[petsc-users] unreliable AMG in PETSc

[Mark Adams]

Just to reiterate,add, emphasize what what was said. AMG solvers are very
tricky to make robust to all -- even reasonable -- inputs. To say nothing
of all inputs, but there are a finite number of ways the code can segv and
we want fix them -- one by one.  This code is in fact sable, for 2-3 year
now but users find valid ways to create a segv or mysterious failure and we
fix these.  One at a time, but there is a finite number.

Many PC can be unsymmetric (ILU, MG with F-cycles) and in the case of ILU
indefinite to boot (thus the fix that Barry talked about).  And as Jed says
CG seems to be pretty robust to this.  I've seen PETSc CG return negative
eigenvalues for large deformation elasticity that do in fact go indefinite
(buckling) but it worked fine and Newton eventually converged to an SPD
system.

AMG (MG in general) should not be indefinite with valid inputs, for scalar
Laplacian at least. So a V-cycle preconditioner for an SPD matrix, with an
SPD smoother should stay SPD.  It might die but it should not be indefinite.

Mark

On Thu, Oct 23, 2014 at 2:12 PM, Jed Brown <jed at jedbrown.org> wrote:

> Barry Smith <bsmith at mcs.anl.gov> writes:
> >    It is any interesting question if there is anything one can “do” to
> >    a preconditioner to insure that it is SPD or detect if it may not
> >    be BEFORE actually running the CG with that preconditioned.
>
> You can use an eigensolver for the extreme eigenvalues of the iteration
> matrix for the smoother.  And if it's unstable, report that.  This is
> one thing that the petsc-eig plugin (which I'll update) can do, but it's
> too expensive to do by default.
>
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