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

[Thomas Witkowski]

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> 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
>
>