What Jacobi Cannot Kill in 10,000 Sweeps, a V-Cycle Kills in 10 — The Real Secret of Multigrid
·6 min read
Swap the grid, swap the frequency: how a hierarchy converts stubborn low modes into easy ones
Implicit Diffusion and the Thomas Algorithm — Buying Stability with One Tridiagonal Solve
·4 min read
Past the explicit blow-up wall, the cost of unconditional stability is one O(N) sweep
When Characteristics Collide, a Shock Is Born — Burgers and the (x,t) Plane
·5 min read
How nonlinear self-advection breaks a smooth curve into a shock.
Quadtree AMR — Letting the Mesh Grow Where It Needs To
·6 min read
Forty years of adaptive mesh data structures and refinement criteria, since Berger–Oliger
When Lax–Wendroff Shook at a Step — Building a 2nd-Order TVD Advection Scheme with Flux Limiters
·5 min read
Sidestep Godunov's theorem to build a monotone 2nd-order advection scheme
Choosing a CFD Linear Solver: Comparing Convergence Speeds from Jacobi to BiCGSTAB
·5 min read
Comparing the characteristics and convergence speeds of the four major Krylov subspace solvers with code and simulation.