Stokes pressure sub-solve runs at its 200-iteration cap — the inner Schur solve is silently unconverged and dominates solve time

[lmoresi]

With the outer fixed to fgmres (#624), the measured bottleneck of a genuine Stokes solve moves squarely to the pressure sub-solve: fieldsplit_pressure runs fgmres+gasm with ksp_rtol = solver tolerance and ksp_max_it = 200, and the iteration readout sits AT 134-200 per outer application — 200 is the cap, so the Schur solve routinely exits unconverged (the "repeating iteration count is a cap" pattern; converged reason is never checked on the sub-block). On the 85k-cell contrast benchmark (~/+Simulations/place_route_health/) the pressure block accounts for most of the ~285-308 s genuine solve, for both velocity preconditioners (custom-P FMG and GAMG), which is why the velocity-block choice moves the total by only ~8%.

Two directions, not mutually exclusive:

1. Make the inner Schur affordable: a better pressure preconditioner than gasm-on-a11 for discontinuous P0 pressure with variable viscosity (the eta-scaled pressure mass matrix is the standard candidate), so the cap is never reached.
2. Make the inexactness deliberate: if the design intent is an inexact inner Schur under a flexible outer (the CITCOM margin design), the tolerance/cap should say so explicitly and cheaply (far fewer than 200 iterations), instead of paying 200 iterations for an accuracy that is then not achieved anyway.

Either way the current default pays maximum cost for unconverged inner solves, silently.

Underworld development team with AI support from Claude Code

[lmoresi]

Element-pairing dependence measured (same 85k-cell mesh, contrast, tolerance, fgmres outer, gamg velocity — only the pressure space changed):

• P2-P0 discontinuous (the contact/fault tests' pairing): genuine solve 307.7 s, pressure block 134 its (and AT the 200 cap during other applications)
• P2-P1 continuous (Taylor-Hood): genuine solve 147.5 s, pressure block 43 its

The mass-preconditioned Schur iteration count scales with the inverse square of the inf-sup constant, and P2-P0's is the weakest of the common stable pairs — the grind is substantially the PAIRING, not the gasm preconditioner alone. Cumulative ledger for the genuine solve since the start of this campaign: 543.9 s (gmres outer, P0disc) -> 147.5 s (fgmres outer, Taylor-Hood), 3.7x, with no change to the operator being solved.

The pairing is not a free choice, though: P0 per-cell pressure exists in the fault stream for a reason — a per-cell field carries the pressure jump across a conforming/split fault exactly, where Taylor-Hood's continuous pressure smears it. So the resolution splits: (1) where the physics does not need a discontinuous pressure (damage-zone contrast, smooth rheology), Taylor-Hood should be the recommended pairing and this cost difference documented; (2) where P0disc is required, the Schur solve still needs either a better preconditioner or a deliberately cheap inexact-inner setting — 200 paid-and-unconverged iterations remains the wrong default.

Underworld development team with AI support from Claude Code

[lmoresi]

The pairing verdict carries to the SPLIT-fault contact configuration, answering whether P0disc is required there at all. The split duplicates topology, so every nodal field — pressure included — is discontinuous exactly at the slit, and the contact machinery pairs velocity DOFs only (pressure on the two lips is independent, as the physics wants). Measured on the composed chain (85k-cell edge_split adapt child, place route, frictionless contact, identical mesh and tolerances):

• P2-P0disc: 258 s, peak slip 0.1740, no-opening leak 0
• P2-P1 Taylor-Hood: 126 s, peak slip 0.1800, no-opening leak 0

2.05x, with the machinery unchanged. The slip answers differ 3-4% at this resolution (different pressure spaces; TH's pressure is higher order). The P0disc pairing remains physics-led ONLY for a conforming-but-UNSPLIT interface carrying a sharp per-cell viscosity jump — on a split fault the jump comes from the topology for free, and Taylor-Hood should be the recommended pairing for the contact stream.

Also noted: the contact solve goes through the rotated path, which builds its own fieldsplit KSP — its timings were unchanged by the #624 outer fix (249 -> 258 s, noise), consistent with that path setting its own Krylov types.

Underworld development team with AI support from Claude Code