Series: combustion-foundations
A fully self-contained first-principles walkthrough of stiffness, implicit integration, Newton solves, GMRES, and structure-aware preconditioning for chemistry ODE systems — with an interactive lab embedded to explore the solver data directly.
An interactive visual lab embedded in the Newton–GMRES article — explore solver traces from a 60-species stiff chemistry system and see why preconditioning collapses GMRES iteration counts from 172 to 4.
Problem
Solver internals are opaque from text alone. The interaction between nonlinear residual reduction and inner linear convergence — and the dramatic impact of preconditioning — is best understood by seeing real solver traces directly.
Outcome
An interactive lab embedded in the full article, giving readers a hands-on way to explore Newton outer iterations, GMRES convergence curves, and the sparsity structure that explains why banded preconditioning wins.