[petsc-users] Matrix-free generalised eigenvalue problem

[Quentin Chevalier]

Hello Jose,

I guess I expected B to not be inverted but instead used as a mass for a
problem-specific inner product since I specified GHEP as a problem type.
p50 of the same user manual <https://slepc.upv.es/documentation/slepc.pdf>
seems to imply that that would indeed be the case. I don't see what problem
there would be with using a shell B matrix as a weighting matrix, as long
as a mat utility is provided of course.

I tried the first approach - I set up my KSP as CG since B is hermitian
positive-definite (I made a mistake in my first email), but I'm getting a
KSPSolve has not converged, reason DIVERGED_ITS error. I'm letting it run
for 1000 iterations already so it seems suspiciously slow for a CG solver.

I'm grappling with a shell preconditioner now to try and speed it up, but
I'm unsure which one allows for shell matrices.

Thank you for your time,

Quentin


On Wed, 12 Jul 2023 at 19:24, Jose E. Roman <jroman at dsic.upv.es> wrote:
>
> By default, it is solving the problem as B^{-1}*A*x=lambda*x (see chapter
on Spectral Transformation). That is why A can be a shell matrix without
problem. But B needs to be an explicit matrix in order to compute an LU
factorization. If B is also a shell matrix then you should set an iterative
solver for the associated KSP (see examples in the chapter).
>
> An alternative is to create a shell matrix M that computes the action of
B^{-1}*A, then pass M to the EPS solver as a standard eigenproblem.
>
> Jose
>
>
> > El 12 jul 2023, a las 19:04, Quentin Chevalier <
quentin.chevalier at polytechnique.edu> escribió:
> >
> > Hello PETSc Users,
> >
> > I have a generalised eigenvalue problem : Ax= lambda Bx
> > I used to have only A as a matrix-free method, I used mumps and an LU
preconditioner, everything worked fine.
> >
> > Now B is matrix-free as well, and my solver is returning an error :
"MatSolverType mumps does not support matrix type python", which is ironic
given it seem to handle A quite fine.
> >
> > I have read in the user manual here that there some methods may require
additional methods to be supplied for B like MATOP_GET_DIAGONAL but it's
unclear to me exactly what I should be implementing and what is the best
solver for my case.
> >
> > A is hermitian, B is hermitian positive but not positive-definite or
real. Therefore I have specified a GHEP problem type to the EPS object.
> >
> > I use PETSc in complex mode through the petsc4py bridge.
> >
> > Any help on how to get EPS to work for a generalised matrix-free case
would be welcome. Performance is not a key issue here - I have a tractable
high value case on hand.
> >
> > Thank you for your time,
> >
> > Quentin
>
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