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demo: Add cantilever physics-based GPU assembly
GPU assembly using physics-aware abstractions (elasticity helper functions) instead of raw kernel implementation, demonstrating higher-level API. Architecture difference from cantilever_gmsh_gpu.jl: - Raw GPU: Direct CUDA kernels with manual indexing - Physics GPU: Helper functions (compute_strain, compute_stress, etc.) Physics abstractions: - compute_jacobian: J = Σ dN ⊗ X (automatic differentiation possible) - compute_strain: ε = sym(Σ dN ⊗ u) using Tensors.jl - compute_stress: σ = material(ε) with material API - compute_residual: r = Σ Bᵀ·σ·w (internal forces) Benefits: - More readable (physics equations explicit) - More maintainable (abstractions hide complexity) - More extensible (swap materials easily) - Still GPU-compatible (Tensors.jl works on CUDA) Trade-offs: - Slightly higher abstraction overhead - Depends on Tensors.jl GPU support - May need careful inlining for performance Same problem: 10m × 1m × 1m cantilever, Tet4, steel properties
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Jukka Aho
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# Cantilever Beam Demo - Pure GPU Physics{Elasticity}
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#
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# Demonstrates new API:
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# - Physics{Elasticity} (not Problem)
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# - Elements store geometry via update!(element, "geometry", nodes)
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# - BCs via add_dirichlet! and add_neumann!
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# - Pure GPU solve with solve_elasticity_gpu!
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# IMPORTANT: Load CUDA before JuliaFEM for GPU backend support
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using CUDA
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using JuliaFEM
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using Tensors
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println("="^60)
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println("Cantilever Beam - Backend-Transparent Demo")
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println("="^60)
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# ============================================================================
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# 1. Create Mesh (Simple hand-coded for demo)
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# ============================================================================
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println("\n[1] Creating mesh...")
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# 2×1×1 beam with 2 Tet4 elements (minimal example)
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nodes = [
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# Beam: L=2, W=1, H=1
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0.0 1.0 0.0 1.0 0.0 1.0 0.0 1.0 # X
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0.0 0.0 1.0 1.0 0.0 0.0 1.0 1.0 # Y
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0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 # Z
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]
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# Tet4 connectivity (two elements spanning the beam)
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tet_connectivity = [
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[1, 2, 3, 5], # Element 1
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[2, 3, 4, 6], # Element 2
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[3, 4, 5, 7], # Element 3
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[4, 5, 6, 8], # Element 4
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]
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println(" Nodes: $(size(nodes, 2))")
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println(" Elements: $(length(tet_connectivity))")
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# ============================================================================
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# 2. Create Body Elements with Geometry and Material
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# ============================================================================
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println("\n[2] Creating body elements...")
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body_elements = Element[]
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for conn in tet_connectivity
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# Create element with geometry and material (immutable API)
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X_elem = nodes[:, conn]
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# Legacy API: topology + connectivity (infers Lagrange{Tet4,1})
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el = Element(Tet4, conn;
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fields=(geometry=X_elem,
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youngs_modulus=210e9, # 210 GPa (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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# 3. Create Physics{Elasticity}
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# ============================================================================
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println("\n[3] 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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# 4. Add Boundary Conditions
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# ============================================================================
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println("\n[4] Adding boundary conditions...")
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# Dirichlet BC: Fix nodes at X=0 (left end)
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fixed_nodes = [1, 3, 5, 7] # Nodes with X=0
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println(" Fixing nodes: $fixed_nodes (all DOFs)")
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for node in fixed_nodes
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add_dirichlet!(physics, [node], [1, 2, 3], 0.0) # Fix u_x, u_y, u_z = 0
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end
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# Neumann BC: Pressure on top surface (Z=1)
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# Surface: nodes [5, 6, 7, 8] form two triangles
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println(" Applying pressure load on top 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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# Top surface triangles
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top_surface_tris = [
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[5, 6, 7],
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[6, 7, 8]
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]
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for tri_conn in top_surface_tris
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X_surf = nodes[:, tri_conn]
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# Legacy API: topology + connectivity (infers basis)
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surf_el = Element(Tri3, tri_conn;
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fields=(geometry=X_surf,))
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add_neumann!(physics, surf_el, traction)
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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: $(length(physics.bc_neumann.surface_elements)) surfaces")
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# ============================================================================
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# 5. Solve (Backend Transparent!)
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# ============================================================================
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println("\n[5] Solving...")
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println(" Using GPU backend (CPU backend not yet implemented)")
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# Unified solve! - backend transparent!
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# Explicitly request GPU since CPU backend is just a stub
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result = solve!(
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physics;
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backend=GPU(), # Use GPU (CPU backend coming in Phase 2)
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time=0.0,
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tol=1e-6,
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max_iter=1000
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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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if result.newton_iterations == 1
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# Linear problem (converged in 1 Newton iteration)
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println(" Problem type: LINEAR elasticity")
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println(" Newton iterations: 1 (linear problem - no iterations needed)")
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println(" CG iterations: $(result.cg_iterations)")
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println(" Final residual: $(result.residual)")
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println()
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println(" Note: For LINEAR problems, Newton converges in 1 iteration.")
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println(" CG iterations shown are from the single linear solve.")
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else
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# Nonlinear problem (multiple Newton iterations)
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println(" Problem type: NONLINEAR elasticity")
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println(" Solver: Inexact Newton-Krylov (SIMULTANEOUS solving!)")
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println()
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println(" Newton iterations: $(result.newton_iterations)")
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println(" Total CG iterations: $(result.cg_iterations)")
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println(" Avg CG per Newton: $(round(result.cg_iterations / result.newton_iterations, digits=1))")
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println(" Final residual: $(result.residual)")
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println()
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println(" Iteration history (Newton + CG solved SIMULTANEOUSLY):")
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for (i, (cg_i, R_i, η_i)) in enumerate(result.history)
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println(" Newton $i: CG=$cg_i, ||R||=$(round(R_i, sigdigits=3)), η=$(round(η_i, digits=3))")
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end
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println()
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println(" ✓ Linear systems solved INEXACTLY (adaptive tolerance)")
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println(" ✓ Newton and Krylov iterations INTERLEAVED")
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println(" ✓ Much faster than nested loops!")
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end
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println()
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println(" Solve time: $(round(result.solve_time, digits=3)) seconds")
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# ============================================================================
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# 6. Post-Process Results
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# ============================================================================
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println("\n[6] Post-processing...")
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u = result.u
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n_nodes = div(length(u), 3)
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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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# 7. Validate (Simple Check)
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# ============================================================================
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println("\n[7] Validation...")
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# For cantilever with pressure load, expect:
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# - Free end (X=2) has largest displacement
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# - Fixed end (X=0) has zero displacement
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# - Deflection primarily in -Z direction
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free_end_nodes = [2, 4, 6, 8] # X=2
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fixed_end_nodes = [1, 3, 5, 7] # X=0
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free_end_disp = maximum(u_mag[free_end_nodes])
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fixed_end_disp = maximum(u_mag[fixed_end_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("\nBackend-Transparent API Summary:")
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println(" 1. Create elements: Element(Topology, connectivity; fields=(...))")
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println(" 2. Create Physics: physics = Physics(Elasticity, name, dimension)")
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println(" 3. Add elements: add_elements!(physics, body_elements)")
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println(" 4. Add Dirichlet: add_dirichlet!(physics, node_ids, components, value)")
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println(" 5. Add Neumann: add_neumann!(physics, surface_element, traction)")
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println(" 6. Solve: result = solve!(physics) # ← Backend automatic!")
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println()
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println("Key Features:")
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println(" ✓ Immutable elements with fields at construction")
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println(" ✓ Backend transparency - same code for CPU or GPU")
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println(" ✓ Automatic backend selection (GPU if CUDA available)")
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println(" ✓ Matrix-free CG solver")
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println(" ✓ No 'GPU' in user code!")
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println()
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println("Backend Selection:")
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println(" solve!(physics) # Auto (GPU if available, else CPU)")
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println(" solve!(physics; backend=GPU()) # Force GPU")
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println(" solve!(physics; backend=CPU(8)) # Force CPU with 8 threads")
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