GAMG defaults deviate from PETSc's and cripple it: pc_mg_type=additive, and block size 1 on vector fields

[lmoresi]

Two deviations from PETSc's defaults, both costly

Underworld sets pc_mg_type = "additive" in every GAMG bundle
(petsc_generic_snes_solvers.pyx lines 3260, 4173, 5189, and 6073 for the
Stokes velocity block). PETSc's default for GAMG is multiplicative.
Additive multigrid is a strictly weaker cycle — the levels do not see each
other's corrections.

And the velocity operator reaches GAMG with block size 1 on a
two-component field. GAMG then aggregates each scalar degree of freedom
independently rather than aggregating nodes, which is the standard way to
cripple algebraic multigrid on a vector problem.

Measured

SolKz, unit box, constant viscosity, Taylor-Hood P2-P1, 11 727 unknowns,
refinement 2 — nothing hard is happening here:

GAMG configuration	cycles per velocity solve	flops	wall
as Underworld configures it	243–347	1.155e10	1.38 s
pc_mg_type=multiplicative	74–118	6.892e9	0.90 s
block size 2	84–120	4.599e9	0.70 s
both corrected	34–47	3.121e9	0.54 s

Seven times the cycles and 3.7 times the arithmetic, for two settings.

At larger sizes the uncorrected configuration is worse still: at 186 879
unknowns it needs up to 4 136 cycles per velocity solve, which overruns any
reasonable ksp_max_it and then silently reports a truncated solve.

Why it matters beyond performance

GAMG is what every solver falls back to when the mesh carries no refinement
hierarchy, which is the common case. So this is the default path for most
users, and it is slow for reasons that have nothing to do with the method.

It also makes any geometric-versus-algebraic comparison meaningless: a
measurement against this configuration is measuring our own settings.

Suggested fix

Remove pc_mg_type = "additive" and let PETSc choose. Deviating from a PETSc
default wants a recorded reason, and there is no comment giving one here.

Set the block size on the operator for vector fields so GAMG aggregates nodes.
The matrix is built by PETSc from the DM, so the natural place is wherever the
section is set up rather than after the fact.

Worth checking the other three call sites for the same reasoning, and whether
pc_gamg_agg_nsmooths=2 and pc_gamg_repartition=true have recorded
justifications or are also inherited without one.

Underworld development team with AI support from Claude Code