Solving Without Inverting the Matrix — GMRES and the Arnoldi Subspace
·7 min read
On a 40 by 40 Poisson problem, 1600 unknowns reach a residual of 8.74e-11 in 78 matrix-vector products, and the true residual is 9.02e-11.
When Explicit Blows Up, Solve Implicit Without Inverting the Matrix — LU-SGS
·6 min read
Explicit CFL at 0.3 stalls for days. Backward Euler and two LU-SGS sweeps carry a Burgers shock through CFL 5 in 49 steps, with no full-matrix inverse.
Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB
·5 min read
On a 60-unknown Poisson system Jacobi is still at residual 2.11e-2 after 2000 sweeps, while CG reaches 1.87e-13 in exactly 60 steps.