[petsc-users] Multigrid with defect correction

[Jed Brown]

Matt Landreman <matt.landreman at gmail.com> writes:
> 3. Is it at all sensible to do this second kind of defect correction with
> _algebraic_ multigrid? Perhaps Amat for each level could be formed from the
> high-order matrix at the fine level by the Galerkin operator R A P, after
> getting all the restriction matrices created by gamg for Pmat?

Note that defect correction is most commonly used for
transport-dominated processes for which the high order discretization is
not h-elliptic.  AMG heuristics are typically really bad for such
problems so stabilizing a smoother isn't really a relevant issue.  Also,
it is usually used for strongly nonlinear problems where AMG's setup
costs are likely overkill.  This is not to say that defect correction
AMG won't work, but there is reason to believe that it doesn't matter
for many important problems.
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