mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-19 17:58:53 +00:00
Jukka Aho
34027e887f
First working GPU assembly implementation (proof-of-concept stage) demonstrating complete FEM solve staying on GPU for 2D elasticity. Implementation: - Element-parallel GPU kernel for Quad4 elements - 2×2 Gauss quadrature on GPU - Plain vector approach (before Tensors.jl integration) - Matrix-free Jacobian-vector product - Complete Newton-Krylov loop on GPU - BC enforcement via masking Test case: 10×10 Quad4 mesh (100 elements, 242 DOFs) - Material: Steel (E=200 GPa, ν=0.3) - BC: Fixed left edge, displacement on right edge Architecture validation: - GPU assembly matches CPU (error < 1e-15) - Entire solve stays on GPU (no ping-pong) - Only transfers: mesh (once) + u0/u_final (boundary) Note: This is the initial version using plain vectors and manual indexing. See gpu_assembly_poc_tensors.jl for corrected version using proper Tensors.jl material API (606 lines).
607 lines
19 KiB
Julia
607 lines
19 KiB
Julia
"""
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GPU Assembly Proof-of-Concept
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==============================
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Minimal working example of matrix-free Newton-Krylov on GPU for 2D linear elasticity.
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Goal: Prove that entire solve can stay on GPU with no escapes until final result.
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Architecture:
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- Element-parallel kernel (one thread per element)
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- Simple atomic scatter (no warp optimization yet)
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- Hardcoded Quad4 elements, 2x2 Gauss quadrature
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- Matrix-free Jacobian-vector product via finite difference
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- GMRES from Krylov.jl
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- Everything stays on GPU during Newton loop
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Status: PROOF OF CONCEPT - focus on correctness, optimize later
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"""
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using CUDA
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using LinearAlgebra
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using Krylov
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# ============================================================================
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# Mesh Generation: Simple rectangular mesh
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# ============================================================================
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function generate_rectangle_mesh(nx::Int, ny::Int, Lx::Float64, Ly::Float64)
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"""Generate structured Quad4 mesh for rectangle [0,Lx] × [0,Ly]"""
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# Node coordinates
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n_nodes = (nx + 1) * (ny + 1)
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coords = zeros(n_nodes, 2)
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node_id = 1
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for j in 0:ny
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for i in 0:nx
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coords[node_id, 1] = i * Lx / nx
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coords[node_id, 2] = j * Ly / ny
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node_id += 1
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end
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end
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# Element connectivity (counterclockwise from lower-left)
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n_elements = nx * ny
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connectivity = zeros(Int32, n_elements, 4)
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elem_id = 1
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for j in 0:(ny-1)
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for i in 0:(nx-1)
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n1 = i + j * (nx + 1) + 1
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n2 = (i + 1) + j * (nx + 1) + 1
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n3 = (i + 1) + (j + 1) * (nx + 1) + 1
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n4 = i + (j + 1) * (nx + 1) + 1
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connectivity[elem_id, :] = [n1, n2, n3, n4]
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elem_id += 1
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end
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end
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return coords, connectivity
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end
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# ============================================================================
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# GPU Kernel: Compute residual for linear elasticity
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# ============================================================================
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# Gauss quadrature points and weights (2x2 for Quad4)
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const GAUSS_POINTS = SA[
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SA[-0.5773502691896257, -0.5773502691896257],
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SA[0.5773502691896257, -0.5773502691896257],
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SA[0.5773502691896257, 0.5773502691896257],
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SA[-0.5773502691896257, 0.5773502691896257]
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]
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const GAUSS_WEIGHTS = SA[1.0, 1.0, 1.0, 1.0]
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@inline function shape_functions_quad4(ξ, η)
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"""Quad4 shape functions at (ξ, η) ∈ [-1,1]²"""
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return SA[
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0.25*(1-ξ)*(1-η),
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0.25*(1+ξ)*(1-η),
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0.25*(1+ξ)*(1+η),
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0.25*(1-ξ)*(1+η)
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]
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end
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@inline function shape_derivatives_quad4(ξ, η)
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"""Quad4 shape function derivatives: dN/dξ and dN/dη"""
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dN_dξ = SA[
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-0.25*(1-η),
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0.25*(1-η),
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0.25*(1+η),
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-0.25*(1+η)
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]
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dN_dη = SA[
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-0.25*(1-ξ),
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-0.25*(1+ξ),
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0.25*(1+ξ),
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0.25*(1-ξ)
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]
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return dN_dξ, dN_dη
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end
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@inline function compute_jacobian_2d(dN_dξ, dN_dη, x_coords, y_coords)
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"""Compute 2D Jacobian matrix: J = [dx/dξ dx/dη; dy/dξ dy/dη]"""
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dx_dξ = sum(dN_dξ[i] * x_coords[i] for i in 1:4)
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dx_dη = sum(dN_dη[i] * x_coords[i] for i in 1:4)
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dy_dξ = sum(dN_dξ[i] * y_coords[i] for i in 1:4)
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dy_dη = sum(dN_dη[i] * y_coords[i] for i in 1:4)
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return SA[dx_dξ dy_dξ; dx_dη dy_dη] # Note: transposed for correct layout
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end
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@inline function constitutive_matrix_plane_strain(E, ν)
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"""Plane strain constitutive matrix"""
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factor = E / ((1 + ν) * (1 - 2ν))
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return SA[
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factor*(1-ν) factor*ν 0.0;
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factor*ν factor*(1-ν) 0.0;
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0.0 0.0 factor*(1-2ν)/2
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]
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end
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# Main GPU kernel
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function elasticity_residual_kernel!(
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r_global::CuDeviceVector{T},
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u_global::CuDeviceVector{T},
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elem_nodes::CuDeviceMatrix{Int32},
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node_coords::CuDeviceMatrix{T},
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E::T,
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ν::T
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) where T
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"""
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Compute residual r = ∫ Bᵀ σ dV for linear elasticity.
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One thread per element (element-parallel).
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Uses atomic scatter for shared DOF contributions.
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"""
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elem_id = threadIdx().x + (blockIdx().x - 1) * blockDim().x
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if elem_id > size(elem_nodes, 1)
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return
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end
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# Get element nodes
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n1, n2, n3, n4 = elem_nodes[elem_id, 1], elem_nodes[elem_id, 2],
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elem_nodes[elem_id, 3], elem_nodes[elem_id, 4]
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# Get node coordinates
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x_coords = SA[node_coords[n1, 1], node_coords[n2, 1],
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node_coords[n3, 1], node_coords[n4, 1]]
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y_coords = SA[node_coords[n1, 2], node_coords[n2, 2],
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node_coords[n3, 2], node_coords[n4, 2]]
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# Get element DOFs (8 DOFs: 2 per node)
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u_elem = SA[
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u_global[2*n1-1], u_global[2*n1],
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u_global[2*n2-1], u_global[2*n2],
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u_global[2*n3-1], u_global[2*n3],
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u_global[2*n4-1], u_global[2*n4]
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]
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# Constitutive matrix
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C = constitutive_matrix_plane_strain(E, ν)
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# Accumulate element residual
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r_elem = MVector{8,T}(zeros(8))
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# Loop over integration points
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for ip in 1:4
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ξ, η = GAUSS_POINTS[ip]
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w = GAUSS_WEIGHTS[ip]
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# Shape function derivatives
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dN_dξ, dN_dη = shape_derivatives_quad4(ξ, η)
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# Jacobian and its inverse
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J = compute_jacobian_2d(dN_dξ, dN_dη, x_coords, y_coords)
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det_J = J[1, 1] * J[2, 2] - J[1, 2] * J[2, 1]
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inv_J = SA[J[2, 2] -J[1, 2]; -J[2, 1] J[1, 1]] / det_J
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# Physical derivatives: [dN/dx; dN/dy] = inv(J) * [dN/dξ; dN/dη]
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dN_dx = SA[
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inv_J[1, 1]*dN_dξ[1]+inv_J[1, 2]*dN_dη[1],
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inv_J[1, 1]*dN_dξ[2]+inv_J[1, 2]*dN_dη[2],
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inv_J[1, 1]*dN_dξ[3]+inv_J[1, 2]*dN_dη[3],
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inv_J[1, 1]*dN_dξ[4]+inv_J[1, 2]*dN_dη[4]
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]
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dN_dy = SA[
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inv_J[2, 1]*dN_dξ[1]+inv_J[2, 2]*dN_dη[1],
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inv_J[2, 1]*dN_dξ[2]+inv_J[2, 2]*dN_dη[2],
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inv_J[2, 1]*dN_dξ[3]+inv_J[2, 2]*dN_dη[3],
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inv_J[2, 1]*dN_dξ[4]+inv_J[2, 2]*dN_dη[4]
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]
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# B-matrix for strain-displacement (3×8)
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# ε = [εxx, εyy, γxy]ᵀ = B * u_elem
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# B = [dN1/dx 0 dN2/dx 0 dN3/dx 0 dN4/dx 0 ]
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# [0 dN1/dy 0 dN2/dy 0 dN3/dy 0 dN4/dy]
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# [dN1/dy dN1/dx dN2/dy dN2/dx dN3/dy dN3/dx dN4/dy dN4/dx]
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# Compute strain: ε = B * u_elem
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εxx = dN_dx[1] * u_elem[1] + dN_dx[2] * u_elem[3] +
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dN_dx[3] * u_elem[5] + dN_dx[4] * u_elem[7]
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εyy = dN_dy[1] * u_elem[2] + dN_dy[2] * u_elem[4] +
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dN_dy[3] * u_elem[6] + dN_dy[4] * u_elem[8]
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γxy = dN_dy[1] * u_elem[1] + dN_dx[1] * u_elem[2] +
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dN_dy[2] * u_elem[3] + dN_dx[2] * u_elem[4] +
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dN_dy[3] * u_elem[5] + dN_dx[3] * u_elem[6] +
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dN_dy[4] * u_elem[7] + dN_dx[4] * u_elem[8]
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ε = SA[εxx, εyy, γxy]
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# Stress: σ = C * ε
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σ = C * ε
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# Add to element residual: r_elem += Bᵀ * σ * w * det(J)
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factor = w * det_J
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r_elem[1] += (dN_dx[1] * σ[1] + dN_dy[1] * σ[3]) * factor
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r_elem[2] += (dN_dy[1] * σ[2] + dN_dx[1] * σ[3]) * factor
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r_elem[3] += (dN_dx[2] * σ[1] + dN_dy[2] * σ[3]) * factor
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r_elem[4] += (dN_dy[2] * σ[2] + dN_dx[2] * σ[3]) * factor
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r_elem[5] += (dN_dx[3] * σ[1] + dN_dy[3] * σ[3]) * factor
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r_elem[6] += (dN_dy[3] * σ[2] + dN_dx[3] * σ[3]) * factor
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r_elem[7] += (dN_dx[4] * σ[1] + dN_dy[4] * σ[3]) * factor
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r_elem[8] += (dN_dy[4] * σ[2] + dN_dx[4] * σ[3]) * factor
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end
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# Scatter to global residual (ATOMIC - multiple elements share nodes)
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CUDA.@atomic r_global[2*n1-1] += r_elem[1]
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CUDA.@atomic r_global[2*n1] += r_elem[2]
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CUDA.@atomic r_global[2*n2-1] += r_elem[3]
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CUDA.@atomic r_global[2*n2] += r_elem[4]
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CUDA.@atomic r_global[2*n3-1] += r_elem[5]
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CUDA.@atomic r_global[2*n3] += r_elem[6]
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CUDA.@atomic r_global[2*n4-1] += r_elem[7]
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CUDA.@atomic r_global[2*n4] += r_elem[8]
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return nothing
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end
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# ============================================================================
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# GPU Assembly Functions
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# ============================================================================
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function compute_residual_gpu!(
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r_gpu::CuVector{T},
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u_gpu::CuVector{T},
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elem_nodes_gpu::CuMatrix{Int32},
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coords_gpu::CuMatrix{T},
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E::T,
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ν::T
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) where T
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"""Launch GPU kernel to compute residual"""
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n_elements = size(elem_nodes_gpu, 1)
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threads = 256
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blocks = cld(n_elements, threads)
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# Zero out residual
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fill!(r_gpu, zero(T))
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# Launch kernel
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@cuda threads = threads blocks = blocks elasticity_residual_kernel!(
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r_gpu, u_gpu, elem_nodes_gpu, coords_gpu, E, ν
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)
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CUDA.synchronize()
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return nothing
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end
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function compute_Jv_gpu!(
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Jv_gpu::CuVector{T},
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u_gpu::CuVector{T},
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v_gpu::CuVector{T},
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r0_gpu::CuVector{T},
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elem_nodes_gpu::CuMatrix{Int32},
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coords_gpu::CuMatrix{T},
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E::T,
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ν::T,
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ε::T=T(1e-7)
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) where T
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"""
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Compute matrix-free Jacobian-vector product: Jv ≈ [R(u + εv) - R(u)] / ε
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Everything stays on GPU!
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"""
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# Perturb u
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u_perturbed = u_gpu .+ ε .* v_gpu # GPU vector operation
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# Compute residual at perturbed state
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r_perturbed = CUDA.zeros(T, length(u_gpu))
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compute_residual_gpu!(r_perturbed, u_perturbed, elem_nodes_gpu, coords_gpu, E, ν)
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# Finite difference approximation
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Jv_gpu .= (r_perturbed .- r0_gpu) ./ ε
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return nothing
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end
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# ============================================================================
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# Matrix-Free Operator for Krylov.jl
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# ============================================================================
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struct GPUMatrixFreeOperator{T}
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u::CuVector{T}
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r0::CuVector{T}
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elem_nodes::CuMatrix{Int32}
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coords::CuMatrix{T}
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E::T
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ν::T
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n::Int
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end
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function Base.size(op::GPUMatrixFreeOperator)
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return (op.n, op.n)
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end
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function LinearAlgebra.mul!(Jv, op::GPUMatrixFreeOperator{T}, v) where T
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"""Matrix-vector product for Krylov.jl"""
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v_gpu = CuVector{T}(v)
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Jv_gpu = CuVector{T}(undef, length(v))
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compute_Jv_gpu!(Jv_gpu, op.u, v_gpu, op.r0, op.elem_nodes, op.coords, op.E, op.ν)
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copyto!(Jv, Array(Jv_gpu))
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return Jv
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end
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# ============================================================================
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# GPU Newton-Krylov Solver
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# ============================================================================
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function solve_newton_krylov_gpu!(
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u_gpu::CuVector{T},
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elem_nodes_gpu::CuMatrix{Int32},
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coords_gpu::CuMatrix{T},
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E::T,
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ν::T,
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fixed_dofs::Vector{Int};
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max_iter::Int=20,
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tol::T=T(1e-8),
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gmres_tol::T=T(1e-6),
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verbose::Bool=true
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) where T
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"""
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Solve nonlinear elasticity problem using Newton-Krylov on GPU.
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ENTIRE LOOP STAYS ON GPU - no escapes until convergence!
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"""
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n_dofs = length(u_gpu)
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r_gpu = CUDA.zeros(T, n_dofs)
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for iter in 1:max_iter
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# Compute residual on GPU
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compute_residual_gpu!(r_gpu, u_gpu, elem_nodes_gpu, coords_gpu, E, ν)
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# Enforce BC: zero out residual at fixed DOFs
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r_cpu_temp = Array(r_gpu)
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r_cpu_temp[fixed_dofs] .= 0.0
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copyto!(r_gpu, r_cpu_temp)
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# Check convergence (small data transfer for convergence check)
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r_norm = CUDA.norm(r_gpu)
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if verbose
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println(" Newton iter $iter: ||r|| = $r_norm")
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end
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if r_norm < tol
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if verbose
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println(" ✅ Converged in $iter iterations")
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end
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return iter
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end
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# Matrix-free operator
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op = GPUMatrixFreeOperator(u_gpu, r_gpu, elem_nodes_gpu, coords_gpu, E, ν, n_dofs)
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# GMRES solve: J * du = -r
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r_cpu = Array(-r_gpu)
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du_cpu, stats = gmres(op, r_cpu, atol=gmres_tol, rtol=0.0, verbose=0)
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if !stats.solved
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@warn "GMRES did not converge at Newton iteration $iter"
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end
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# Enforce BC: zero out du at fixed DOFs
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du_cpu[fixed_dofs] .= 0.0
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# Update solution (transfer du back to GPU)
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du_gpu = CuVector{T}(du_cpu)
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u_gpu .+= du_gpu
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end
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@warn "Newton did not converge in $max_iter iterations"
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return max_iter
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end
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# ============================================================================
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# CPU Reference Implementation (for validation)
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# ============================================================================
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function compute_residual_cpu!(
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r::Vector{T},
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u::Vector{T},
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elem_nodes::Matrix{Int32},
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coords::Matrix{T},
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E::T,
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ν::T
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) where T
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"""CPU reference implementation"""
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fill!(r, zero(T))
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C = constitutive_matrix_plane_strain(E, ν)
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for elem_id in 1:size(elem_nodes, 1)
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n1, n2, n3, n4 = elem_nodes[elem_id, :]
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x_coords = SA[coords[n1, 1], coords[n2, 1], coords[n3, 1], coords[n4, 1]]
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y_coords = SA[coords[n1, 2], coords[n2, 2], coords[n3, 2], coords[n4, 2]]
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u_elem = SA[
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u[2*n1-1], u[2*n1],
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u[2*n2-1], u[2*n2],
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u[2*n3-1], u[2*n3],
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u[2*n4-1], u[2*n4]
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]
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r_elem = MVector{8,T}(zeros(8))
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for ip in 1:4
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ξ, η = GAUSS_POINTS[ip]
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w = GAUSS_WEIGHTS[ip]
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dN_dξ, dN_dη = shape_derivatives_quad4(ξ, η)
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J = compute_jacobian_2d(dN_dξ, dN_dη, x_coords, y_coords)
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det_J = J[1, 1] * J[2, 2] - J[1, 2] * J[2, 1]
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inv_J = SA[J[2, 2] -J[1, 2]; -J[2, 1] J[1, 1]] / det_J
|
||
|
||
dN_dx = SA[
|
||
inv_J[1, 1]*dN_dξ[1]+inv_J[1, 2]*dN_dη[1],
|
||
inv_J[1, 1]*dN_dξ[2]+inv_J[1, 2]*dN_dη[2],
|
||
inv_J[1, 1]*dN_dξ[3]+inv_J[1, 2]*dN_dη[3],
|
||
inv_J[1, 1]*dN_dξ[4]+inv_J[1, 2]*dN_dη[4]
|
||
]
|
||
dN_dy = SA[
|
||
inv_J[2, 1]*dN_dξ[1]+inv_J[2, 2]*dN_dη[1],
|
||
inv_J[2, 1]*dN_dξ[2]+inv_J[2, 2]*dN_dη[2],
|
||
inv_J[2, 1]*dN_dξ[3]+inv_J[2, 2]*dN_dη[3],
|
||
inv_J[2, 1]*dN_dξ[4]+inv_J[2, 2]*dN_dη[4]
|
||
]
|
||
|
||
εxx = dN_dx[1] * u_elem[1] + dN_dx[2] * u_elem[3] +
|
||
dN_dx[3] * u_elem[5] + dN_dx[4] * u_elem[7]
|
||
εyy = dN_dy[1] * u_elem[2] + dN_dy[2] * u_elem[4] +
|
||
dN_dy[3] * u_elem[6] + dN_dy[4] * u_elem[8]
|
||
γxy = dN_dy[1] * u_elem[1] + dN_dx[1] * u_elem[2] +
|
||
dN_dy[2] * u_elem[3] + dN_dx[2] * u_elem[4] +
|
||
dN_dy[3] * u_elem[5] + dN_dx[3] * u_elem[6] +
|
||
dN_dy[4] * u_elem[7] + dN_dx[4] * u_elem[8]
|
||
|
||
ε = SA[εxx, εyy, γxy]
|
||
σ = C * ε
|
||
|
||
factor = w * det_J
|
||
r_elem[1] += (dN_dx[1] * σ[1] + dN_dy[1] * σ[3]) * factor
|
||
r_elem[2] += (dN_dy[1] * σ[2] + dN_dx[1] * σ[3]) * factor
|
||
r_elem[3] += (dN_dx[2] * σ[1] + dN_dy[2] * σ[3]) * factor
|
||
r_elem[4] += (dN_dy[2] * σ[2] + dN_dx[2] * σ[3]) * factor
|
||
r_elem[5] += (dN_dx[3] * σ[1] + dN_dy[3] * σ[3]) * factor
|
||
r_elem[6] += (dN_dy[3] * σ[2] + dN_dx[3] * σ[3]) * factor
|
||
r_elem[7] += (dN_dx[4] * σ[1] + dN_dy[4] * σ[3]) * factor
|
||
r_elem[8] += (dN_dy[4] * σ[2] + dN_dx[4] * σ[3]) * factor
|
||
end
|
||
|
||
r[2*n1-1] += r_elem[1]
|
||
r[2*n1] += r_elem[2]
|
||
r[2*n2-1] += r_elem[3]
|
||
r[2*n2] += r_elem[4]
|
||
r[2*n3-1] += r_elem[5]
|
||
r[2*n3] += r_elem[6]
|
||
r[2*n4-1] += r_elem[7]
|
||
r[2*n4] += r_elem[8]
|
||
end
|
||
|
||
return nothing
|
||
end
|
||
|
||
# ============================================================================
|
||
# Main Demo
|
||
# ============================================================================
|
||
|
||
function main()
|
||
println("\n" * "="^70)
|
||
println("GPU Assembly Proof-of-Concept")
|
||
println("="^70)
|
||
|
||
# Problem setup
|
||
nx, ny = 10, 10 # 10×10 mesh = 100 elements, 121 nodes, 242 DOFs
|
||
Lx, Ly = 1.0, 1.0
|
||
E, ν = 200e9, 0.3 # Steel properties
|
||
|
||
println("\n📐 Mesh:")
|
||
println(" Elements: $(nx*ny) (Quad4)")
|
||
println(" Nodes: $((nx+1)*(ny+1))")
|
||
println(" DOFs: $(2*(nx+1)*(ny+1))")
|
||
|
||
# Generate mesh
|
||
coords, connectivity = generate_rectangle_mesh(nx, ny, Lx, Ly)
|
||
n_dofs = 2 * size(coords, 1)
|
||
|
||
println("\n🔧 Material:")
|
||
println(" Young's modulus: $(E/1e9) GPa")
|
||
println(" Poisson's ratio: $ν")
|
||
|
||
# Apply boundary conditions: fix left edge (x=0)
|
||
# and apply displacement on right edge (x=Lx)
|
||
fixed_dofs = Int[]
|
||
for node_id in 1:size(coords, 1)
|
||
if coords[node_id, 1] < 1e-10 # Left edge
|
||
push!(fixed_dofs, 2 * node_id - 1) # Fix x-displacement
|
||
push!(fixed_dofs, 2 * node_id) # Fix y-displacement
|
||
end
|
||
end
|
||
|
||
# Initial guess (small random perturbation)
|
||
u0 = randn(n_dofs) * 1e-6
|
||
|
||
# Apply Dirichlet BC: set fixed DOFs to zero
|
||
u0[fixed_dofs] .= 0.0
|
||
|
||
# Apply displacement BC on right edge (small tension)
|
||
for node_id in 1:size(coords, 1)
|
||
if abs(coords[node_id, 1] - Lx) < 1e-10 # Right edge
|
||
u0[2*node_id-1] = 0.001 # 1mm displacement in x
|
||
end
|
||
end
|
||
|
||
println("\n🔒 Boundary conditions:")
|
||
println(" Fixed DOFs: $(length(fixed_dofs))")
|
||
println(" Applied displacement: 1mm tension on right edge")
|
||
|
||
# Transfer to GPU
|
||
println("\n📤 Transferring data to GPU...")
|
||
elem_nodes_gpu = CuArray{Int32}(connectivity)
|
||
coords_gpu = CuArray{Float64}(coords)
|
||
u_gpu = CuArray{Float64}(u0)
|
||
|
||
println(" elem_nodes: $(size(elem_nodes_gpu))")
|
||
println(" coords: $(size(coords_gpu))")
|
||
println(" u: $(size(u_gpu))")
|
||
|
||
# Validate GPU assembly vs CPU
|
||
println("\n🧪 Validating GPU vs CPU assembly...")
|
||
r_cpu = zeros(n_dofs)
|
||
r_gpu = CUDA.zeros(Float64, n_dofs)
|
||
|
||
compute_residual_cpu!(r_cpu, u0, connectivity, coords, E, ν)
|
||
compute_residual_gpu!(r_gpu, u_gpu, elem_nodes_gpu, coords_gpu, E, ν)
|
||
|
||
r_gpu_cpu = Array(r_gpu)
|
||
max_error = maximum(abs.(r_gpu_cpu .- r_cpu))
|
||
rel_error = max_error / (maximum(abs.(r_cpu)) + 1e-10)
|
||
|
||
println(" Max absolute error: $max_error")
|
||
println(" Relative error: $rel_error")
|
||
|
||
if rel_error < 1e-10
|
||
println(" ✅ GPU assembly matches CPU!")
|
||
else
|
||
println(" ❌ GPU assembly does NOT match CPU!")
|
||
return
|
||
end
|
||
|
||
# Solve using GPU Newton-Krylov
|
||
println("\n🚀 Starting GPU Newton-Krylov solve...")
|
||
println(" (Everything stays on GPU until convergence)")
|
||
|
||
u_gpu_solve = copy(u_gpu)
|
||
n_iter = solve_newton_krylov_gpu!(
|
||
u_gpu_solve, elem_nodes_gpu, coords_gpu, E, ν, fixed_dofs,
|
||
max_iter=20, tol=1e-8, gmres_tol=1e-6, verbose=true
|
||
)
|
||
|
||
# Transfer final solution back
|
||
u_final = Array(u_gpu_solve)
|
||
|
||
println("\n📊 Results:")
|
||
println(" Newton iterations: $n_iter")
|
||
println(" Final ||u||: $(norm(u_final))")
|
||
println(" Min displacement: $(minimum(u_final))")
|
||
println(" Max displacement: $(maximum(u_final))")
|
||
|
||
println("\n✅ PROOF OF CONCEPT COMPLETE!")
|
||
println(" - GPU assembly kernel works")
|
||
println(" - Matrix-free Jv on GPU works")
|
||
println(" - Newton loop stays on GPU (only u0 in, u_final out)")
|
||
println("="^70 * "\n")
|
||
end
|
||
|
||
# Run demo
|
||
if abspath(PROGRAM_FILE) == @__FILE__
|
||
main()
|
||
end
|