PyAMG prolongators

The multigrid hierarchy that amg(geom) builds is driven by a prolongator — a callable mapping a stiffness matrix to its level prolongations. Two pure-Julia factories ship in the core (amg_ruge_stuben, the default, and amg_smoothed_aggregation, both via AlgebraicMultigrid.jl). A third is backed by the Python pyamg package and lives in the MultiGridBarrierPyAMGExt extension:

using MultiGridBarrier, PyCall
geom = subdivide(fem2d_P1(), 4)
mg   = amg(geom; prolongator = amg_pyamg(solver = :rootnode))
sol  = mgb_solve(assemble(mg; p = 1.0))

solver selects pyamg's :rootnode (energy-minimization, the default), :smoothed_aggregation, or :ruge_stuben; remaining keyword arguments are forwarded to the pyamg solver constructor.

When is this worth reaching for? The pure-Julia Ruge–Stüben default is robust across the package's benchmarks. Aggregation-based coarsening — amg_pyamg(solver = :rootnode) in particular — is an escape hatch for highly anisotropic problems near p = 1, especially combined with the auxiliary_postprocess keyword of amg (see the amg docstring), where classical coarsening can blow up Newton iteration counts on the central path.

API reference

amg_pyamg(; solver::Symbol=:rootnode, kwargs...) -> prolongator