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.
At acoustic CFL 10 the preconditioner multiplied the error by 100 every sweep — the one arrow a block preconditioner throws away
·10 min read
Block Gauss-Seidel discards a pressure-velocity feedback whose gain is exactly the acoustic CFL squared. A 1D acoustic model measures the cost.
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.