[petsc-users] Slepc JD and GD converge to wrong eigenpair

[Toon Weyens]

Dear Jose,

Thanks for the answer. I am looking for the smallest real, indeed.

I have, just now, accidentally figured out that I can get correct
convergence by increasing NCV to higher values, so that's covered! I
thought I had checked this before, but apparently not. It's converging well
now, and rather fast (still about 8 times faster than Krylov-Schur).

The issue now is that it scales rather badly: If I use 2 or more MPI
processes, the time required to solve it goes up drastically. A small test
case, on my Ubuntu 16.04 laptop, takes 10 seconds (blazing fast) for 1 MPI
process, 25 for 2, 33 for 3, 59 for 4, etc... It is a machine with 8 cores,
so i don't really understand why this is.

Are there other methods that can actually maintain the time required to
solve for multiple MPI process? Or, preferable, decrease it (why else would
I use multiple processes if not for memory restrictions)?

I will never have to do something bigger than a generalized non-Hermitian
ev problem of, let's say, 5000 blocks of 200x200 complex values per block,
and a band size of about 11 blocks wide (so a few GB per matrix max).

Thanks so much!

On Wed, Mar 29, 2017 at 9:54 AM Jose E. Roman <jroman at dsic.upv.es> wrote:

>
> > El 29 mar 2017, a las 9:08, Toon Weyens <toon.weyens at gmail.com>
> escribió:
> >
> > I started looking for alternatives from the standard Krylov-Schur method
> to solve the generalized eigenvalue problem Ax = kBx in my code. These
> matrices have a block-band structure (typically 5, 7 or 9 blocks wide, with
> block sizes of the order 20) of size typically 1000 blocks. This eigenvalue
> problem results from the minimization of the energy of a perturbed
> plasma-vacuum system in order to investigate its stability. So far, I've
> not taken advantage of the Hermiticity of the problem.
> >
> > For "easier" problems, especially the Generalized Davidson method
> converges like lightning, sometimes up to 100 times faster than
> Krylov-Schur.
> >
> > However, for slightly more complicated problems, GD converges to the
> wrong eigenpair: There is certainly an eigenpair with an eigenvalue lower
> than 0 (i.e. unstable), but the solver never gets below some small,
> positive value, to which it wrongly converges.
>
> I would need to know the settings you are using. Are you doing
> smallest_real? Maybe you can try target_magnitude with harmonic extraction.
>
> >
> > Is it possible to improve this behavior? I tried changing the
> preconditioner, but it did not work.
> >
> > Might it be possible to use Krylov-Schur until reaching some precision,
> and then switching to JD to quickly converge?
>
> Yes, you can do this, using EPSSetInitialSpace() in the second solve. But,
> depending on the settings, this may not buy you much.
>
> Jose
>
> >
> > Thanks!
>
>
>
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