[petsc-users] Using Petsc with multiple RHS

[Alexander Grayver]

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