[petsc-dev] New implementation of PtAP based on all-at-once algorithm

[Smith, Barry F.]

  Excellent! Thanks

   Barry


> On Apr 11, 2019, at 6:08 PM, Fande Kong via petsc-dev <petsc-dev at mcs.anl.gov> wrote:
> 
> Hi Developers,
> 
> I just want to share a good news.  It is known PETSc-ptap-scalable is taking too much memory for some applications because it needs to build intermediate data structures.  According to Mark's suggestions, I implemented the  all-at-once algorithm that does not cache any intermediate data. 
> 
> I did some comparison,  the new implementation is actually scalable in terms of the memory usage and the compute time even though it is still  slower than "ptap-scalable".   There are some memory profiling results (see the attachments). The new all-at-once implementation use the similar amount of memory as hypre, but it way faster than hypre.
> 
> For example, for a problem with 14,893,346,880 unknowns using 10,000 processor cores,  There are timing results:
> 
> Hypre algorithm:
> 
> MatPtAP               50 1.0 3.5353e+03 1.0 0.00e+00 0.0 1.9e+07 3.3e+04 6.0e+02 33  0  1  0 17  33  0  1  0 17     0
> MatPtAPSymbolic       50 1.0 2.3969e-0213.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00  0  0  0  0  0   0  0  0  0  0     0
> MatPtAPNumeric        50 1.0 3.5353e+03 1.0 0.00e+00 0.0 1.9e+07 3.3e+04 6.0e+02 33  0  1  0 17  33  0  1  0 17     0
> 
> PETSc scalable PtAP:
> 
> MatPtAP               50 1.0 1.1453e+02 1.0 2.07e+09 3.8 6.6e+07 2.0e+05 7.5e+02  2  1  4  6 20   2  1  4  6 20 129418
> MatPtAPSymbolic       50 1.0 5.1562e+01 1.0 0.00e+00 0.0 4.1e+07 1.4e+05 3.5e+02  1  0  3  3  9   1  0  3  3  9     0
> MatPtAPNumeric        50 1.0 6.3072e+01 1.0 2.07e+09 3.8 2.4e+07 3.1e+05 4.0e+02  1  1  2  4 11   1  1  2  4 11 235011
> 
> New implementation of the all-at-once algorithm:
> 
> MatPtAP               50 1.0 2.2153e+02 1.0 0.00e+00 0.0 1.0e+08 1.4e+05 6.0e+02  4  0  7  7 17   4  0  7  7 17     0
> MatPtAPSymbolic       50 1.0 1.1055e+02 1.0 0.00e+00 0.0 7.9e+07 1.2e+05 2.0e+02  2  0  5  4  6   2  0  5  4  6     0
> MatPtAPNumeric        50 1.0 1.1102e+02 1.0 0.00e+00 0.0 2.6e+07 2.0e+05 4.0e+02  2  0  2  3 11   2  0  2  3 11     0
> 
> 
> You can see here the all-at-once is a bit slower than ptap-scalable, but it uses only much less memory.   
> 
> 
> Fande
>  
> <hypre_ptap.png><petsc_ptap_allatonce.png><petsc_ptap_scalable.png>