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

[Matthew Knepley]

On Wed, Mar 29, 2017 at 6:58 AM, Toon Weyens <toon.weyens at gmail.com> wrote:

> 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.
>

For any scalability question, we need to see the output of

  -log_view -ksp_view -ksp_monitor_true_residual -ksp_converged_reason

and other EPS options which I forget unfortunately. What seems likely here
is that you
are using a PC which is not scalable, so iteration would be going up.

  Thanks,

     Matt


> 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!
>>
>>
>>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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