Add a "bulletproof" smoother strategy: Schwarz, to take the solver off the suspect list

[lmoresi]

What

A third variant on the geometric-MG smoother axis, selected by solver.strategy = "bulletproof": gmres/8 preconditioned by additive Schwarz instead of SOR. Each subdomain solve inverts the local coupling directly, so the smoother does not depend on the operator being close to symmetric or elliptic — which SOR does.

Why

Its purpose is diagnostic as much as numerical. When a run misbehaves and the linear solve, the transport scheme and the mesh resolution are all candidates, rerunning under this variant takes the first off the list.

That is not hypothetical — it is how this variant earned its way in. Creeping Oldroyd-B past a confined cylinder (Wi 0.4, β = 0.59, three levels), where the viscoelastic velocity block carries upper-convected stretching terms and a stress layer thinner than a cell. Same problem, one option key changed:

smoother	the failing step	drag
sor	26947 s	−4642
asm	115 s	86.05

90% of the inner velocity solves hit their iteration cap under sor, 77% under asm. It then produced the same wrong drag as every other smoother, at the same step, which is what identified the real fault as lying outside the linear algebra.

Cost on a benign operator

Smaller than expected. SolCx (free-slip Stokes, viscosity jump), velocity error identical to four significant figures in every case:

case	default	fast	bulletproof
32², contrast 1e6	15.5 s	11.3 s	12.0 s
32², contrast 1e8	15.9 s	10.6 s	12.6 s
48², 3 levels, 1e6	157.0 s	112.2 s	135.6 s

Faster than the current default, 10–20% behind fast. So it is an opt-in, not a change of default: fast still wins where the operator is benign, and nothing here justifies displacing a measured default.

Notes for review

• Every variant still writes the same option keys — that invariant is what keeps the stale-key derivation variant-independent. This is why the variant takes PETSc's own Schwarz defaults rather than tuning overlap, which would need a key the others do not have.
• It covers the velocity smoother only. A fuller "take the solver off the table" switch would extend the same idea to the coarse solve and the pressure block; that is deliberately not in this PR.
• Not measured on a genuinely easy operator: SolCx is singular at uniform viscosity, so the cheapest case where Schwarz should lose most clearly is untested here.

Check

tests/test_1021_mg_option_bundle.py — 19 passed. tests/test_1015_analytic_solcx.py — 4 passed. The SolCx comparison above was run directly.

🤖 Generated with Claude Code

https://claude.ai/code/session_018T2VHUGaZiQVJ95qQ4DiSL

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