[petsc-users] KSP with large sparse kronecker product

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

> 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.

Also note that if each panel of the Kronecker product is small enough to solve an eigenproblem, you may want to use fast diagonalization to compute an exact inverse. The eigenproblem will have a dense solution (even though the matrix is sparse), but a few dense eigenproblems of size a hundred or thousand could be faster than solving iteratively with systems in the millions.