Newton–GMRES Interactive Lab
This lab is part of a fully self-contained article that walks through the complete chain from stiffness → implicit stepping → Newton → GMRES → preconditioning. The interactive exploration is embedded directly in that article, right after the section that explains what the experiment showed.
The full experience — article, math, and interactive lab together — lives in the Newton–GMRES and Preconditioning for Stiff Chemistry article. Read through section 12 and the lab will appear inline.
What the lab shows
One implicit timestep of a 60-species stiff chemistry system, solved three ways:
- No preconditioner — 172 total GMRES iterations across 8 Newton steps
- Diagonal preconditioner — 153 iterations across 8 Newton steps
- Banded ILU preconditioner — 4 iterations across 4 Newton steps
The lab lets you inspect the Newton residual progression for each strategy, click any Newton step to see the GMRES convergence history (log scale) for all three strategies side by side, and see the Jacobian sparsity pattern that explains why banded wins.
Why these two pieces are together
The article builds the conceptual framework; the lab makes the numbers tangible. Neither is complete without the other. The article tells you why banded preconditioning should win; the lab lets you see by how much at every single Newton step.