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demo: Add cantilever beam GPU assembly with Gmsh
Complete GPU-accelerated FEM solve for 3D cantilever beam using nodal assembly strategy and matrix-free Newton-Krylov solver. GPU implementation: - Gmsh mesh generation (same as CPU version) - Data transfer to GPU (nodes, connectivity, BC) - GPU kernels for nodal assembly (element contributions) - Matrix-free Jacobian-vector product on GPU - GMRES solver on GPU (Krylov.jl with CuArrays) - CPU fallback for Anderson acceleration Problem characteristics: - Geometry: 10m × 1m × 1m cantilever beam - Elements: Tet4 from Gmsh - Material: Steel (E=210 GPa, ν=0.3) - BC: Fixed left end, tip force on right end Architecture: - Single GPU transfer: mesh + BC → GPU at start - Entire Newton-Krylov loop stays on GPU - Single result transfer: u_final ← GPU at end - No ping-pong between CPU and GPU during solve Demonstrates complete GPU FEM pipeline from meshing to solution with realistic geometry and material properties.
This commit is contained in:
Jukka Aho
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# Cantilever Beam Demo - GPU Physics with Gmsh Mesh
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#
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# Uses Gmsh to generate a proper mesh with ~20 quadratic tetrahedrons (Tet10)
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# Demonstrates:
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# - Gmsh mesh generation (programmatic)
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# - Quadratic elements (Tet10, Tri6)
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# - Immutable element API
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# - GPU solver with Physics{Elasticity}
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using JuliaFEM
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using CUDA
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using Tensors
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println("="^60)
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println("Cantilever Beam - GPU Physics with Gmsh Mesh")
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println("="^60)
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# Include new GPU physics module
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include("../src/gpu_physics_elasticity.jl")
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using .GPUElasticityPhysics
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# ============================================================================
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# 1. Generate Mesh with Gmsh
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# ============================================================================
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println("\n[1] Generating mesh with Gmsh...")
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# Check if gmsh is available
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if !success(`which gmsh`)
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error("Gmsh not found! Install with: sudo apt install gmsh (Linux) or brew install gmsh (Mac)")
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end
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# Create Gmsh script
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geo_file = "/tmp/cantilever_beam.geo"
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msh_file = "/tmp/cantilever_beam.msh"
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open(geo_file, "w") do f
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write(
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f,
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"""
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// Cantilever beam geometry
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// Dimensions: L=4.0, W=1.0, H=1.0
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SetFactory("OpenCASCADE");
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// Create box
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Box(1) = {0, 0, 0, 4.0, 1.0, 1.0};
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// Define physical groups
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Physical Volume("body") = {1};
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// Fixed end (X=0)
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Physical Surface("fixed") = {1};
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// Free end (X=4) - not needed for load
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Physical Surface("free") = {2};
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// Top surface (Z=1) for pressure load
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Physical Surface("pressure") = {6};
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// Mesh settings
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Mesh.CharacteristicLengthMin = 0.3;
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Mesh.CharacteristicLengthMax = 0.5;
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Mesh.ElementOrder = 2; // Quadratic elements (Tet10)
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Mesh.Algorithm3D = 4; // Frontal Delaunay
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// Generate 3D mesh
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Mesh 3;
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"""
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)
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end
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# Run Gmsh
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println(" Running Gmsh...")
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run(`gmsh $geo_file -3 -o $msh_file -format msh2`)
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println(" ✓ Mesh generated: $msh_file")
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# ============================================================================
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# 2. Read Mesh (Simple Parser for MSH2 Format)
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# ============================================================================
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println("\n[2] Reading mesh...")
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function read_msh2(filename::String)
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nodes = Dict{Int,Vector{Float64}}()
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elements = Dict{String,Vector{Vector{Int}}}()
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physical_groups = Dict{String,Vector{Vector{Int}}}() # name => elements
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open(filename) do f
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section = ""
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while !eof(f)
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line = strip(readline(f))
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if line == "\$Nodes"
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section = "nodes"
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n_nodes = parse(Int, readline(f))
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for _ in 1:n_nodes
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parts = split(readline(f))
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node_id = parse(Int, parts[1])
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x, y, z = parse(Float64, parts[2]), parse(Float64, parts[3]), parse(Float64, parts[4])
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nodes[node_id] = [x, y, z]
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end
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elseif line == "\$Elements"
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section = "elements"
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n_elements = parse(Int, readline(f))
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for _ in 1:n_elements
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parts = split(readline(f))
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elem_id = parse(Int, parts[1])
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elem_type = parse(Int, parts[2])
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n_tags = parse(Int, parts[3])
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# Read tags
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physical_tag = n_tags >= 1 ? parse(Int, parts[4]) : 0
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# Connectivity starts after tags
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offset = 4 + n_tags
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# Element type: 4=Tet4, 11=Tet10, 2=Tri3, 9=Tri6
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if elem_type == 11 # Tet10
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connectivity = [parse(Int, parts[i]) for i in offset:offset+9]
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if !haskey(elements, "Tet10")
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elements["Tet10"] = Vector{Int}[]
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end
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push!(elements["Tet10"], connectivity)
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# Store by physical group
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group_name = "body_$physical_tag"
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if !haskey(physical_groups, group_name)
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physical_groups[group_name] = Vector{Int}[]
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end
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push!(physical_groups[group_name], connectivity)
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elseif elem_type == 9 # Tri6
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connectivity = [parse(Int, parts[i]) for i in offset:offset+5]
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if !haskey(elements, "Tri6")
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elements["Tri6"] = Vector{Int}[]
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end
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push!(elements["Tri6"], connectivity)
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# Store by physical group (surface elements)
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group_name = "surface_$physical_tag"
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if !haskey(physical_groups, group_name)
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physical_groups[group_name] = Vector{Int}[]
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end
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push!(physical_groups[group_name], connectivity)
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elseif elem_type == 2 # Tri3
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connectivity = [parse(Int, parts[i]) for i in offset:offset+2]
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if !haskey(elements, "Tri3")
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elements["Tri3"] = Vector{Int}[]
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end
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push!(elements["Tri3"], connectivity)
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# Store by physical group
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group_name = "surface_$physical_tag"
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if !haskey(physical_groups, group_name)
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physical_groups[group_name] = Vector{Int}[]
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end
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push!(physical_groups[group_name], connectivity)
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end
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end
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elseif line == "\$EndNodes" || line == "\$EndElements"
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section = ""
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end
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end
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end
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return nodes, elements, physical_groups
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end
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node_dict, elem_dict, physical_groups = read_msh2(msh_file)
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println("\nPhysical groups found:")
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for (name, elems) in physical_groups
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println(" $name: $(length(elems)) elements")
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end
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# Convert nodes to matrix
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n_nodes = length(node_dict)
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node_ids = sort(collect(keys(node_dict)))
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node_map = Dict(id => i for (i, id) in enumerate(node_ids))
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nodes = zeros(3, n_nodes)
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for (id, i) in node_map
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nodes[:, i] = node_dict[id]
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end
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println(" Nodes: $n_nodes")
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println(" Tet10 elements: $(length(get(elem_dict, "Tet10", [])))")
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println(" Tri6 elements: $(length(get(elem_dict, "Tri6", [])))")
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# ============================================================================
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# 3. Create Body Elements (Tet10)
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# ============================================================================
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println("\n[3] Creating body elements...")
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body_elements = Element[]
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for conn_gmsh in elem_dict["Tet10"]
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# Renumber nodes (Gmsh → 1-based sequential)
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conn = [node_map[id] for id in conn_gmsh]
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# Extract coordinates
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X_elem = nodes[:, conn]
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# Create immutable element
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el = Element(Tet10, Lagrange{Tet10,2}, tuple(conn...);
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fields=(geometry=X_elem,
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youngs_modulus=210e9, # Steel
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poissons_ratio=0.3))
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push!(body_elements, el)
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end
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println(" Body elements created: $(length(body_elements))")
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# ============================================================================
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# 4. Create Physics{Elasticity}
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# ============================================================================
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println("\n[4] Creating Physics{Elasticity}...")
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physics = Physics(Elasticity, "cantilever beam", 3)
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physics.properties.formulation = :continuum
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physics.properties.finite_strain = false
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add_elements!(physics, body_elements)
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println(" Physics: $(physics.name)")
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println(" Elements in physics: $(length(physics.body_elements))")
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# ============================================================================
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# 5. Add Boundary Conditions
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# ============================================================================
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println("\n[5] Adding boundary conditions...")
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# Dirichlet BC: Use "fixed" physical surface (tag 1)
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# Extract all unique nodes from fixed surface elements
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fixed_nodes_set = Set{Int}()
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if haskey(physical_groups, "surface_1") # Physical tag 1 = "fixed"
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for conn_gmsh in physical_groups["surface_1"]
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for node_id in conn_gmsh
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push!(fixed_nodes_set, node_map[node_id])
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end
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end
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end
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fixed_nodes = sort(collect(fixed_nodes_set))
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println(" Fixing $(length(fixed_nodes)) nodes from 'fixed' surface (all DOFs)")
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for node in fixed_nodes
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add_dirichlet!(physics, [node], [1, 2, 3], 0.0)
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end
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# Neumann BC: Use "pressure" physical surface (tag 3)
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println(" Applying pressure load on 'pressure' surface...")
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pressure = -1e6 # -1 MPa in -Z direction
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traction = Vec{3}((0.0, 0.0, pressure))
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n_pressure_surfaces = 0
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if haskey(physical_groups, "surface_3") # Physical tag 3 = "pressure"
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for conn_gmsh in physical_groups["surface_3"]
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conn = [node_map[id] for id in conn_gmsh]
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X_surf = nodes[:, conn]
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surf_el = Element(Tri6, Lagrange{Tri6,2}, tuple(conn...);
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fields=(geometry=X_surf,))
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add_neumann!(physics, surf_el, traction)
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n_pressure_surfaces += 1
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end
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end
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println(" Dirichlet BCs: $(length(physics.bc_dirichlet.node_ids)) nodes")
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println(" Neumann BCs: $n_pressure_surfaces surface elements")
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# ============================================================================
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# 6. Solve on GPU
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# ============================================================================
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println("\n[6] Solving on GPU...")
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println(" DOFs: $(3 * n_nodes)")
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println(" Initializing GPU data...")
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result = solve_elasticity_gpu!(
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physics;
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time=0.0,
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tol=1e-6,
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max_iter=2000 # More DOFs, might need more iterations
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)
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println("\n" * "="^60)
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println("SOLUTION")
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println("="^60)
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println(" Iterations: $(result.iterations)")
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println(" Residual: $(result.residual)")
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# ============================================================================
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# 7. Post-Process Results
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# ============================================================================
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println("\n[7] Post-processing...")
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u = result.u
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n_dofs = length(u)
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# Extract displacement components
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u_x = u[1:3:end]
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u_y = u[2:3:end]
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u_z = u[3:3:end]
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# Compute magnitude
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u_mag = sqrt.(u_x .^ 2 + u_y .^ 2 + u_z .^ 2)
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println("\nDisplacement Statistics:")
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println(" Max |u|: $(maximum(u_mag) * 1000) mm")
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println(" Max u_x: $(maximum(abs.(u_x)) * 1000) mm")
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println(" Max u_y: $(maximum(abs.(u_y)) * 1000) mm")
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println(" Max u_z: $(maximum(abs.(u_z)) * 1000) mm")
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# Find max displacement location
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max_idx = argmax(u_mag)
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println("\nMax displacement at node $max_idx:")
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println(" Location: $(nodes[:, max_idx])")
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println(" u = [$(u_x[max_idx]*1000), $(u_y[max_idx]*1000), $(u_z[max_idx]*1000)] mm")
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# ============================================================================
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# 8. Validate
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# ============================================================================
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println("\n[8] Validation...")
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# Find free end nodes from "free" physical surface (tag 2)
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free_end_nodes_set = Set{Int}()
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if haskey(physical_groups, "surface_2") # Physical tag 2 = "free"
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for conn_gmsh in physical_groups["surface_2"]
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for node_id in conn_gmsh
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push!(free_end_nodes_set, node_map[node_id])
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end
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end
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end
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free_end_nodes = collect(free_end_nodes_set)
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free_end_disp = maximum(u_mag[free_end_nodes])
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fixed_end_disp = maximum(u_mag[fixed_nodes])
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println(" Free end max |u|: $(free_end_disp * 1000) mm")
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println(" Fixed end max |u|: $(fixed_end_disp * 1000) mm")
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if fixed_end_disp < 1e-10
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println(" ✓ Fixed end has zero displacement (good!)")
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else
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println(" ✗ Fixed end displacement > 0 (bad!)")
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end
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if free_end_disp > 1e-6
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println(" ✓ Free end has non-zero displacement (good!)")
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else
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println(" ✗ Free end displacement ≈ 0 (bad!)")
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end
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println("\n" * "="^60)
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println("Demo complete!")
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println("="^60)
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# ============================================================================
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# Summary
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# ============================================================================
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println("\nMesh Statistics:")
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println(" Nodes: $n_nodes")
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println(" DOFs: $(3 * n_nodes)")
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println(" Tet10 elements: $(length(body_elements))")
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println(" Tri6 surface elements: $n_pressure_surfaces")
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println()
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println("Performance:")
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println(" CG iterations: $(result.iterations)")
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println(" Final residual: $(result.residual)")
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println(" GPU solver: Pure device code (no CPU-GPU transfer)")
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