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

[Barry Smith]

> On Oct 27, 2014, at 5:09 PM, Jed Brown <jed at jedbrown.org> wrote:
> 
> 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.  

   Hmm. Is this true? This guy’s matrix causes grief with indefiniteness but since it uses SSOR smoother I think that post-smooth should have been the transpose of the pre smooth automatically? Hmm


  Barry

> This could also be checked, but I don't know how
> to do it without significant wasted work.