Memory management for solving large sparse systems with UMFPACK

Question

I'm using umfpack for solving large systems of equation. However, I'm constantly getting out of memory issues for even modest size problems as pre2, torso3, ohne2 Hamrle3 (all from Tim Devis's collection). The useable memory is 44GB in machine where I'm trying to run.

These problems are not too big that index would be out of 2GB (I'm using 32 bit integers). One way would be try out 64 bit integer version. However, I might be making a mistake in choosing the parameters itself for the symbolic factorization, which right now is all set to default.

Answer 1

I took a look at the sizes of the matrices you listed. I'm not sure I would characterize their size as "modest". ohne2 has only around 181K equations but nearly 7M non-zeros. Hamrle3 has around 1.5M equations which is a significant number for an unsymmetric, direct solver.

If you are running a 32-bit executable on a 64-bit OS, you likely have a full 4GB address space for your process. This seems like it should be enough to factor these matrices. But as the solver progresses, and makes repeated requests for large blocks of memory, the address space becomes fragmented. So when a particularly large block is required for the values in the L or U factors, the OS simply can't find this much contiguous memory in the address space.

As has already been suggested, if you are running on a 64-bit OS, I would simply re-build UMFPACK with 64-bit integers. Even with 44GB of memory, factoring Hamrle3 in a reasonable amount of time might be challenging.

Answer 2

I take it you are getting an error that looks like this:

UMFPACK_ERROR_out_of_memory

With the 32 bit int version this happens if you try to use more than ~2gb. The 64 bit version might be better otherwise you might have to move to mumps or alike.