Problem-suite robustness sweeps

What it measures: iterations-to-tolerance, convergence, achieved residual, and warm wall time across the research problem families in benchmarks/problems.py, each swept over the parameter that makes it hard, next to the jax.scipy.sparse.linalg baseline at identical tolerance and preconditioner. Every family is verified against a dense reference in CI (--verify).

Reproduce:

python -m benchmarks.benchmark_sweeps --json     # full sweep
python -m benchmarks.benchmark_sweeps --verify   # dense verification (CI)

Record: benchmarks/results/sweeps.json (grid 32 unless swept, rtol 1e-8, Jacobi preconditioning, float64, CPU).

Iterations to tolerance (all 16 points converge)

family	sweep	iterations	behavior
Poisson	grid 16 → 64	8 → 44	expected mesh dependence with point Jacobi
convection–diffusion	Pe 0.1 → 100	145 → 35	upwinding adds dominance at high Péclet — the literature’s non-monotone curve
Helmholtz	k 1 → 20	≈19 flat	into the indefinite regime at this size
anisotropic diffusion	ε 1 → 10⁻³	18 → 70 → 20	hardening at ε=10⁻², then grid alignment

The baselines (jax.scipy cg/gmres) do not expose iteration counts; their achieved residuals and warm times are recorded in the JSON. Adapters with full iteration parity (lineax, PETSc) and the Dolan–Moré profile aggregation are the next stage of the benchmark program, together with line/additive preconditioning of the anisotropic family — the sweep above uses plain Jacobi everywhere precisely so the problem hardness, not the preconditioner, is what varies.