[petsc-users] KSP with large sparse kronecker product

[Matthew Knepley]

On Thu, Jan 16, 2025 at 6:26 PM Barry Smith <bsmith at petsc.dev> wrote:

>
>    I don't think we have good code for this case. But it is a good case
> and we should definitely provide support so it would be great to talk
> about.
>
>   Possibly start with the name :-) MATSKAIJ :-)
>

Are you using any preconditioner? If not, you could just use a MATSHELL,
and compute the action of your Kronecker matrix.

  Thanks,

     Matt


>    Barry
>
>
> > On Jan 16, 2025, at 11:00 AM, Donald Planalp <
> donaldrexplanalpjr at outlook.com> wrote:
> >
> >
> > Hello,
> >
> > I am inquiring to see what the best approach for solving a problem I am
> encountering in my quantum mechanics research.
> >
> > For some context, the structure of my problem is solving a linear system
> Ax=b where b=By in parallel. In this case A and B can be written as the sum
> of 4-5 kronecker products. Specifically, A and B are formed by the same
> terms but with a few flipped signs in the sum, and some of the scalings are
> time dependent so currently the sum is performed at each step.
> >
> > The issue I'm having is balancing GMRES solving speed versus memory
> usage. The sparse structure of my matrices is such that A and B (after
> summing) is equivalent in structure to a kronecker product between a matrix
> of size 1000x1000 with 5 nonzeros per row (concentrated along diagonal),
> and a matrix of 2000x2000 with 13 nonzeros per row (banded along diagonal).
> >
> > In this case, the memory usage for explicitly storing the kronecker
> product can be quite large. This seems inefficient since the kronecker
> product contains a lot of repeated information. Further, adding the
> matrices together at each step due to the scaling of time dependence as
> well as dimensionality makes the solver quickly become much slower.
> >
> > I've looked into various matrix types. MATMPIKAIJ seems close, but I
> would require more terms, and all of my matrices are sparse not some of
> them. I've also looked into MATCOMPOSITE to avoid explicit sums at least,
> however the solver time actually becomes slower.
> >
> > I was just curious if there is a better way of handling this using petsc
> that can achieve the best of both worlds, low memory usage and avoiding
> explicit kronecker product evaluation while keeping similar speeds of
> matrix vector products for GMRES.
> >
> > Thank you for your time.
> >
> >
>
>

-- 
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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