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.
[Paper Review] Tired of Differentiating Jacobians by Hand? — Operator-Overloading Automatic Differentiation (ADOO)
·7 min read
Fraysse (2019) seeds dual numbers through an unchanged flux routine and reads a machine-precision Jacobian, with no finite-difference step h to tune.
[Paper Review] GMRES Ran 1000 Times and Still Wouldn't Stop — Physics-Based Block Preconditioning for an All-Speed Melt Pool
·7 min read
At Mach 1e-3, GMRES spun 1000 times and the residual sat at 1e-2. A velocity–pressure Schur complement returns that count to two or three steps.