[petsc-users] Advice for implementing multigrid with fully coupled variable

[zakaryah]

I am trying to solve a system of nonlinear equations in many variables
which are sparsely coupled and represent a field on a structured grid, and
one variable which is coupled to all variables.  I've been using a
DMRedundant for the fully-coupled variable, a DMDA for the other variables,
and a DMComposite to combine the two and create the matrices and vectors
for the nonlinear solver.  This works, but I am having difficulty improving
the performance.

My question concerns using multigrid methods with such a setup.  The
problem can be formulated so that it coarsens properly, i.e. the function
can be written so that it meets the Galerkin condition, and I can calculate
the Jacobian for the coarse grid, etc.  My issue is that I don't see how to
tell PETSc how to actually perform the coarsening.  If I just use SNESSetDM
with the DMComposite, then I can't use FAS for the SNES or MG for the PC
because PETSc doesn't know how to coarsen the DM.  I'm hoping there is some
way to get this to work, perhaps using a shell - any tips?
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