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.
One Integral Read as 0.1406 and 56.91 — Torsion Stress Function and Duct Laminar Flow
·9 min read
A square bar's torsion constant and a square duct's f·Re are one Poisson solution read twice. One linear-triangle FEM run gives both handbook numbers.
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.