cache.ndofs)
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apply_load!(f_body, body, cache, asm, kernel, m)
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f_surf = zeros(cache.ndofs)
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apply_load!(f_surf, surf, cache, asm, kernel, m)
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@test isapprox(f_combined, f_body .+ f_surf; atol = 1e-12)
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println(" Composition (body + surf) verified ✓")
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end
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# ----------------------------------------------------------------------------
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# 7. Zero allocations after warmup
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# ----------------------------------------------------------------------------
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@testset "SurfaceLoad: zero allocations on apply_load!" begin
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println("\n" * "=" ^ 70)
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println("D+++ SurfaceLoad — zero-allocation hot path")
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println("=" ^ 70)
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nx, ny, nz = 4, 4, 2
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mesh = _unit_hex8(nx, ny, nz)
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cache, asm, kernel, m = _setup_elasticity(mesh)
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faces = _top_face_quads(nx, ny, nz)
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load = SurfaceLoad(faces, Vec{3}((1.0, -2.0, 3.0)))
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f = zeros(cache.ndofs)
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apply_load!(f, load, cache, asm, kernel, m) # warmup
|
||||
fill!(f, 0.0)
|
||||
a = @allocated apply_load!(f, load, cache, asm, kernel, m)
|
||||
@test a == 0
|
||||
println(" apply_load!(SurfaceLoad) allocs=$(a)")
|
||||
|
||||
# Heat flux variant
|
||||
cache_h, asm_h, kernel_h, m_h = _setup_heat(mesh)
|
||||
load_h = SurfaceLoad(_top_face_quads(nx, ny, nz), 50.0)
|
||||
f_h = zeros(cache_h.ndofs)
|
||||
apply_load!(f_h, load_h, cache_h, asm_h, kernel_h, m_h)
|
||||
fill!(f_h, 0.0)
|
||||
a_h = @allocated apply_load!(f_h, load_h, cache_h, asm_h, kernel_h, m_h)
|
||||
@test a_h == 0
|
||||
println(" apply_load!(SurfaceLoad heat) allocs=$(a_h)")
|
||||
end
|
||||
|
||||
# Local helper — `mean` from Statistics, but we want to avoid the dep
|
||||
mean(xs) = sum(xs) / length(xs)
|
||||
Reference in New Issue
Block a user