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 :-) Barry > On Jan 16, 2025, at 11:00 AM, Donald Planalp <donaldrexplanal...@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. > >
