[petsc-users] using preconditioner with SLEPc

[Dave May]

On Mon 8. Feb 2021 at 15:49, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Feb 8, 2021 at 9:37 AM Jose E. Roman <jroman at dsic.upv.es> wrote:
>
>> The problem can be written as A0*v=omega*B0*v and you want the
>> eigenvalues omega closest to zero. If the matrices were explicitly
>> available, you would do shift-and-invert with target=0, that is
>>
>>   (A0-sigma*B0)^{-1}*B0*v=theta*v    for sigma=0, that is
>>
>>   A0^{-1}*B0*v=theta*v
>>
>> and you compute EPS_LARGEST_MAGNITUDE eigenvalues theta=1/omega.
>>
>> Matt: I guess you should have EPS_LARGEST_MAGNITUDE instead of
>> EPS_SMALLEST_REAL in your code. Are you getting the eigenvalues you need?
>> EPS_SMALLEST_REAL will give slow convergence.
>>
>
> Thanks Jose! I am not understanding some step. I want the smallest
> eigenvalues. Should I use EPS_SMALLEST_MAGNITUDE? I appear to get what I
> want
> using SMALLEST_REAL, but as you say it might be slower than it has to be.
>


With shift-and-invert you want to use EPS_LARGEST_MAGNITUDE as Jose says.
The largest magnitude v eigenvalues you obtain (see Jose equation above)
from the transformed system correspond to the smallest magnitude omega
eigenvalues of the original problem.

Cheers
Dave


> Also, sometime I would like to talk about incorporating the multilevel
> eigensolver. I am sure you could make lots of improvements to my initial
> attempt. I will send
> you a separate email, since I am getting serious about testing it.
>
>   Thanks,
>
>      Matt
>
>
>> Florian: I would not recommend setting the KSP matrices directly, it may
>> produce strange side-effects. We should have an interface function to pass
>> this matrix. Currently there is STPrecondSetMatForPC() but it has two
>> problems: (1) it is intended for STPRECOND, so cannot be used with
>> Krylov-Schur, and (2) it is not currently available in the python interface.
>>
>> The approach used by Matt is a workaround that does not use ST, so you
>> can handle linear solves with a KSP of your own.
>>
>> As an alternative, since your problem is symmetric, you could try LOBPCG,
>> assuming that the leftmost eigenvalues are those that you want (e.g. if all
>> eigenvalues are non-negative). In that case you could use
>> STPrecondSetMatForPC(), but the remaining issue is calling it from python.
>>
>> If you are using the git repo, I could add the relevant code.
>>
>> Jose
>>
>>
>>
>> > El 8 feb 2021, a las 14:22, Matthew Knepley <knepley at gmail.com>
>> escribió:
>> >
>> > On Mon, Feb 8, 2021 at 7:04 AM Florian Bruckner <e0425375 at gmail.com>
>> wrote:
>> > Dear PETSc / SLEPc Users,
>> >
>> > my question is very similar to the one posted here:
>> > https://lists.mcs.anl.gov/pipermail/petsc-users/2018-August/035878.html
>> >
>> > The eigensystem I would like to solve looks like:
>> > B0 v = 1/omega A0 v
>> > B0 and A0 are both hermitian, A0 is positive definite, but only given
>> as a linear operator (matshell). I am looking for the largest eigenvalues
>> (=smallest omega).
>> >
>> > I also have a sparse approximation P0 of the A0 operator, which i would
>> like to use as precondtioner, using something like this:
>> >
>> >         es = SLEPc.EPS().create(comm=fd.COMM_WORLD)
>> >         st = es.getST()
>> >         ksp = st.getKSP()
>> >         ksp.setOperators(self.A0, self.P0)
>> >
>> > Unfortunately PETSc still complains that it cannot create a
>> preconditioner for a type 'python' matrix although P0.type == 'seqaij' (but
>> A0.type == 'python').
>> > By the way, should P0 be an approximation of A0 or does it have to
>> include B0?
>> >
>> > Right now I am using the krylov-schur method. Are there any
>> alternatives if A0 is only given as an operator?
>> >
>> > Jose can correct me if I say something wrong.
>> >
>> > When I did this, I made a shell operator for the action of A0^{-1} B0
>> which has a KSPSolve() in it, so you can use your P0 preconditioning
>> matrix, and
>> > then handed that to EPS. You can see me do it here:
>> >
>> >
>> https://gitlab.com/knepley/bamg/-/blob/master/src/coarse/bamgCoarseSpace.c#L123
>> >
>> > I had a hard time getting the embedded solver to work the way I wanted,
>> but maybe that is the better way.
>> >
>> >   Thanks,
>> >
>> >      Matt
>> >
>> > thanks for any advice
>> > best wishes
>> > Florian
>> >
>> >
>> > --
>> > 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
>> >
>> > https://www.cse.buffalo.edu/~knepley/
>>
>>
>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
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