[petsc-users] LU factorization and solution of independent matrices does not scale, why?

[Jack Poulson]

Hi Thomas,

Network topology is important. Since most machines are not fully connected,
random subsets of four processes will become more scattered about the
cluster as you increase your total number of processes.

Jack
On Dec 20, 2012 12:39 PM, "Thomas Witkowski" <Thomas.Witkowski at tu-dresden.de>
wrote:

> I cannot use the information from log_summary, as I have three different
> LU factorizations and solve (local matrices and two hierarchies of coarse
> grids). Therefore, I use the following work around to get the timing of the
> solve I'm intrested in:
>
>     MPI::COMM_WORLD.Barrier();
>     wtime = MPI::Wtime();
>     KSPSolve(*(data->ksp_schur_**primal_local), tmp_primal, tmp_primal);
>     FetiTimings::fetiSolve03 += (MPI::Wtime() - wtime);
>
> The factorization is done explicitly before with "KSPSetUp", so I can
> measure the time for LU factorization. It also does not scale! For 64
> cores, I takes 0.05 seconds, for 1024 cores 1.2 seconds. In all
> calculations, the local coarse space matrices defined on four cores have
> exactly the same number of rows and exactly the same number of non zero
> entries. So, from my point of view, the time should be absolutely constant.
>
> Thomas
>
> Zitat von Barry Smith <bsmith at mcs.anl.gov>:
>
>
>>   Are you timing ONLY the time to factor and solve the subproblems?  Or
>> also the time to get the data to the collection of 4 cores at a  time?
>>
>>    If you are only using LU for these problems and not elsewhere in  the
>> code you can get the factorization and time from MatLUFactor()  and
>> MatSolve() or you can use stages to put this calculation in its  own stage
>> and use the MatLUFactor() and MatSolve() time from that  stage.
>> Also look at the load balancing column for the factorization and  solve
>> stage, it is well balanced?
>>
>>    Barry
>>
>> On Dec 20, 2012, at 2:16 PM, Thomas Witkowski  <
>> thomas.witkowski at tu-dresden.**de <thomas.witkowski at tu-dresden.de>> wrote:
>>
>>  In my multilevel FETI-DP code, I have localized course matrices,  which
>>> are defined on only a subset of all MPI tasks, typically  between 4 and 64
>>> tasks. The MatAIJ and the KSP objects are both  defined on a MPI
>>> communicator, which is a subset of  MPI::COMM_WORLD. The LU factorization
>>> of the matrices is computed  with either MUMPS or superlu_dist, but both
>>> show some scaling  property I really wonder of: When the overall problem
>>> size is  increased, the solve with the LU factorization of the local
>>>  matrices does not scale! But why not? I just increase the number of  local
>>> matrices, but all of them are independent of each other. Some  example: I
>>> use 64 cores, each coarse matrix is spanned by 4 cores  so there are 16 MPI
>>> communicators with 16 coarse space matrices.  The problem need to solve 192
>>> times with the coarse space systems,  and this takes together 0.09 seconds.
>>> Now I increase the number of  cores to 256, but let the local coarse space
>>> be defined again on  only 4 cores. Again, 192 solutions with these coarse
>>> spaces are  required, but now this takes 0.24 seconds. The same for 1024
>>> cores,  and we are at 1.7 seconds for the local coarse space solver!
>>>
>>> For me, this is a total mystery! Any idea how to explain, debug and
>>>  eventually how to resolve this problem?
>>>
>>> Thomas
>>>
>>
>>
>>
>
>
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