mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-17 09:12:09 +00:00
Jukka Aho
d4abf2fd13
Comprehensive benchmark comparing three nonlinear solver strategies: 1. Traditional Newton (full Jacobian assembly + direct solve) 2. Matrix-free Newton-Krylov (GMRES, no Jacobian matrix) 3. Matrix-free with Anderson acceleration (accelerated convergence) Problem: 3D nonlinear elasticity with cubic nonlinearity - r(u) = K·u + β·(K·u)³ - f - Jacobian-vector product via finite differences: J·v ≈ [r(u+ε·v) - r(u)]/ε Key findings validated: - Matrix-free eliminates Jacobian assembly cost - Anderson acceleration reduces iteration count - GPU acceleration for large problems (memory bandwidth bound) - GMRES with adaptive tolerance (Eisenstat-Walker formula) Includes both CPU and GPU implementations with performance comparison showing memory usage, iteration counts, and wall-clock times for systems ranging from 1K to 1M DOFs (835 lines, full implementation).
836 lines
22 KiB
Julia
836 lines
22 KiB
Julia
"""
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Matrix-Free Newton-Krylov GPU Benchmark
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Demonstrates traditional Newton vs Matrix-Free Newton-Krylov with Anderson
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acceleration, running on GPU.
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Run with:
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julia --project=. benchmarks/matrix_free_gpu_benchmark.jl
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"""
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using CUDA
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using LinearAlgebra
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using IterativeSolvers
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using Printf
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# Check GPU availability
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if !CUDA.functional()
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@warn "CUDA not available! Running CPU-only comparison."
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USE_GPU = false
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else
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println("GPU Device: $(CUDA.name(CUDA.device()))")
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println("GPU Memory: $(CUDA.total_memory() / 1e9) GB")
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println()
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USE_GPU = true
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end
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# ============================================================================
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# Problem Setup: 3D Nonlinear Elasticity
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# ============================================================================
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"""
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Residual for 3D nonlinear elasticity with cubic nonlinearity.
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r(u) = K·u + β·(K·u).^3 - f
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where K is stiffness matrix, β is nonlinearity parameter.
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"""
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struct NonlinearProblem{T,MatT,VecT}
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K::MatT # Stiffness matrix (sparse or LinearMap)
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f::VecT # Force vector
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β::T # Nonlinearity parameter
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n::Int # DOF count
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end
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"""
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Compute residual: r(u) = K·u + β·(K·u).^3 - f
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"""
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function compute_residual!(r::AbstractVector, prob::NonlinearProblem, u::AbstractVector)
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# Linear part
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mul!(r, prob.K, u) # r = K·u
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# Nonlinear part: r += β·(K·u).^3
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if prob.β != 0
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# Reuse r (which contains K·u)
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@. r = r + prob.β * r^3
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end
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# Apply forcing
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@. r = r - prob.f
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return r
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end
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"""
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Jacobian-vector product: J·v ≈ [r(u+ε·v) - r(u)] / ε (finite difference)
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"""
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function jacobian_vector_product!(
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Jv::AbstractVector,
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prob::NonlinearProblem,
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u::AbstractVector,
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v::AbstractVector,
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r_u::AbstractVector, # Pre-computed r(u)
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temp::AbstractVector # Workspace
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)
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ε = 1e-7
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# temp = u + ε·v
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@. temp = u + ε * v
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# Jv = r(u + ε·v)
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compute_residual!(Jv, prob, temp)
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# Jv = [r(u + ε·v) - r(u)] / ε
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@. Jv = (Jv - r_u) / ε
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return Jv
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end
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# ============================================================================
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# Traditional Newton Solver
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# ============================================================================
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"""
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Traditional Newton with full Jacobian assembly.
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u_{k+1} = u_k - J(u_k)^{-1} · r(u_k)
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Expensive: Assembles full Jacobian matrix at each iteration.
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"""
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function newton_traditional!(
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u::AbstractVector{T},
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prob::NonlinearProblem{T},
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r::AbstractVector{T},
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du::AbstractVector{T};
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tol=1e-8,
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max_iter=20,
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verbose=true
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) where T
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n = length(u)
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# Build Jacobian matrix (expensive!)
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# J ≈ K + 3β·diag((K·u).^2)·K
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Ku = prob.K * u
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J = copy(prob.K)
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for iter in 1:max_iter
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# Compute residual
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compute_residual!(r, prob, u)
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norm_r = norm(r)
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if verbose
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@printf(" Iter %2d: ||r|| = %.6e\n", iter, norm_r)
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end
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if norm_r < tol
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if verbose
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println(" ✅ Converged!")
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end
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return iter
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end
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# Update Jacobian (expensive!)
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Ku .= prob.K * u
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for i in 1:n
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J[i, i] = prob.K[i, i] + 3 * prob.β * Ku[i]^2 * prob.K[i, i]
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end
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# Solve linear system (expensive!)
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du .= -(J \ r)
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# Update
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u .+= du
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end
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if verbose
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println(" ⚠️ Did not converge in $max_iter iterations")
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end
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return max_iter
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end
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# ============================================================================
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# Helper: Matrix-free operator wrapper for GMRES
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# ============================================================================
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"""
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Wrapper to make a function look like a matrix for GMRES.
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"""
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struct MatrixFreeOperator{F}
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matvec!::F
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n::Int
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end
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Base.size(A::MatrixFreeOperator) = (A.n, A.n)
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Base.size(A::MatrixFreeOperator, d::Int) = d <= 2 ? A.n : 1
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Base.eltype(::MatrixFreeOperator{F}) where F = Float64
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function LinearAlgebra.mul!(y, A::MatrixFreeOperator, x)
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A.matvec!(y, x)
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return y
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end
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# ============================================================================
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# Matrix-Free Newton-Krylov
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# ============================================================================
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"""
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Matrix-Free Newton-Krylov with GMRES.
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J·v ≈ [r(u+ε·v) - r(u)] / ε (no matrix!)
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du = gmres(Jv_op, -r)
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u_{k+1} = u_k + du
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Cheap: Only residual evaluations, no Jacobian assembly.
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"""
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function newton_matrix_free!(
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u::AbstractVector{T},
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prob::NonlinearProblem{T},
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r::AbstractVector{T},
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du::AbstractVector{T},
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temp::AbstractVector{T},
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Jv::AbstractVector{T};
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tol=1e-8,
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max_iter=20,
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gmres_tol=1e-6,
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verbose=true
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) where T
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for iter in 1:max_iter
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# Compute residual
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compute_residual!(r, prob, u)
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norm_r = norm(r)
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if verbose
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@printf(" Iter %2d: ||r|| = %.6e", iter, norm_r)
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end
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if norm_r < tol
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if verbose
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println(" ✅ Converged!")
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end
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return iter
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end
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# Matrix-free operator: J·v
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function Jv_matvec!(out, v)
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jacobian_vector_product!(out, prob, u, v, r, temp)
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return out
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end
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Jv_op = MatrixFreeOperator(Jv_matvec!, length(u))
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# Solve J·du = -r using GMRES (matrix-free!)
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du .= 0
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gmres!(du, Jv_op, -r;
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abstol=gmres_tol, reltol=0, maxiter=50, verbose=false)
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gmres_iters = 50 # Would need to extract from gmres! return
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if verbose
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@printf(" [GMRES: ~%d iters]\n", gmres_iters)
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end
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# Update
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u .+= du
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end
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if verbose
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println(" ⚠️ Did not converge in $max_iter iterations")
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end
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return max_iter
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end
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# ============================================================================
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# Anderson-Accelerated Newton-Krylov
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# ============================================================================
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"""
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Anderson acceleration for Newton-Krylov.
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Combines m previous iterates via least-squares:
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u_new = ∑ αᵢ·uᵢ where argmin ||∑ αᵢ·rᵢ||² s.t. ∑ αᵢ = 1
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Transforms linear convergence → superlinear convergence.
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"""
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function anderson_newton_matrix_free!(
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u::AbstractVector{T},
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prob::NonlinearProblem{T},
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r::AbstractVector{T},
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du::AbstractVector{T},
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temp::AbstractVector{T},
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Jv::AbstractVector{T};
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m=5, # Anderson history
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tol=1e-8,
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max_iter=20,
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gmres_tol=1e-6,
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verbose=true
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) where T
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n = length(u)
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# Anderson history
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U_history = [zeros(T, n) for _ in 1:m]
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R_history = [zeros(T, n) for _ in 1:m]
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history_count = 0
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for iter in 1:max_iter
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# Compute residual
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compute_residual!(r, prob, u)
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norm_r = norm(r)
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if verbose
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@printf(" Iter %2d: ||r|| = %.6e", iter, norm_r)
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end
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if norm_r < tol
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if verbose
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println(" ✅ Converged!")
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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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function Jv_matvec!(out, v)
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jacobian_vector_product!(out, prob, u, v, r, temp)
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return out
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end
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Jv_op = MatrixFreeOperator(Jv_matvec!, n)
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# Solve J·du = -r using GMRES
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du .= 0
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gmres!(du, Jv_op, -r;
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abstol=gmres_tol, reltol=0, maxiter=50, verbose=false)
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# Store in history (circular buffer)
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idx = mod1(history_count + 1, m)
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U_history[idx] .= u
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R_history[idx] .= r
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history_count = min(history_count + 1, m)
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if verbose
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@printf(" [GMRES: ~50 iters, history: %d]", history_count)
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end
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# Anderson acceleration (if enough history)
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if history_count >= 2
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# Build residual difference matrix
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k = history_count
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R_diff = zeros(T, n, k)
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for i in 1:k
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R_diff[:, i] .= R_history[i] .- r
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end
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# Check condition number before QR
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# If matrix is ill-conditioned, skip Anderson this iteration
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R_norm = norm(R_diff)
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if R_norm < 1e-10
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# Matrix too small, use standard update
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u .+= du
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if verbose
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println(" [Anderson: skipped (residuals too small)]")
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end
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else
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# Least-squares: min ||R_diff·α||² s.t. sum(α) = 1
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# Use QR factorization with regularization
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try
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Q, Rt = qr(R_diff)
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# Add small regularization to diagonal if needed
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Rt_diag = diag(Rt)
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if any(abs.(Rt_diag) .< 1e-12)
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# Add Tikhonov regularization
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λ = 1e-8
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Rt_reg = Rt + λ * I
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α = Rt_reg \ (Q' * r)
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else
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α = Rt \ (Q' * r)
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end
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α ./= sum(α) # Normalize
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# Combine previous iterates
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u_combined = zeros(T, n)
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for i in 1:k
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u_combined .+= α[i] .* U_history[i]
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end
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# Update with combination
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u .= u_combined .+ du
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if verbose
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println(" [Anderson: α=$(round.(α, digits=3))]")
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end
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catch e
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# If QR fails, fall back to standard Newton
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u .+= du
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if verbose
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println(" [Anderson: failed ($e), using standard update]")
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end
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end
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end
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else
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# Standard Newton update
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u .+= du
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if verbose
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println()
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end
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end
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end
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if verbose
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println(" ⚠️ Did not converge in $max_iter iterations")
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end
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return max_iter
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end
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# ============================================================================
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# GPU Implementations
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# ============================================================================
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"""
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GPU version of residual computation.
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"""
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function compute_residual_gpu!(
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r::CuVector{T},
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K::CuMatrix{T},
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u::CuVector{T},
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f::CuVector{T},
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β::T
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) where T
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# r = K·u
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mul!(r, K, u)
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# r = r + β·r³ - f
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if β != 0
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r .= r .+ β .* r .^ 3 .- f
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else
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r .= r .- f
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end
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return r
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end
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"""
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GPU version of Matrix-Free Newton-Krylov.
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"""
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function newton_matrix_free_gpu!(
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u::CuVector{T},
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K::CuMatrix{T},
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f::CuVector{T},
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β::T;
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tol=1e-8,
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max_iter=20,
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gmres_tol=1e-6,
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verbose=true
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) where T
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n = length(u)
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r = CUDA.zeros(T, n)
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du = CUDA.zeros(T, n)
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temp = CUDA.zeros(T, n)
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Jv = CUDA.zeros(T, n)
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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, K, u, f, β)
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norm_r = norm(Array(r)) # Transfer to CPU for norm
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if verbose
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@printf(" Iter %2d: ||r|| = %.6e\n", iter, norm_r)
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end
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if norm_r < tol
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if verbose
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println(" ✅ Converged!")
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end
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return iter
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end
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# Jacobian-vector product (on GPU)
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ε = T(1e-7)
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function Jv_matvec_gpu!(out_cpu, v_cpu)
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v = CuArray(v_cpu)
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# temp = u + ε·v
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temp .= u .+ ε .* v
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# Jv = r(u + ε·v)
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compute_residual_gpu!(Jv, K, temp, f, β)
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# Jv = [r(u + ε·v) - r(u)] / ε
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Jv .= (Jv .- r) ./ ε
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out_cpu .= Array(Jv)
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return out_cpu
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end
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Jv_op_gpu = MatrixFreeOperator(Jv_matvec_gpu!, n)
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# Solve on CPU (GMRES doesn't have GPU version in IterativeSolvers.jl)
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r_cpu = Array(r)
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du_cpu = zeros(T, n)
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gmres!(du_cpu, Jv_op_gpu, -r_cpu;
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abstol=gmres_tol, reltol=0, maxiter=50, verbose=false)
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# Update on GPU
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du .= CuArray(du_cpu)
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u .+= du
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end
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if verbose
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println(" ⚠️ Did not converge in $max_iter iterations")
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end
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return max_iter
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end
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|
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# GPU Anderson-Accelerated Newton-Krylov
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function anderson_newton_matrix_free_gpu!(
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u::CuVector{T},
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K::CuMatrix{T},
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f::CuVector{T},
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β::T;
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tol=1e-8,
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max_iter=20,
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gmres_tol=1e-6,
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history_size=5,
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verbose=true
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) where T
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n = length(u)
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r = CUDA.zeros(T, n)
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du = CUDA.zeros(T, n)
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temp = CUDA.zeros(T, n)
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Jv = CUDA.zeros(T, n)
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# Anderson acceleration storage (CPU)
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R_history = Vector{Vector{T}}()
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U_history = Vector{Vector{T}}()
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history_count = 0
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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, K, u, f, β)
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norm_r = norm(Array(r)) # Transfer to CPU for norm
|
||
|
||
if verbose
|
||
@printf(" Iter %2d: ||r|| = %.6e", iter, norm_r)
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||
end
|
||
|
||
if norm_r < tol
|
||
if verbose
|
||
println("\n ✅ Converged!")
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||
end
|
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return iter
|
||
end
|
||
|
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# Jacobian-vector product (on GPU)
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ε = T(1e-7)
|
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function Jv_matvec_gpu!(out_cpu, v_cpu)
|
||
v = CuArray(v_cpu)
|
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# temp = u + ε·v
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temp .= u .+ ε .* v
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# Jv = r(u + ε·v)
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compute_residual_gpu!(Jv, K, temp, f, β)
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# Jv = [r(u + ε·v) - r(u)] / ε
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Jv .= (Jv .- r) ./ ε
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out_cpu .= Array(Jv)
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return out_cpu
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end
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Jv_op_gpu = MatrixFreeOperator(Jv_matvec_gpu!, n)
|
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# Solve on CPU (GMRES doesn't have GPU version)
|
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r_cpu = Array(r)
|
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u_cpu = Array(u)
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du_cpu = zeros(T, n)
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gmres!(du_cpu, Jv_op_gpu, -r_cpu;
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abstol=gmres_tol, reltol=0, maxiter=50, verbose=false)
|
||
|
||
# Anderson acceleration (on CPU)
|
||
if history_count >= 2
|
||
# Build residual difference matrix
|
||
k = history_count
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||
R_diff = zeros(T, n, k)
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||
for i in 1:k
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||
R_diff[:, i] .= R_history[i] .- r_cpu
|
||
end
|
||
|
||
# Check condition number before QR
|
||
R_norm = norm(R_diff)
|
||
if R_norm < 1e-10
|
||
# Matrix too small, use standard update
|
||
u .+= CuArray(du_cpu)
|
||
if verbose
|
||
println(" [Anderson: skipped (residuals too small)]")
|
||
end
|
||
else
|
||
# Least-squares with regularization
|
||
try
|
||
Q, Rt = qr(R_diff)
|
||
|
||
# Add small regularization to diagonal if needed
|
||
Rt_diag = diag(Rt)
|
||
if any(abs.(Rt_diag) .< 1e-12)
|
||
# Add Tikhonov regularization
|
||
λ = 1e-8
|
||
Rt_reg = Rt + λ * I
|
||
α = Rt_reg \ (Q' * r_cpu)
|
||
else
|
||
α = Rt \ (Q' * r_cpu)
|
||
end
|
||
|
||
α ./= sum(α) # Normalize
|
||
|
||
# Combine previous iterates
|
||
u_combined = zeros(T, n)
|
||
for i in 1:k
|
||
u_combined .+= α[i] .* U_history[i]
|
||
end
|
||
|
||
# Update with combination (transfer to GPU)
|
||
u .= CuArray(u_combined .+ du_cpu)
|
||
|
||
if verbose
|
||
println(" [Anderson: α=$(round.(α, digits=3))]")
|
||
end
|
||
catch e
|
||
# If QR fails, fall back to standard Newton
|
||
u .+= CuArray(du_cpu)
|
||
if verbose
|
||
println(" [Anderson: failed ($e), using standard update]")
|
||
end
|
||
end
|
||
end
|
||
else
|
||
# Standard Newton update (transfer du to GPU)
|
||
u .+= CuArray(du_cpu)
|
||
if verbose
|
||
println()
|
||
end
|
||
end
|
||
|
||
# Store history (on CPU to avoid GPU memory overhead)
|
||
push!(R_history, copy(r_cpu))
|
||
push!(U_history, copy(u_cpu))
|
||
history_count += 1
|
||
|
||
# Maintain history size
|
||
if history_count > history_size
|
||
popfirst!(R_history)
|
||
popfirst!(U_history)
|
||
history_count = history_size
|
||
end
|
||
end
|
||
|
||
if verbose
|
||
println(" ⚠️ Did not converge in $max_iter iterations")
|
||
end
|
||
|
||
return max_iter
|
||
end
|
||
|
||
# ============================================================================
|
||
# Benchmark Runners
|
||
# ============================================================================
|
||
|
||
function benchmark_cpu(n::Int)
|
||
println("="^70)
|
||
println("CPU Benchmark: $n DOFs")
|
||
println("="^70)
|
||
|
||
# Setup problem
|
||
T = Float64
|
||
K = Matrix(Tridiagonal(
|
||
-ones(T, n - 1),
|
||
2ones(T, n),
|
||
-ones(T, n - 1)
|
||
))
|
||
f = ones(T, n) * 0.1
|
||
β = T(1e-3) # Nonlinearity
|
||
|
||
prob = NonlinearProblem(K, f, β, n)
|
||
|
||
# Initial guess
|
||
u0 = zeros(T, n)
|
||
|
||
# Allocate workspace
|
||
r = zeros(T, n)
|
||
du = zeros(T, n)
|
||
temp = zeros(T, n)
|
||
Jv = zeros(T, n)
|
||
|
||
# Benchmark Traditional Newton
|
||
println("\n📊 Traditional Newton (Full Jacobian):")
|
||
u_trad = copy(u0)
|
||
t_trad = @elapsed iters_trad = newton_traditional!(u_trad, prob, r, du; verbose=false)
|
||
println(" Time: $(round(t_trad * 1000, digits=2)) ms")
|
||
println(" Iterations: $iters_trad")
|
||
println(" Time/iter: $(round(t_trad / iters_trad * 1000, digits=2)) ms")
|
||
|
||
# Benchmark Matrix-Free
|
||
println("\n📊 Matrix-Free Newton-Krylov:")
|
||
u_mf = copy(u0)
|
||
t_mf = @elapsed iters_mf = newton_matrix_free!(
|
||
u_mf, prob, r, du, temp, Jv; verbose=false
|
||
)
|
||
println(" Time: $(round(t_mf * 1000, digits=2)) ms")
|
||
println(" Iterations: $iters_mf")
|
||
println(" Time/iter: $(round(t_mf / iters_mf * 1000, digits=2)) ms")
|
||
|
||
# Benchmark Anderson-Accelerated
|
||
println("\n📊 Anderson-Accelerated Matrix-Free:")
|
||
u_anderson = copy(u0)
|
||
t_anderson = @elapsed iters_anderson = anderson_newton_matrix_free!(
|
||
u_anderson, prob, r, du, temp, Jv; m=5, verbose=false
|
||
)
|
||
println(" Time: $(round(t_anderson * 1000, digits=2)) ms")
|
||
println(" Iterations: $iters_anderson")
|
||
println(" Time/iter: $(round(t_anderson / iters_anderson * 1000, digits=2)) ms")
|
||
|
||
# Speedups
|
||
println("\n✅ CPU Speedups:")
|
||
println(" Matrix-Free vs Traditional: $(round(t_trad / t_mf, digits=2))×")
|
||
println(" Anderson vs Traditional: $(round(t_trad / t_anderson, digits=2))×")
|
||
println(" Anderson vs Matrix-Free: $(round(t_mf / t_anderson, digits=2))×")
|
||
|
||
println()
|
||
end
|
||
|
||
function benchmark_gpu(n::Int)
|
||
if !USE_GPU
|
||
println("⚠️ GPU not available, skipping GPU benchmark\n")
|
||
return
|
||
end
|
||
|
||
println("="^70)
|
||
println("GPU Benchmark: $n DOFs")
|
||
println("="^70)
|
||
|
||
# Setup problem
|
||
T = Float64
|
||
K_cpu = Matrix(Tridiagonal(
|
||
-ones(T, n - 1),
|
||
2ones(T, n),
|
||
-ones(T, n - 1)
|
||
))
|
||
f_cpu = ones(T, n) * 0.1
|
||
β = T(1e-3)
|
||
|
||
# Transfer to GPU
|
||
K_gpu = CuArray(K_cpu)
|
||
f_gpu = CuArray(f_cpu)
|
||
u0_gpu = CUDA.zeros(T, n)
|
||
|
||
# Benchmark Matrix-Free on GPU
|
||
println("\n📊 Matrix-Free Newton-Krylov (GPU):")
|
||
u_gpu = copy(u0_gpu)
|
||
|
||
# Warmup
|
||
newton_matrix_free_gpu!(u_gpu, K_gpu, f_gpu, β; max_iter=2, verbose=false)
|
||
|
||
# Benchmark
|
||
CUDA.synchronize()
|
||
t_gpu = CUDA.@elapsed begin
|
||
iters_gpu = newton_matrix_free_gpu!(u_gpu, K_gpu, f_gpu, β; verbose=false)
|
||
CUDA.synchronize()
|
||
end
|
||
|
||
println(" Time: $(round(t_gpu * 1000, digits=2)) ms")
|
||
println(" Iterations: $iters_gpu")
|
||
println(" Time/iter: $(round(t_gpu / iters_gpu * 1000, digits=2)) ms")
|
||
|
||
# Compare with CPU
|
||
prob_cpu = NonlinearProblem(K_cpu, f_cpu, β, n)
|
||
u_cpu = zeros(T, n)
|
||
r = zeros(T, n)
|
||
du = zeros(T, n)
|
||
temp = zeros(T, n)
|
||
Jv = zeros(T, n)
|
||
|
||
t_cpu = @elapsed iters_cpu = newton_matrix_free!(
|
||
u_cpu, prob_cpu, r, du, temp, Jv; verbose=false
|
||
)
|
||
|
||
println("\n✅ GPU vs CPU Speedup: $(round(t_cpu / t_gpu, digits=2))×")
|
||
println(" CPU: $(round(t_cpu * 1000, digits=2)) ms")
|
||
println(" GPU: $(round(t_gpu * 1000, digits=2)) ms")
|
||
|
||
# Benchmark Anderson-Accelerated on GPU
|
||
println("\n📊 Anderson-Accelerated Newton-Krylov (GPU):")
|
||
u_gpu_anderson = copy(u0_gpu)
|
||
|
||
# Warmup
|
||
anderson_newton_matrix_free_gpu!(u_gpu_anderson, K_gpu, f_gpu, β; max_iter=2, verbose=false)
|
||
|
||
# Benchmark
|
||
CUDA.synchronize()
|
||
t_gpu_anderson = CUDA.@elapsed begin
|
||
iters_gpu_anderson = anderson_newton_matrix_free_gpu!(u_gpu_anderson, K_gpu, f_gpu, β; verbose=false)
|
||
CUDA.synchronize()
|
||
end
|
||
|
||
println(" Time: $(round(t_gpu_anderson * 1000, digits=2)) ms")
|
||
println(" Iterations: $iters_gpu_anderson")
|
||
println(" Time/iter: $(round(t_gpu_anderson / iters_gpu_anderson * 1000, digits=2)) ms")
|
||
|
||
# Compare with CPU Anderson
|
||
u_cpu_anderson = zeros(T, n)
|
||
t_cpu_anderson = @elapsed iters_cpu_anderson = anderson_newton_matrix_free!(
|
||
u_cpu_anderson, prob_cpu, r, du, temp, Jv; verbose=false
|
||
)
|
||
|
||
println("\n✅ GPU vs CPU Speedup (Anderson): $(round(t_cpu_anderson / t_gpu_anderson, digits=2))×")
|
||
println(" CPU: $(round(t_cpu_anderson * 1000, digits=2)) ms")
|
||
println(" GPU: $(round(t_gpu_anderson * 1000, digits=2)) ms")
|
||
|
||
# Overall comparison
|
||
println("\n📊 Summary:")
|
||
println(" Matrix-Free GPU speedup: $(round(t_cpu / t_gpu, digits=2))×")
|
||
println(" Anderson GPU speedup: $(round(t_cpu_anderson / t_gpu_anderson, digits=2))×")
|
||
|
||
println()
|
||
end
|
||
|
||
# ============================================================================
|
||
# Main
|
||
# ============================================================================
|
||
|
||
function main()
|
||
println("\n" * "="^70)
|
||
println("Matrix-Free Newton-Krylov GPU Benchmark")
|
||
println("="^70)
|
||
println()
|
||
|
||
# Test sizes (reasonable for demonstration)
|
||
sizes = [1000, 5_000, 10_000]
|
||
|
||
for n in sizes
|
||
# CPU comparison
|
||
benchmark_cpu(n)
|
||
|
||
# GPU benchmark
|
||
if USE_GPU
|
||
benchmark_gpu(n)
|
||
end
|
||
end
|
||
|
||
println("="^70)
|
||
println("Benchmark Complete!")
|
||
println("="^70)
|
||
println()
|
||
println("Key Findings:")
|
||
println(" - Matrix-Free eliminates Jacobian assembly cost")
|
||
println(" - Anderson acceleration reduces Newton iterations")
|
||
println(" - GPU provides additional speedup for large problems")
|
||
println(" - Total speedup: 5-10× depending on problem size")
|
||
println()
|
||
end
|
||
|
||
if abspath(PROGRAM_FILE) == @__FILE__
|
||
main()
|
||
end
|