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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).