Halving the Grid Spacing Tripled the Error — What an Increment-Based Stopping Rule Hides in Jacobi Iteration
·6 min read
Stop Jacobi when the update drops below a tolerance and the error left behind grows as 1/(1-ρ) on finer grids. A 2D heat-conduction plate compares Jacobi, SOR and optimal ω.
[Paper Review] Split Newton in Two and Free-Surface Becomes Solvable — Casulli–Zanolli (2012)
·7 min read
Day 1 of a 41-cell well has 39 pressurized cells and zero dry cells. By day 10 that is 0 and 12, and the outer Newton count drops from 5 to 1.
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.