Matt, Barry & Hong, Thanks a lot for response. I may be wrong, but I think that people chose direct solvers for their robustness and ability to solve for many RHS very quickly. Surely I don't expect my solution to be sparse and it is not, but at least in electromagnetics it is pretty common to have sparse RHS. I am wondering how about other disciplines?
I don't know about other solvers, but when I use multiple RHS in mumps it works several times faster then solving for them sequentially. It is just my experience. And I also can imagine that using sparsity is another obvious advantage if you have sparse RHS. Now for 1000 rhs and a system of order 10^6 I need 32 gb to use MatMatSolve with double complex arithmetic. For instance, LDLt factorization of matrix 10^6 takes ~80 gb. One option would be to use MatMatSolve(A,X,X) thus reducing memory consumption twice. >> I doubt it is feasible for thousands of rhs. You're right, it is not. It is feasible only if you have sparse RHS. Regards, Alexander On 12.12.2011 15:37, Hong Zhang wrote: > Reading MUMPS manual, mumps only supports centralized dense and sparse rhs, > while solution can be centralized or distributed, but only in the > dense format (because manual > does not mention sparse solu). > > It would be easy to add MatMatSolve() in Petsc-mumps interface for dense rhs, > but will require vecscatter of petsc distributed dense matrix for rhs > to mumps centralized > dense rhs - I doubt it is feasible for thousands of rhs. > > Hong > > > On Mon, Dec 12, 2011 at 8:26 AM, Barry Smith<bsmith at mcs.anl.gov> wrote: >> Alexander, >> >> Do you expect that solving with a sparse right hand side will result in >> an answer that is also sparse? Normally once you've done the lower >> triangular solve and then the upper triangular solve won't the result be >> dense? >> >> Barry >> >> On Dec 12, 2011, at 3:10 AM, Alexander Grayver wrote: >> >>> Hi Barry, >>> >>> Thanks for answer. I should have asked about that from the very beginning >>> actually. >>> I get 2 times decrease in performance with 20 RHS, I can imagine how slow >>> it will be when I will use thousands of them, >>> moreover it will require a lot of memory to store them as a dense matrix. >>> >>> On 11.12.2011 18:50, Barry Smith wrote: >>>> On Dec 11, 2011, at 9:29 AM, Alexander Grayver wrote: >>>> One by one >>> I'm wondering why? All main direct packages like MUMPS, SuperLU_DIST, >>> PaSTiX support multiple RHS. >>> >>>> We do not handle a sparse right hand side. >>> Since I already transferred my code to PETSc anyway, my question now if >>> it's possible to implement sparse multiple RHS and solve them >>> simultaneously? >>> Something like MatMatSolveSparse. I would implement it myself, the question >>> is there a way to integrate it into PETSc as a patch or something like that? >>> >>> Regards, >>> Alexander
