[petsc-dev] Bad scaling of GAMG in FieldSplit

[Pierre Jolivet]

Hello,
I’m using GAMG on a shifted Laplacian with these options:
-st_fieldsplit_pressure_ksp_type preonly
-st_fieldsplit_pressure_pc_composite_type additive
-st_fieldsplit_pressure_pc_type composite
-st_fieldsplit_pressure_sub_0_ksp_pc_type jacobi
-st_fieldsplit_pressure_sub_0_pc_type ksp
-st_fieldsplit_pressure_sub_1_ksp_pc_gamg_square_graph 10
-st_fieldsplit_pressure_sub_1_ksp_pc_type gamg
-st_fieldsplit_pressure_sub_1_pc_type ksp

and I end up with the following logs on 512 (top) and 2048 (bottom) processes:
MatMult          1577790 1.0 3.1967e+03 1.2 4.48e+12 1.6 7.6e+09 5.6e+03 0.0e+00  7 71 75 63  0   7 71 75 63  0 650501
MatMultAdd        204786 1.0 1.3412e+02 5.5 1.50e+10 1.7 5.5e+08 2.7e+02 0.0e+00  0  0  5  0  0   0  0  5  0  0 50762
MatMultTranspose  204786 1.0 4.6790e+01 4.3 1.50e+10 1.7 5.5e+08 2.7e+02 0.0e+00  0  0  5  0  0   0  0  5  0  0 145505
[..]
KSPSolve_FS_3       7286 1.0 7.5506e+02 1.0 9.14e+11 1.8 7.3e+09 1.5e+03 2.6e+05  2 14 71 16 34   2 14 71 16 34 539009

MatMult          1778795 1.0 3.5511e+03 4.1 1.46e+12 1.9 4.0e+10 2.4e+03 0.0e+00  7 66 75 61  0   7 66 75 61  0 728371
MatMultAdd        222360 1.0 2.5904e+0348.0 4.31e+09 1.9 2.4e+09 1.3e+02 0.0e+00 14  0  4  0  0  14  0  4  0  0  2872
MatMultTranspose  222360 1.0 1.8736e+03421.8 4.31e+09 1.9 2.4e+09 1.3e+02 0.0e+00  0  0  4  0  0   0  0  4  0  0  3970
[..]
KSPSolve_FS_3       7412 1.0 2.8939e+03 1.0 2.66e+11 2.1 3.5e+10 6.1e+02 2.7e+05 17 11 67 14 28  17 11 67 14 28 148175

MatMultAdd and MatMultTranspose (performed by GAMG) somehow ruin the scalability of the overall solver. The pressure space “only” has 3M unknowns so I’m guessing that’s why GAMG is having a hard time strong scaling. For the other fields, the matrix is somehow distributed nicely, i.e., I don’t want to change the overall distribution of the matrix.
Do you have any suggestion to improve the performance of GAMG in that scenario? I had two ideas in mind but please correct me if I’m wrong or if this is not doable:
1) before setting up GAMG, first use a PCTELESCOPE to avoid having too many processes work on this small problem
2) have the sub_0_ and the sub_1_ work on two different nonoverlapping communicators of size PETSC_COMM_WORLD/2, do the solve concurrently, and then sum the solutions (only worth doing because of -pc_composite_type additive). I have no idea if this easily doable with PETSc command line arguments

Thanks in advance for your guidance,
Pierre