[petsc-dev] [petsc-users] unreliable AMG in PETSc

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:
> Definitely debuggability. 

Thanks.

> It would be great if we automatically diagnose the failure of
> definiteness (I assume all these retain symmetry).

So long as a symmetric operator is input.

> Maybe we are already doing this. Then we should improve the error
> message to give the user easy options for fixing it.

We only notice it at a higher level.  The smoother could check whether
its action is SPD with respect to each vector it is applied to at the
cost of a dot product (check that x^T S x > 0).

Actually, the problem is more subtle because if one wants an SPD
multigrid cycle, they only need that the post-smoother is the transpose
of the pre-smoother.  This could also be checked, but I don't know how
to do it without significant wasted work.
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