[petsc-users] unreliable AMG in PETSc

[Jed Brown]

Arne Morten Kvarving <arne.morten.kvarving at sintef.no> writes:

> thanks for educating me! i wasn't aware richardson could break definiteness.

This is usually caused by the Richardson parameter being too aggressive.
An analogous breakdown occurs with Chebyshev when the eigenvalue
estimate is too small.

> one small thing that could perhaps be added is to warn if the matrix is 
> marked spd and ksp is cg ? i will add this in our code for sure.

Do you mean if the matrix is _not_ marked SPD?  Interestingly, CG is
often tolerant of weak asymmetry, such as you get with nonsymmetric
enforcement of Dirichlet boundary conditions.  That tolerance can be
considered robust when the first application of the preconditioner
solves those equations contributing to asymmetry, in which case further
iterations take place in a "benign" subspace in which the operator is
SPD (so long as the preconditioner does not undo this).

We don't have a good system for offering advice or things to check and
PETSc's convention is always to make solvers silent unless information
is requested.  We could have -ksp_view note when a matrix has not been
marked SPD.  Or we could (with much more effort) create a new feature
"-ksp_analyze" that runs some fairly expensive tests and offers advice.


Thanks for your feedback and test suite.
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