Need PETSc solver settings for GAMG equivalent to ML when running in parallel

[baagaard-usgs]

Describe the bug

We get very slow convergence and GMRES restart errors when we use the GAMG preconditioner for the displacement and fault Lagrange multiplier blocks when running in parallel with a fault. Using ML instead gives robust results.

To Reproduce

PETSc branch: knepley/pylith
PyLith branch: main

cd examples/strikeslip-2d
pylith step01_slip.cfg --nodes=2

Good PETSc settings

[pylithapp.problem]
petsc_defaults.solver = False

[pyliathapp.petsc]
fieldsplit_displacement_ksp_type = preonly
fieldsplit_displacement_pc_type = ml
fieldsplit_lagrange_multiplier_fault_ksp_type = preonly
fieldsplit_lagrange_multiplier_fault_pc_type = ml

pc_fieldsplit_schur_factorization_type = lower
pc_fieldsplit_schur_precondition = selfp
pc_fieldsplit_schur_scale = 1.0
pc_fieldsplit_type = schur
pc_type = fieldsplit
pc_use_amat = true

Bad PETSc settings (slow convergence, GMRES restart errors)

[pylithapp.problem]
petsc_defaults.solver = False

[pyliathapp.petsc]
fieldsplit_displacement_ksp_type = preonly
fieldsplit_displacement_pc_type = gamg
fieldsplit_lagrange_multiplier_fault_ksp_type = preonly
fieldsplit_lagrange_multiplier_fault_pc_type = gamg

pc_fieldsplit_schur_factorization_type = lower
pc_fieldsplit_schur_precondition = selfp
pc_fieldsplit_schur_scale = 1.0
pc_fieldsplit_type = schur
pc_type = fieldsplit
pc_use_amat = true

Desired solution

Find default PETSc settings for GAMG that give nearly the same results as ML when running in parallel with a fault.