Rotated free-slip silently ignores a mesh-owned custom-FMG hierarchy (adapt children fall back to GAMG)

[lmoresi]

A mesh.adapt() refinement child carries its static coarse tail as mesh._custom_mg_coarse_meshes. On the standard solve path, auto_inject_custom_mg turns that into a registered solver._custom_mg so every solver on an adapted mesh drives geometric MG with no per-solver call. Under rotated free-slip that never happens, and the solve silently falls back to GAMG.

Measured

velocity_pc as reported by solver._rotated_freeslip_info (annulus, rotated free-slip on Upper):

configuration	velocity_pc
no hierarchy at all	GAMG
mesh-owned tail (what adapt() leaves)	GAMG
explicit set_custom_fmg	custom-FMG

The mesh-owned case is indistinguishable from having no hierarchy at all.

Repro: ~/+Simulations/rotated_pmat_audit/mesh_owned_fmg_pickup.py.

Cause

Two facts that only bite in combination:

• auto_inject_custom_mg(self, field_id=0) is invoked from the standard Stokes solve at petsc_generic_snes_solvers.pyx:8825 — after the rotated free-slip dispatch at :8682 has already early-returned into rotated_bc.solve_rotated_freeslip.
• rotated_bc._build_rotated_custom_Pl consults only solver._custom_mg. It never looks at solver.mesh._custom_mg_coarse_meshes.

So the auto-pickup that exists precisely to make adapted meshes get FMG for free is unreachable from the one BC that most needs geometric MG.

Why it matters

This is the adapt-on-top-faults workflow's own configuration: a fault resolved by local refinement on an adapt() child, with rotated strong free-slip (chosen over Nitsche because it composes with transverse isotropy). That combination is exactly the one that loses its multigrid, and it loses it silently — the solve converges, just on a much weaker preconditioner.

The adapt-on-top-faults skill documents the plain refined Annulus case ("native FMG is ignored; to get FMG you must build a coarse-mesh tail and call set_custom_fmg"). The adapt-child case is worse and is not documented: the hierarchy genuinely exists and is discarded.

Suggested fix

Not a reordering — the injection is late on the standard path because the velocity sub-PC is only reachable once the monolithic Jacobian is assembled, and the rotated path builds its own IS-based fieldsplit inside rotated_bc anyway.

Instead, _build_rotated_custom_Pl should fall back to the mesh-owned tail when no solver-set hierarchy is registered: build a CustomMGHierarchy([*coarse, solver.mesh], field_id=0) itself, with the same opportunistic try/except and barycentric→RBF builder fallback auto_inject_custom_mg uses (see #424), so a failed build degrades to GAMG rather than crashing the solve.

Worth also asserting velocity_pc == "custom-FMG" in a test on an adapt child, now that the rotated solve reports it (#465).

Found while auditing the rotated preconditioner in #465; not fixed there to keep that change scoped.

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