[petsc-users] Debugging suggestions: GAMG

[Jed Brown]

Mark Adams <mfadams at lbl.gov> writes:

> That is odd. Are these problems symmetric positive definite?
>
> Eigen estimates are a pain in practice but I've never seen this. Hypre has
> (better) smoothers that don't need this and the AMG algorithm does not need
> them either. I think ML does pretty much the same thing as me.

We could certainly offer an "l1 Jacobi" for operator smoothing; it's
effectively using the Gershgorin bound, though it can be very
pessimistic.

At a minimum, it would be useful diagnostic information and we could
stop the Krylov estimate early if its maxbound (which includes safety
and is non-increasing with iteration) exceeds the Gershgorin bound.

> If SPD then you definitely want '-pc_gamg_esteig_ksp_type cg'. CG converges
> faster and is more robust.

Mark, this comes up a lot.  Should we select it by default if MAT_SPD is set?

> Even if not strictly SPD like with large
> deformation or plasticity CG is probably better. You can run with -info and
> grep on GAMG to see what eigen (high) estimates it came up with for each
> level. They should be >1 and < 4, or so.
>
> I wonder if your LAPACK is funky. You might try a fresh build (delete the
> "arch" directory) and download LAPACK, but this problem will go away with
> CG.

Sanjay, you could use the debugger to print out the small dense matrix
that LAPACK is choking on.  It isn't supposed to divide by zero ever.