I Added 64x the Cores and Weak-Scaling Efficiency Fell to 16.3% — The Trap of Measuring It by Refining the Grid
·9 min read
Why Krylov iterations grew 6.1x in a weak-scaling study that refined the grid, and how adding one multigrid level put the efficiency curve back to flat.
Where Jacobi Dies on a Boundary-Layer Mesh — the Linelet Line-Implicit Preconditioner
·8 min read
On a 64 by 48 mesh, Jacobi climbs from 18 sweeps at aspect ratio 1 to 5471 at 1000, while a wall-normal linelet finishes in 2.
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.
What Jacobi Cannot Kill in 10,000 Sweeps, a V-Cycle Kills in 10 — The Real Secret of Multigrid
·6 min read
On a 64-cell Poisson problem, twenty V-cycles drive the residual below 1e-10 while Jacobi, at four sweeps a step, stalls near 1e-2.
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.