Custom-P V-cycles across a cut level cost more than they save (7x slower than GAMG at 11x fewer iterations)

[lmoresi]

With the cut mesh inheriting the adapt tail (add_conforming_sheet, PR #589), the velocity-block geometric MG installs and converges in 4 iterations against GAMG's 46 — and still loses the wall time 7x. Instrumented A/B on an 85k-cell cut child (same mesh, operator, tolerance; warm solves, setup excluded; scripts in ~/+Simulations/place_route_health/):

• inherited tail: warm 60.2 s, velocity block mg, 4 its (~13 s per preconditioner application)
• stripped: warm 8.5 s, velocity block gamg, 46 its

The finest transfer crosses the CUT: the cut child sets _refine_dofs_coincide=False (a cut vertex is not an edge midpoint), so the exact nested prolongation cannot apply and the transfer comes from the geometric builder. The #576/#579 FMG wins (2.2x smooth, 13x banded) were measured on UNCUT adapt children with exact transfers. A cheap sparse transfer across a cut level is the missing piece before the inherited tail pays for itself; until then GAMG remains the right default on cut children, and the tail's value is that split-aware or exact-transfer improvements have somewhere to land.

Related: #424 (dense RBF transfer cliff). Also observed: cold solves at this size are setup-dominated (~700-750 s of JIT/assembly against 8.5-60 s of Krylov), so preconditioner comparisons must be made on warm solves.

Underworld development team with AI support from Claude Code

[lmoresi]

Decomposed with a third timed solve (same run, operator unchanged): cold 784.7 s, warm 60.9 s, warm2 60.5 s. The ~52-55 s custom-P premium recurs on EVERY solve — it is per-solve SETUP (the geometric transfer build: re-triangulating the coarse DOF cloud and locating ~350k fine velocity DOFs, plus the Galerkin RAP chain), not cycle application. The 4 V-cycles themselves are cheap; the iteration win (4 vs 46) is real and currently thrown away by rebuilding transfers that depend only on the meshes.

Fix shape, in order of payoff:

1. Cache the built transfers on the mesh (keyed by the level chain and field layout) so repeated solves — a time loop above all — pay the build once. This alone should flip the comparison for any run with more than a handful of solves.
2. The hybrid transfer (exact nested prolongation away from the cavity, geometric only in the cut's footprint): _refine_dofs_coincide=False is declared mesh-wide, but the cut only disturbs vertices inside the carve — everywhere else the fine DOFs coincide with the adapt child's and the exact 1/2,1/2 transfer applies. This cuts the build cost as well as improving the transfer.

Underworld development team with AI support from Claude Code

[lmoresi]

The re-install guard landed on feature/fault-outcrop-3d-cap (PR #589). Correction to this issue's framing after deeper measurement: the fast 'warm repeat' solves were near-no-ops (warm start from the solver's own converged solution), so the honest comparison is a GENUINE solve with perturbed operator values. On that arena, with the fgmres outer (#624): guarded custom-P 284.6 s vs GAMG 307.7 s at 85k cells — custom-P now ahead on wall time as well as iterations (mg:4 vs gamg:54 on the velocity block). Both arms are dominated by the pressure sub-solve at its gasm iteration cap (#625), which bounds what any velocity-block improvement can show. The hybrid cut-crossing transfer remains open here; the 55 s/solve re-install waste is fixed.

Underworld development team with AI support from Claude Code