Hi Matt,<br><br>Thanks for your reply. Just now I have carried out a series of tests with k=2, 4, 8, 12 and 16 cores on the first server again with the -log_summary option. From 8 cores to 12 cores, a small speed up has been found this time, but from 12 cores to 16 cores, the computation time increase!<br>
Attached please find these 5 log files. Thank you very much!<br><br>mpiexec -n <i>k</i> ./AMG_Solver_MPI -pc_type jacobi -ksp_type bicg -log_summary<br>Here, I use ksp bicg instead of gmres, because the two ksp gives almost the same speed up performance, as I have tried many times.<br>
----------------------<br>(1) k=2 <br>----------------------<br>Process 1 of total 2 on wmss04<br>Process 0 of total 2 on wmss04<br>The dimension of Matrix A is n = 1177754<br>Begin Assembly:<br>Begin Assembly:<br>End Assembly.<br>
End Assembly.<br>=========================================================<br>Begin the solving: <br>=========================================================<br>The current time is: Mon Dec 20 17:42:23 2010<br>
<br>KSP Object:<br> type: bicg<br> maximum iterations=10000, initial guess is zero<br> tolerances: relative=1e-07, absolute=1e-50, divergence=10000<br> left preconditioning<br> using PRECONDITIONED norm type for convergence test<br>
PC Object:<br> type: jacobi<br> linear system matrix = precond matrix:<br> Matrix Object:<br> type=mpisbaij, rows=1177754, cols=1177754<br> total: nonzeros=49908476, allocated nonzeros=49908476<br> block size is 1<br>
<br>norm(b-Ax)=1.25862e-06<br>Norm of error 1.25862e-06, Iterations 1475<br>=========================================================<br>The solver has finished successfully! <br>=========================================================<br>
The solving time is 762.874 seconds.<br>The time accuracy is 1e-06 second.<br>The current time is Mon Dec 20 17:55:06 2010<br><br>************************************************************************************************************************<br>
*** WIDEN YOUR WINDOW TO 120 CHARACTERS. Use 'enscript -r -fCourier9' to print this document ***<br>************************************************************************************************************************<br>
<br>---------------------------------------------- PETSc Performance Summary: ----------------------------------------------<br><br>./AMG_Solver_MPI on a linux-gnu named wmss04 with 2 processors, by cheny Mon Dec 20 18:55:06 2010<br>
Using Petsc Release Version 3.1.0, Patch 5, Mon Sep 27 11:51:54 CDT 2010<br><br> Max Max/Min Avg Total <br>Time (sec): 8.160e+02 1.00000 8.160e+02<br>Objects: 3.000e+01 1.00000 3.000e+01<br>
Flops: 3.120e+11 1.04720 3.050e+11 6.100e+11<br>Flops/sec: 3.824e+08 1.04720 3.737e+08 7.475e+08<br>MPI Messages: 2.958e+03 1.00068 2.958e+03 5.915e+03<br>MPI Message Lengths: 9.598e+08 1.00034 3.245e+05 1.919e+09<br>
MPI Reductions: 4.483e+03 1.00000<br><br>Flop counting convention: 1 flop = 1 real number operation of type (multiply/divide/add/subtract)<br> e.g., VecAXPY() for real vectors of length N --> 2N flops<br>
and VecAXPY() for complex vectors of length N --> 8N flops<br><br>Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages --- -- Message Lengths -- -- Reductions --<br> Avg %Total Avg %Total counts %Total Avg %Total counts %Total <br>
0: Main Stage: 8.1603e+02 100.0% 6.0997e+11 100.0% 5.915e+03 100.0% 3.245e+05 100.0% 4.467e+03 99.6% <br><br>------------------------------------------------------------------------------------------------------------------------<br>
See the 'Profiling' chapter of the users' manual for details on interpreting output.<br>Phase summary info:<br> Count: number of times phase was executed<br> Time and Flops: Max - maximum over all processors<br>
Ratio - ratio of maximum to minimum over all processors<br> Mess: number of messages sent<br> Avg. len: average message length<br> Reduct: number of global reductions<br> Global: entire computation<br>
Stage: stages of a computation. Set stages with PetscLogStagePush() and PetscLogStagePop().<br> %T - percent time in this phase %F - percent flops in this phase<br> %M - percent messages in this phase %L - percent message lengths in this phase<br>
%R - percent reductions in this phase<br> Total Mflop/s: 10e-6 * (sum of flops over all processors)/(max time over all processors)<br>------------------------------------------------------------------------------------------------------------------------<br>
Event Count Time (sec) Flops --- Global --- --- Stage --- Total<br> Max Ratio Max Ratio Max Ratio Mess Avg len Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s<br>
------------------------------------------------------------------------------------------------------------------------<br><br>--- Event Stage 0: Main Stage<br><br>MatMult 1476 1.0 3.4220e+02 1.0 1.48e+11 1.0 3.0e+03 3.2e+05 0.0e+00 41 47 50 50 0 41 47 50 50 0 846<br>
MatMultTranspose 1475 1.0 3.4208e+02 1.0 1.48e+11 1.0 3.0e+03 3.2e+05 0.0e+00 42 47 50 50 0 42 47 50 50 0 846<br>MatAssemblyBegin 1 1.0 1.5492e-0281.5 0.00e+00 0.0 0.0e+00 0.0e+00 3.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>
MatAssemblyEnd 1 1.0 8.1615e-02 1.0 0.00e+00 0.0 1.0e+01 1.1e+05 1.2e+01 0 0 0 0 0 0 0 0 0 0 0<br>MatView 1 1.0 1.5807e-04 3.2 0.00e+00 0.0 0.0e+00 0.0e+00 1.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>
VecView 1 1.0 1.0809e+01 2.1 0.00e+00 0.0 2.0e+00 2.4e+06 0.0e+00 1 0 0 0 0 1 0 0 0 0 0<br>VecDot 2950 1.0 2.0457e+01 1.9 3.47e+09 1.0 0.0e+00 0.0e+00 3.0e+03 2 1 0 0 66 2 1 0 0 66 340<br>
VecNorm 1477 1.0 1.2103e+01 1.7 1.74e+09 1.0 0.0e+00 0.0e+00 1.5e+03 1 1 0 0 33 1 1 0 0 33 287<br>VecCopy 4 1.0 1.0110e-02 1.2 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<br>
VecSet 8855 1.0 6.0069e+00 1.1 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0<br>VecAXPY 4426 1.0 1.8430e+01 1.2 5.21e+09 1.0 0.0e+00 0.0e+00 0.0e+00 2 2 0 0 0 2 2 0 0 0 566<br>
VecAYPX 2948 1.0 1.3610e+01 1.2 3.47e+09 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 510<br>VecAssemblyBegin 6 1.0 9.1116e-0317.7 0.00e+00 0.0 0.0e+00 0.0e+00 1.8e+01 0 0 0 0 0 0 0 0 0 0 0<br>
VecAssemblyEnd 6 1.0 1.7405e-05 1.1 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<br>VecPointwiseMult 2952 1.0 1.7966e+01 1.1 1.74e+09 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 194<br>
VecScatterBegin 2951 1.0 8.6552e-01 1.1 0.00e+00 0.0 5.9e+03 3.2e+05 0.0e+00 0 0100100 0 0 0100100 0 0<br>VecScatterEnd 2951 1.0 2.7126e+01 8.3 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 2 0 0 0 0 2 0 0 0 0 0<br>
KSPSetup 1 1.0 3.9254e-02 1.3 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<br>KSPSolve 1 1.0 7.5170e+02 1.0 3.12e+11 1.0 5.9e+03 3.2e+05 4.4e+03 92100100100 99 92100100100 99 811<br>
PCSetUp 1 1.0 1.9073e-06 1.0 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<br>PCApply 2952 1.0 1.8043e+01 1.1 1.74e+09 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 193<br>
------------------------------------------------------------------------------------------------------------------------<br><br>Memory usage is given in bytes:<br><br>Object Type Creations Destructions Memory Descendants' Mem.<br>
Reports information only for process 0.<br><br>--- Event Stage 0: Main Stage<br><br> Matrix 3 3 339744648 0<br> Vec 18 18 62239872 0<br> Vec Scatter 2 2 1736 0<br>
Index Set 4 4 974736 0<br> Krylov Solver 1 1 832 0<br> Preconditioner 1 1 872 0<br> Viewer 1 1 544 0<br>
========================================================================================================================<br>Average time to get PetscTime(): 1.21593e-06<br>Average time for MPI_Barrier(): 1.44005e-05<br>Average time for zero size MPI_Send(): 1.94311e-05<br>
#PETSc Option Table entries:<br>-ksp_type bicg<br>-log_summary<br>-pc_type jacobi<br>#End of PETSc Option Table entries<br>Compiled without FORTRAN kernels<br>Compiled with full precision matrices (default)<br>sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 8<br>
Configure run at: Tue Nov 23 15:54:45 2010<br>Configure options: --known-level1-dcache-size=65536 --known-level1-dcache-linesize=64 --known-level1-dcache-assoc=2 --known-memcmp-ok=1 --known-sizeof-char=1 --known-sizeof-void-p=8 --known-sizeof-short=2 --known-sizeof-int=4 --known-sizeof-long=8 --known-sizeof-long-long=8 --known-sizeof-float=4 --known-sizeof-double=8 --known-sizeof-size_t=8 --known-bits-per-byte=8 --known-sizeof-MPI_Comm=4 --known-sizeof-MPI_Fint=4 --known-mpi-long-double=1 --with-cc=gcc --with-cxx=g++ --with-F77=ifort --with-FC=ifort --download-f-blas-lapack=1 --download-superlu-dist=1 --download-hypre=1 --download-trilinos=1 --download-parmetis=1 --download-mumps=1 --download-scalapack=1 --download-blacs=1 --download-mpich=1 --with-debugging=0 --with-batch --known-mpi-shared=1<br>
-----------------------------------------<br>Libraries compiled on Tue Nov 23 15:57:11 CET 2010 on wmss04 <br>Machine characteristics: Linux wmss04 2.6.16.60-0.21-smp #1 SMP Tue May 6 12:41:02 UTC 2008 x86_64 x86_64 x86_64 GNU/Linux <br>
Using PETSc directory: /sun42/cheny/petsc-3.1-p5-optimized<br>Using PETSc arch: linux-gnu-c-opt<br>-----------------------------------------<br>Using C compiler: /sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/bin/mpicc -Wall -Wwrite-strings -Wno-strict-aliasing -O <br>
Using Fortran compiler: /sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/bin/mpif90 -Wall -Wno-unused-variable -O <br>-----------------------------------------<br>Using include paths: -I/sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/include -I/sun42/cheny/petsc-3.1-p5-optimized/include -I/sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/include <br>
------------------------------------------<br>Using C linker: /sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/bin/mpicc -Wall -Wwrite-strings -Wno-strict-aliasing -O <br>Using Fortran linker: /sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/bin/mpif90 -Wall -Wno-unused-variable -O <br>
Using libraries: -Wl,-rpath,/sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/lib -L/sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/lib -lpetsc -Wl,-rpath,/sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/lib -L/sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/lib -lHYPRE -lmpichcxx -lstdc++ -lcmumps -ldmumps -lsmumps -lzmumps -lmumps_common -lpord -lparmetis -lmetis -lscalapack -lblacs -lflapack -lfblas -lnsl -laio -lrt -L/sun42/cheny/petsc-3.1-p5-optimized/linux-gnu-c-opt/lib -L/usr/lib64/gcc/x86_64-suse-linux/4.1.2 -L/opt/intel/Compiler/11.0/083/ipp/em64t/lib -L/opt/intel/Compiler/11.0/083/mkl/lib/em64t -L/opt/intel/Compiler/11.0/083/tbb/em64t/cc4.1.0_libc2.4_kernel2.6.16.21/lib -L/usr/x86_64-suse-linux/lib -ldl -lmpich -lpthread -lrt -lgcc_s -lmpichf90 -lgfortran -lm -lm -lmpichcxx -lstdc++ -lmpichcxx -lstdc++ -ldl -lmpich -lpthread -lrt -lgcc_s -ldl <br>
------------------------------------------<br><br><br>----------------------<br>
(2) k=4<br>
----------------------<br>
Process 0 of total 4 on wmss04<br>Process 2 of total 4 on wmss04<br>Process 3 of total 4 on wmss04<br>Process 1 of total 4 on wmss04<br>The dimension of Matrix A is n = 1177754<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>
Begin Assembly:<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>=========================================================<br>Begin the solving: <br>=========================================================<br>
The current time is: Mon Dec 20 17:33:24 2010<br><br>KSP Object:<br> type: bicg<br> maximum iterations=10000, initial guess is zero<br> tolerances: relative=1e-07, absolute=1e-50, divergence=10000<br> left preconditioning<br>
using PRECONDITIONED norm type for convergence test<br>PC Object:<br> type: jacobi<br> linear system matrix = precond matrix:<br> Matrix Object:<br> type=mpisbaij, rows=1177754, cols=1177754<br> total: nonzeros=49908476, allocated nonzeros=49908476<br>
block size is 1<br><br>norm(b-Ax)=1.28342e-06<br>Norm of error 1.28342e-06, Iterations 1473<br>=========================================================<br>The solver has finished successfully! <br>
=========================================================<br>The solving time is 450.583 seconds.<br>The time accuracy is 1e-06 second.<br>The current time is Mon Dec 20 17:40:55 2010<br><br>************************************************************************************************************************<br>
*** WIDEN YOUR WINDOW TO 120 CHARACTERS. Use 'enscript -r -fCourier9' to print this document ***<br>************************************************************************************************************************<br>
<br>---------------------------------------------- PETSc Performance Summary: ----------------------------------------------<br><br>./AMG_Solver_MPI on a linux-gnu named wmss04 with 4 processors, by cheny Mon Dec 20 18:40:55 2010<br>
Using Petsc Release Version 3.1.0, Patch 5, Mon Sep 27 11:51:54 CDT 2010<br><br> Max Max/Min Avg Total <br>Time (sec): 4.807e+02 1.00000 4.807e+02<br>Objects: 3.000e+01 1.00000 3.000e+01<br>
Flops: 1.558e+11 1.06872 1.523e+11 6.091e+11<br>Flops/sec: 3.241e+08 1.06872 3.168e+08 1.267e+09<br>MPI Messages: 5.906e+03 2.00017 4.430e+03 1.772e+04<br>MPI Message Lengths: 1.727e+09 2.74432 2.658e+05 4.710e+09<br>
MPI Reductions: 4.477e+03 1.00000<br><br>Flop counting convention: 1 flop = 1 real number operation of type (multiply/divide/add/subtract)<br> e.g., VecAXPY() for real vectors of length N --> 2N flops<br>
and VecAXPY() for complex vectors of length N --> 8N flops<br><br>Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages --- -- Message Lengths -- -- Reductions --<br> Avg %Total Avg %Total counts %Total Avg %Total counts %Total <br>
0: Main Stage: 4.8066e+02 100.0% 6.0914e+11 100.0% 1.772e+04 100.0% 2.658e+05 100.0% 4.461e+03 99.6% <br><br>------------------------------------------------------------------------------------------------------------------------<br>
See the 'Profiling' chapter of the users' manual for details on interpreting output.<br>Phase summary info:<br> Count: number of times phase was executed<br> Time and Flops: Max - maximum over all processors<br>
Ratio - ratio of maximum to minimum over all processors<br> Mess: number of messages sent<br> Avg. len: average message length<br> Reduct: number of global reductions<br> Global: entire computation<br>
Stage: stages of a computation. Set stages with PetscLogStagePush() and PetscLogStagePop().<br> %T - percent time in this phase %F - percent flops in this phase<br> %M - percent messages in this phase %L - percent message lengths in this phase<br>
%R - percent reductions in this phase<br> Total Mflop/s: 10e-6 * (sum of flops over all processors)/(max time over all processors)<br>------------------------------------------------------------------------------------------------------------------------<br>
Event Count Time (sec) Flops --- Global --- --- Stage --- Total<br> Max Ratio Max Ratio Max Ratio Mess Avg len Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s<br>
------------------------------------------------------------------------------------------------------------------------<br><br>--- Event Stage 0: Main Stage<br><br>MatMult 1474 1.0 1.9344e+02 1.1 7.40e+10 1.1 8.8e+03 2.7e+05 0.0e+00 39 47 50 50 0 39 47 50 50 0 1494<br>
MatMultTranspose 1473 1.0 1.9283e+02 1.0 7.40e+10 1.1 8.8e+03 2.7e+05 0.0e+00 40 47 50 50 0 40 47 50 50 0 1498<br>MatAssemblyBegin 1 1.0 1.5624e-0263.8 0.00e+00 0.0 0.0e+00 0.0e+00 3.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>
MatAssemblyEnd 1 1.0 6.3599e-02 1.0 0.00e+00 0.0 3.0e+01 9.3e+04 1.2e+01 0 0 0 0 0 0 0 0 0 0 0<br>MatView 1 1.0 1.8096e-04 2.7 0.00e+00 0.0 0.0e+00 0.0e+00 1.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>
VecView 1 1.0 1.1063e+01 4.7 0.00e+00 0.0 6.0e+00 1.2e+06 0.0e+00 1 0 0 0 0 1 0 0 0 0 0<br>VecDot 2946 1.0 2.5350e+01 2.7 1.73e+09 1.0 0.0e+00 0.0e+00 2.9e+03 3 1 0 0 66 3 1 0 0 66 274<br>
VecNorm 1475 1.0 1.1197e+01 3.0 8.69e+08 1.0 0.0e+00 0.0e+00 1.5e+03 1 1 0 0 33 1 1 0 0 33 310<br>VecCopy 4 1.0 6.0010e-03 1.4 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<br>
VecSet 8843 1.0 3.6737e+00 1.6 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0<br>VecAXPY 4420 1.0 1.4221e+01 1.4 2.60e+09 1.0 0.0e+00 0.0e+00 0.0e+00 3 2 0 0 0 3 2 0 0 0 732<br>
VecAYPX 2944 1.0 1.1377e+01 1.1 1.73e+09 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 610<br>VecAssemblyBegin 6 1.0 2.8596e-0223.6 0.00e+00 0.0 0.0e+00 0.0e+00 1.8e+01 0 0 0 0 0 0 0 0 0 0 0<br>
VecAssemblyEnd 6 1.0 2.4796e-05 1.4 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<br>VecPointwiseMult 2948 1.0 1.7210e+01 1.2 8.68e+08 1.0 0.0e+00 0.0e+00 0.0e+00 3 1 0 0 0 3 1 0 0 0 202<br>
VecScatterBegin 2947 1.0 1.9806e+00 2.4 0.00e+00 0.0 1.8e+04 2.7e+05 0.0e+00 0 0100100 0 0 0100100 0 0<br>VecScatterEnd 2947 1.0 4.3833e+01 7.4 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 6 0 0 0 0 6 0 0 0 0 0<br>
KSPSetup 1 1.0 2.1496e-02 1.6 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<br>KSPSolve 1 1.0 4.3931e+02 1.0 1.56e+11 1.1 1.8e+04 2.7e+05 4.4e+03 91100100100 99 91100100100 99 1386<br>
PCSetUp 1 1.0 3.0994e-06 1.6 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<br>PCApply 2948 1.0 1.7256e+01 1.2 8.68e+08 1.0 0.0e+00 0.0e+00 0.0e+00 3 1 0 0 0 3 1 0 0 0 201<br>
------------------------------------------------------------------------------------------------------------------------<br><br>Memory usage is given in bytes:<br><br>Object Type Creations Destructions Memory Descendants' Mem.<br>
Reports information only for process 0.<br><br>--- Event Stage 0: Main Stage<br><br> Matrix 3 3 169902696 0<br> Vec 18 18 31282096 0<br> Vec Scatter 2 2 1736 0<br>
Index Set 4 4 638616 0<br> Krylov Solver 1 1 832 0<br> Preconditioner 1 1 872 0<br> Viewer 1 1 544 0<br>
========================================================================================================================<br>Average time to get PetscTime(): 1.5974e-06<br>Average time for MPI_Barrier(): 3.48091e-05<br>Average time for zero size MPI_Send(): 1.8537e-05<br>
#PETSc Option Table entries:<br>-ksp_type bicg<br>-log_summary<br>-pc_type jacobi<br>#End of PETSc Option Table entries<br>Compiled without FORTRAN kernels<br>Compiled with full precision matrices (default)<br>sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 8<br>
Configure run at: Tue Nov 23 15:54:45 2010<br>Configure options: --known-level1-dcache-size=65536 --known-level1-dcache-linesize=64 --known-level1-dcache-assoc=2 --known-memcmp-ok=1 --known-sizeof-char=1 --known-sizeof-void-p=8 --known-sizeof-short=2 --known-sizeof-int=4 --known-sizeof-long=8 --known-sizeof-long-long=8 --known-sizeof-float=4 --known-sizeof-double=8 --known-sizeof-size_t=8 --known-bits-per-byte=8 --known-sizeof-MPI_Comm=4 --known-sizeof-MPI_Fint=4 --known-mpi-long-double=1 --with-cc=gcc --with-cxx=g++ --with-F77=ifort --with-FC=ifort --download-f-blas-lapack=1 --download-superlu-dist=1 --download-hypre=1 --download-trilinos=1 --download-parmetis=1 --download-mumps=1 --download-scalapack=1 --download-blacs=1 --download-mpich=1 --with-debugging=0 --with-batch --known-mpi-shared=1<br>
-----------------------------------------<br><br><br><br>----------------------<br>
(3) k=8<br>
----------------------<br>
Process 0 of total 8 on wmss04<br>Process 4 of total 8 on wmss04<br>Process 2 of total 8 on wmss04<br>Process 6 of total 8 on wmss04<br>Process 3 of total 8 on wmss04<br>Process 7 of total 8 on wmss04<br>Process 1 of total 8 on wmss04<br>
Process 5 of total 8 on wmss04<br>The dimension of Matrix A is n = 1177754<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>
End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>=========================================================<br>Begin the solving: <br>
=========================================================<br>The current time is: Mon Dec 20 18:14:59 2010<br><br>KSP Object:<br> type: bicg<br> maximum iterations=10000, initial guess is zero<br> tolerances: relative=1e-07, absolute=1e-50, divergence=10000<br>
left preconditioning<br> using PRECONDITIONED norm type for convergence test<br>PC Object:<br> type: jacobi<br> linear system matrix = precond matrix:<br> Matrix Object:<br> type=mpisbaij, rows=1177754, cols=1177754<br>
total: nonzeros=49908476, allocated nonzeros=49908476<br> block size is 1<br><br>norm(b-Ax)=1.32502e-06<br>Norm of error 1.32502e-06, Iterations 1473<br>=========================================================<br>
The solver has finished successfully! <br>=========================================================<br>The solving time is 311.937 seconds.<br>The time accuracy is 1e-06 second.<br>The current time is Mon Dec 20 18:20:11 2010<br>
<br>************************************************************************************************************************<br>*** WIDEN YOUR WINDOW TO 120 CHARACTERS. Use 'enscript -r -fCourier9' to print this document ***<br>
************************************************************************************************************************<br><br>---------------------------------------------- PETSc Performance Summary: ----------------------------------------------<br>
<br>./AMG_Solver_MPI on a linux-gnu named wmss04 with 8 processors, by cheny Mon Dec 20 19:20:11 2010<br>Using Petsc Release Version 3.1.0, Patch 5, Mon Sep 27 11:51:54 CDT 2010<br><br> Max Max/Min Avg Total <br>
Time (sec): 3.330e+02 1.00000 3.330e+02<br>Objects: 3.000e+01 1.00000 3.000e+01<br>Flops: 7.792e+10 1.09702 7.614e+10 6.091e+11<br>Flops/sec: 2.340e+08 1.09702 2.286e+08 1.829e+09<br>
MPI Messages: 5.906e+03 2.00017 5.169e+03 4.135e+04<br>MPI Message Lengths: 1.866e+09 4.61816 2.430e+05 1.005e+10<br>MPI Reductions: 4.477e+03 1.00000<br><br>Flop counting convention: 1 flop = 1 real number operation of type (multiply/divide/add/subtract)<br>
e.g., VecAXPY() for real vectors of length N --> 2N flops<br> and VecAXPY() for complex vectors of length N --> 8N flops<br><br>Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages --- -- Message Lengths -- -- Reductions --<br>
Avg %Total Avg %Total counts %Total Avg %Total counts %Total <br> 0: Main Stage: 3.3302e+02 100.0% 6.0914e+11 100.0% 4.135e+04 100.0% 2.430e+05 100.0% 4.461e+03 99.6% <br>
<br>------------------------------------------------------------------------------------------------------------------------<br>See the 'Profiling' chapter of the users' manual for details on interpreting output.<br>
Phase summary info:<br> Count: number of times phase was executed<br> Time and Flops: Max - maximum over all processors<br> Ratio - ratio of maximum to minimum over all processors<br> Mess: number of messages sent<br>
Avg. len: average message length<br> Reduct: number of global reductions<br> Global: entire computation<br> Stage: stages of a computation. Set stages with PetscLogStagePush() and PetscLogStagePop().<br> %T - percent time in this phase %F - percent flops in this phase<br>
%M - percent messages in this phase %L - percent message lengths in this phase<br> %R - percent reductions in this phase<br> Total Mflop/s: 10e-6 * (sum of flops over all processors)/(max time over all processors)<br>
------------------------------------------------------------------------------------------------------------------------<br>Event Count Time (sec) Flops --- Global --- --- Stage --- Total<br>
Max Ratio Max Ratio Max Ratio Mess Avg len Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s<br>------------------------------------------------------------------------------------------------------------------------<br>
<br>--- Event Stage 0: Main Stage<br><br>MatMult 1474 1.0 1.4230e+02 1.4 3.70e+10 1.1 2.1e+04 2.4e+05 0.0e+00 38 47 50 50 0 38 47 50 50 0 2031<br>MatMultTranspose 1473 1.0 1.3627e+02 1.1 3.70e+10 1.1 2.1e+04 2.4e+05 0.0e+00 38 47 50 50 0 38 47 50 50 0 2120<br>
MatAssemblyBegin 1 1.0 8.0800e-0324.5 0.00e+00 0.0 0.0e+00 0.0e+00 3.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>MatAssemblyEnd 1 1.0 5.3647e-02 1.0 0.00e+00 0.0 7.0e+01 8.5e+04 1.2e+01 0 0 0 0 0 0 0 0 0 0 0<br>
MatView 1 1.0 2.1791e-04 2.5 0.00e+00 0.0 0.0e+00 0.0e+00 1.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>VecView 1 1.0 1.0902e+0112.1 0.00e+00 0.0 1.4e+01 5.9e+05 0.0e+00 2 0 0 0 0 2 0 0 0 0 0<br>
VecDot 2946 1.0 3.5689e+01 7.6 8.67e+08 1.0 0.0e+00 0.0e+00 2.9e+03 6 1 0 0 66 6 1 0 0 66 194<br>VecNorm 1475 1.0 8.1093e+00 4.0 4.34e+08 1.0 0.0e+00 0.0e+00 1.5e+03 1 1 0 0 33 1 1 0 0 33 428<br>
VecCopy 4 1.0 5.2011e-03 1.3 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<br>VecSet 8843 1.0 3.0491e+00 2.2 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0<br>
VecAXPY 4420 1.0 9.2421e+00 1.6 1.30e+09 1.0 0.0e+00 0.0e+00 0.0e+00 2 2 0 0 0 2 2 0 0 0 1127<br>VecAYPX 2944 1.0 6.8297e+00 1.5 8.67e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 1015<br>
VecAssemblyBegin 6 1.0 2.6218e-0210.7 0.00e+00 0.0 0.0e+00 0.0e+00 1.8e+01 0 0 0 0 0 0 0 0 0 0 0<br>VecAssemblyEnd 6 1.0 3.6240e-05 1.3 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<br>
VecPointwiseMult 2948 1.0 9.6646e+00 1.4 4.34e+08 1.0 0.0e+00 0.0e+00 0.0e+00 3 1 0 0 0 3 1 0 0 0 359<br>VecScatterBegin 2947 1.0 2.2599e+00 2.3 0.00e+00 0.0 4.1e+04 2.4e+05 0.0e+00 1 0100100 0 1 0100100 0 0<br>
VecScatterEnd 2947 1.0 7.7004e+0120.2 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 9 0 0 0 0 9 0 0 0 0 0<br>KSPSetup 1 1.0 1.4287e-02 1.7 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<br>
KSPSolve 1 1.0 3.0090e+02 1.0 7.79e+10 1.1 4.1e+04 2.4e+05 4.4e+03 90100100100 99 90100100100 99 2024<br>PCSetUp 1 1.0 4.0531e-06 2.1 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<br>
PCApply 2948 1.0 9.7001e+00 1.4 4.34e+08 1.0 0.0e+00 0.0e+00 0.0e+00 3 1 0 0 0 3 1 0 0 0 358<br>------------------------------------------------------------------------------------------------------------------------<br>
<br>Memory usage is given in bytes:<br><br>Object Type Creations Destructions Memory Descendants' Mem.<br>Reports information only for process 0.<br><br>--- Event Stage 0: Main Stage<br><br> Matrix 3 3 84944064 0<br>
Vec 18 18 15741712 0<br> Vec Scatter 2 2 1736 0<br> Index Set 4 4 409008 0<br> Krylov Solver 1 1 832 0<br>
Preconditioner 1 1 872 0<br> Viewer 1 1 544 0<br>========================================================================================================================<br>
Average time to get PetscTime(): 3.38554e-06<br>Average time for MPI_Barrier(): 7.40051e-05<br>Average time for zero size MPI_Send(): 1.88947e-05<br>#PETSc Option Table entries:<br>-ksp_type bicg<br>-log_summary<br>-pc_type jacobi<br>
#End of PETSc Option Table entries<br>Compiled without FORTRAN kernels<br>Compiled with full precision matrices (default)<br>sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 8<br>Configure run at: Tue Nov 23 15:54:45 2010<br>
Configure options: --known-level1-dcache-size=65536 --known-level1-dcache-linesize=64 --known-level1-dcache-assoc=2 --known-memcmp-ok=1 --known-sizeof-char=1 --known-sizeof-void-p=8 --known-sizeof-short=2 --known-sizeof-int=4 --known-sizeof-long=8 --known-sizeof-long-long=8 --known-sizeof-float=4 --known-sizeof-double=8 --known-sizeof-size_t=8 --known-bits-per-byte=8 --known-sizeof-MPI_Comm=4 --known-sizeof-MPI_Fint=4 --known-mpi-long-double=1 --with-cc=gcc --with-cxx=g++ --with-F77=ifort --with-FC=ifort --download-f-blas-lapack=1 --download-superlu-dist=1 --download-hypre=1 --download-trilinos=1 --download-parmetis=1 --download-mumps=1 --download-scalapack=1 --download-blacs=1 --download-mpich=1 --with-debugging=0 --with-batch --known-mpi-shared=1<br>
-----------------------------------------<br><br><br><br>----------------------<br>
(4) k=12 <br>
----------------------<br>
Process 1 of total 12 on wmss04<br>Process 5 of total 12 on wmss04<br>Process 2 of total 12 on wmss04<br>Process 9 of total 12 on wmss04<br>Process 6 of total 12 on wmss04<br>Process 7 of total 12 on wmss04<br>Process 10 of total 12 on wmss04<br>
Process 3 of total 12 on wmss04<br>Process 11 of total 12 on wmss04<br>Process 4 of total 12 on wmss04<br>Process 8 of total 12 on wmss04<br>Process 0 of total 12 on wmss04<br>The dimension of Matrix A is n = 1177754<br>Begin Assembly:<br>
Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>End Assembly.<br>
End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.End Assembly.<br>End Assembly.<br>End Assembly.<br><br>End Assembly.<br>End Assembly.<br>=========================================================<br>
Begin the solving: <br>=========================================================<br>The current time is: Mon Dec 20 17:56:36 2010<br><br>KSP Object:<br> type: bicg<br> maximum iterations=10000, initial guess is zero<br>
tolerances: relative=1e-07, absolute=1e-50, divergence=10000<br> left preconditioning<br> using PRECONDITIONED norm type for convergence test<br>PC Object:<br> type: jacobi<br> linear system matrix = precond matrix:<br>
Matrix Object:<br> type=mpisbaij, rows=1177754, cols=1177754<br> total: nonzeros=49908476, allocated nonzeros=49908476<br> block size is 1<br><br>norm(b-Ax)=1.28414e-06<br>Norm of error 1.28414e-06, Iterations 1473<br>
=========================================================<br>The solver has finished successfully! <br>=========================================================<br>The solving time is 291.503 seconds.<br>
The time accuracy is 1e-06 second.<br>The current time is Mon Dec 20 18:01:28 2010<br><br>************************************************************************************************************************<br>*** WIDEN YOUR WINDOW TO 120 CHARACTERS. Use 'enscript -r -fCourier9' to print this document ***<br>
************************************************************************************************************************<br><br>---------------------------------------------- PETSc Performance Summary: ----------------------------------------------<br>
<br>./AMG_Solver_MPI on a linux-gnu named wmss04 with 12 processors, by cheny Mon Dec 20 19:01:28 2010<br>Using Petsc Release Version 3.1.0, Patch 5, Mon Sep 27 11:51:54 CDT 2010<br><br> Max Max/Min Avg Total <br>
Time (sec): 3.089e+02 1.00012 3.089e+02<br>Objects: 3.000e+01 1.00000 3.000e+01<br>Flops: 5.197e+10 1.11689 5.074e+10 6.089e+11<br>Flops/sec: 1.683e+08 1.11689 1.643e+08 1.971e+09<br>
MPI Messages: 5.906e+03 2.00017 5.415e+03 6.498e+04<br>MPI Message Lengths: 1.887e+09 6.23794 2.345e+05 1.524e+10<br>MPI Reductions: 4.477e+03 1.00000<br><br>Flop counting convention: 1 flop = 1 real number operation of type (multiply/divide/add/subtract)<br>
e.g., VecAXPY() for real vectors of length N --> 2N flops<br> and VecAXPY() for complex vectors of length N --> 8N flops<br><br>Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages --- -- Message Lengths -- -- Reductions --<br>
Avg %Total Avg %Total counts %Total Avg %Total counts %Total <br> 0: Main Stage: 3.0887e+02 100.0% 6.0890e+11 100.0% 6.498e+04 100.0% 2.345e+05 100.0% 4.461e+03 99.6% <br>
<br>------------------------------------------------------------------------------------------------------------------------<br>See the 'Profiling' chapter of the users' manual for details on interpreting output.<br>
Phase summary info:<br> Count: number of times phase was executed<br> Time and Flops: Max - maximum over all processors<br> Ratio - ratio of maximum to minimum over all processors<br> Mess: number of messages sent<br>
Avg. len: average message length<br> Reduct: number of global reductions<br> Global: entire computation<br> Stage: stages of a computation. Set stages with PetscLogStagePush() and PetscLogStagePop().<br> %T - percent time in this phase %F - percent flops in this phase<br>
%M - percent messages in this phase %L - percent message lengths in this phase<br> %R - percent reductions in this phase<br> Total Mflop/s: 10e-6 * (sum of flops over all processors)/(max time over all processors)<br>
------------------------------------------------------------------------------------------------------------------------<br>Event Count Time (sec) Flops --- Global --- --- Stage --- Total<br>
Max Ratio Max Ratio Max Ratio Mess Avg len Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s<br>------------------------------------------------------------------------------------------------------------------------<br>
<br>--- Event Stage 0: Main Stage<br><br>MatMult 1474 1.0 1.4069e+02 2.1 2.47e+10 1.1 3.2e+04 2.3e+05 0.0e+00 35 47 50 50 0 35 47 50 50 0 2054<br>MatMultTranspose 1473 1.0 1.3272e+02 1.8 2.47e+10 1.1 3.2e+04 2.3e+05 0.0e+00 34 47 50 50 0 34 47 50 50 0 2175<br>
MatAssemblyBegin 1 1.0 6.4070e-0314.6 0.00e+00 0.0 0.0e+00 0.0e+00 3.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>MatAssemblyEnd 1 1.0 6.2698e-02 1.0 0.00e+00 0.0 1.1e+02 8.2e+04 1.2e+01 0 0 0 0 0 0 0 0 0 0 0<br>
MatView 1 1.0 2.4605e-04 2.3 0.00e+00 0.0 0.0e+00 0.0e+00 1.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>VecView 1 1.0 1.1164e+0182.6 0.00e+00 0.0 2.2e+01 3.9e+05 0.0e+00 2 0 0 0 0 2 0 0 0 0 0<br>
VecDot 2946 1.0 1.1499e+0234.8 5.78e+08 1.0 0.0e+00 0.0e+00 2.9e+03 13 1 0 0 66 13 1 0 0 66 60<br>VecNorm 1475 1.0 1.0804e+01 7.7 2.90e+08 1.0 0.0e+00 0.0e+00 1.5e+03 2 1 0 0 33 2 1 0 0 33 322<br>
VecCopy 4 1.0 6.9451e-03 2.2 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<br>VecSet 8843 1.0 2.9336e+00 2.6 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0<br>
VecAXPY 4420 1.0 1.0803e+01 2.3 8.68e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 2 0 0 0 2 2 0 0 0 964<br>VecAYPX 2944 1.0 6.6637e+00 2.1 5.78e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 1041<br>
VecAssemblyBegin 6 1.0 3.7719e-0214.7 0.00e+00 0.0 0.0e+00 0.0e+00 1.8e+01 0 0 0 0 0 0 0 0 0 0 0<br>VecAssemblyEnd 6 1.0 5.3883e-05 1.7 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<br>
VecPointwiseMult 2948 1.0 8.7972e+00 2.3 2.89e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 395<br>VecScatterBegin 2947 1.0 3.3624e+00 4.3 0.00e+00 0.0 6.5e+04 2.3e+05 0.0e+00 1 0100100 0 1 0100100 0 0<br>
VecScatterEnd 2947 1.0 8.0508e+0119.1 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 12 0 0 0 0 12 0 0 0 0 0<br>KSPSetup 1 1.0 1.1752e-02 1.7 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<br>
KSPSolve 1 1.0 2.8016e+02 1.0 5.20e+10 1.1 6.5e+04 2.3e+05 4.4e+03 91100100100 99 91100100100 99 2173<br>PCSetUp 1 1.0 5.9605e-06 2.1 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<br>
PCApply 2948 1.0 8.8313e+00 2.3 2.89e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 393<br>------------------------------------------------------------------------------------------------------------------------<br>
<br>Memory usage is given in bytes:<br><br>Object Type Creations Destructions Memory Descendants' Mem.<br>Reports information only for process 0.<br><br>--- Event Stage 0: Main Stage<br><br> Matrix 3 3 56593044 0<br>
Vec 18 18 10534536 0<br> Vec Scatter 2 2 1736 0<br> Index Set 4 4 305424 0<br> Krylov Solver 1 1 832 0<br>
Preconditioner 1 1 872 0<br> Viewer 1 1 544 0<br>========================================================================================================================<br>
Average time to get PetscTime(): 6.48499e-06<br>Average time for MPI_Barrier(): 0.000102377<br>Average time for zero size MPI_Send(): 2.15967e-05<br>#PETSc Option Table entries:<br>-ksp_type bicg<br>-log_summary<br>-pc_type jacobi<br>
#End of PETSc Option Table entries<br>Compiled without FORTRAN kernels<br>Compiled with full precision matrices (default)<br>sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 8<br>Configure run at: Tue Nov 23 15:54:45 2010<br>
Configure options: --known-level1-dcache-size=65536 --known-level1-dcache-linesize=64 --known-level1-dcache-assoc=2 --known-memcmp-ok=1 --known-sizeof-char=1 --known-sizeof-void-p=8 --known-sizeof-short=2 --known-sizeof-int=4 --known-sizeof-long=8 --known-sizeof-long-long=8 --known-sizeof-float=4 --known-sizeof-double=8 --known-sizeof-size_t=8 --known-bits-per-byte=8 --known-sizeof-MPI_Comm=4 --known-sizeof-MPI_Fint=4 --known-mpi-long-double=1 --with-cc=gcc --with-cxx=g++ --with-F77=ifort --with-FC=ifort --download-f-blas-lapack=1 --download-superlu-dist=1 --download-hypre=1 --download-trilinos=1 --download-parmetis=1 --download-mumps=1 --download-scalapack=1 --download-blacs=1 --download-mpich=1 --with-debugging=0 --with-batch --known-mpi-shared=1<br>
-----------------------------------------<br><br><br>----------------------<br>
(5) k=16 <br>
----------------------<br>Process 0 of total 16 on wmss04<br>Process 8 of total 16 on wmss04<br>Process 4 of total 16 on wmss04<br>Process 12 of total 16 on wmss04<br>Process 2 of total 16 on wmss04<br>Process 6 of total 16 on wmss04<br>
Process 5 of total 16 on wmss04<br>Process 11 of total 16 on wmss04<br>Process 14 of total 16 on wmss04<br>Process 7 of total 16 on wmss04<br>Process Process 15 of total 16 on wmss04<br>3Process 13 of total 16 on wmss04<br>
Process 10 of total 16 on wmss04<br>Process 9 of total 16 on wmss04<br>Process 1 of total 16 on wmss04<br>The dimension of Matrix A is n = 1177754<br> of total 16 on wmss04<br><br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>
Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br><br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br><br>Begin Assembly:<br>Begin Assembly:<br>Begin Assembly:<br><br>
Begin Assembly:<br>Begin Assembly:<br>End Assembly.<br>End Assembly.End Assembly.<br>End Assembly.End Assembly.End Assembly.End Assembly.<br>End Assembly.<br>End Assembly.<br>End Assembly.End Assembly.<br><br>End Assembly.<br>
End Assembly.<br>End Assembly.<br>End Assembly.End Assembly.<br><br><br><br>=========================================================<br>Begin the solving: <br>=========================================================<br>
The current time is: Mon Dec 20 18:02:28 2010<br><br>KSP Object:<br> type: bicg<br> maximum iterations=10000, initial guess is zero<br> tolerances: relative=1e-07, absolute=1e-50, divergence=10000<br> left preconditioning<br>
using PRECONDITIONED norm type for convergence test<br>PC Object:<br> type: jacobi<br> linear system matrix = precond matrix:<br> Matrix Object:<br> type=mpisbaij, rows=1177754, cols=1177754<br> total: nonzeros=49908476, allocated nonzeros=49908476<br>
block size is 1<br><br>norm(b-Ax)=1.15892e-06<br>Norm of error 1.15892e-06, Iterations 1497<br>=========================================================<br>The solver has finished successfully! <br>
=========================================================<br>The solving time is 337.91 seconds.<br>The time accuracy is 1e-06 second.<br>The current time is Mon Dec 20 18:08:06 2010<br><br>************************************************************************************************************************<br>
*** WIDEN YOUR WINDOW TO 120 CHARACTERS. Use 'enscript -r -fCourier9' to print this document ***<br>************************************************************************************************************************<br>
<br>---------------------------------------------- PETSc Performance Summary: ----------------------------------------------<br><br>./AMG_Solver_MPI on a linux-gnu named wmss04 with 16 processors, by cheny Mon Dec 20 19:08:06 2010<br>
Using Petsc Release Version 3.1.0, Patch 5, Mon Sep 27 11:51:54 CDT 2010<br><br> Max Max/Min Avg Total <br>Time (sec): 3.534e+02 1.00001 3.534e+02<br>Objects: 3.000e+01 1.00000 3.000e+01<br>
Flops: 3.964e+10 1.13060 3.864e+10 6.182e+11<br>Flops/sec: 1.122e+08 1.13060 1.093e+08 1.749e+09<br>MPI Messages: 1.200e+04 3.99917 7.127e+03 1.140e+05<br>MPI Message Lengths: 1.950e+09 7.80999 1.819e+05 2.074e+10<br>
MPI Reductions: 4.549e+03 1.00000<br><br>Flop counting convention: 1 flop = 1 real number operation of type (multiply/divide/add/subtract)<br> e.g., VecAXPY() for real vectors of length N --> 2N flops<br>
and VecAXPY() for complex vectors of length N --> 8N flops<br><br>Summary of Stages: ----- Time ------ ----- Flops ----- --- Messages --- -- Message Lengths -- -- Reductions --<br> Avg %Total Avg %Total counts %Total Avg %Total counts %Total <br>
0: Main Stage: 3.5342e+02 100.0% 6.1820e+11 100.0% 1.140e+05 100.0% 1.819e+05 100.0% 4.533e+03 99.6% <br><br>------------------------------------------------------------------------------------------------------------------------<br>
See the 'Profiling' chapter of the users' manual for details on interpreting output.<br>Phase summary info:<br> Count: number of times phase was executed<br> Time and Flops: Max - maximum over all processors<br>
Ratio - ratio of maximum to minimum over all processors<br> Mess: number of messages sent<br> Avg. len: average message length<br> Reduct: number of global reductions<br> Global: entire computation<br>
Stage: stages of a computation. Set stages with PetscLogStagePush() and PetscLogStagePop().<br> %T - percent time in this phase %F - percent flops in this phase<br> %M - percent messages in this phase %L - percent message lengths in this phase<br>
%R - percent reductions in this phase<br> Total Mflop/s: 10e-6 * (sum of flops over all processors)/(max time over all processors)<br>------------------------------------------------------------------------------------------------------------------------<br>
Event Count Time (sec) Flops --- Global --- --- Stage --- Total<br> Max Ratio Max Ratio Max Ratio Mess Avg len Reduct %T %F %M %L %R %T %F %M %L %R Mflop/s<br>
------------------------------------------------------------------------------------------------------------------------<br><br>--- Event Stage 0: Main Stage<br><br>MatMult 1498 1.0 1.8860e+02 1.7 1.88e+10 1.1 5.7e+04 1.8e+05 0.0e+00 40 47 50 50 0 40 47 50 50 0 1555<br>
MatMultTranspose 1497 1.0 1.4165e+02 1.3 1.88e+10 1.1 5.7e+04 1.8e+05 0.0e+00 35 47 50 50 0 35 47 50 50 0 2069<br>MatAssemblyBegin 1 1.0 1.0044e-0217.1 0.00e+00 0.0 0.0e+00 0.0e+00 3.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>
MatAssemblyEnd 1 1.0 7.3835e-02 1.0 0.00e+00 0.0 1.8e+02 6.7e+04 1.2e+01 0 0 0 0 0 0 0 0 0 0 0<br>MatView 1 1.0 2.6107e-04 2.0 0.00e+00 0.0 0.0e+00 0.0e+00 1.0e+00 0 0 0 0 0 0 0 0 0 0 0<br>
VecView 1 1.0 1.1282e+01109.0 0.00e+00 0.0 3.0e+01 2.9e+05 0.0e+00 2 0 0 0 0 2 0 0 0 0 0<br>VecDot 2994 1.0 6.7490e+0119.6 4.41e+08 1.0 0.0e+00 0.0e+00 3.0e+03 10 1 0 0 66 10 1 0 0 66 104<br>
VecNorm 1499 1.0 1.3431e+0110.8 2.21e+08 1.0 0.0e+00 0.0e+00 1.5e+03 2 1 0 0 33 2 1 0 0 33 263<br>VecCopy 4 1.0 7.3178e-03 2.6 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<br>
VecSet 8987 1.0 3.1772e+00 3.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 1 0 0 0 0 1 0 0 0 0 0<br>VecAXPY 4492 1.0 1.1361e+01 3.1 6.61e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 2 0 0 0 2 2 0 0 0 931<br>
VecAYPX 2992 1.0 7.3248e+00 2.5 4.40e+08 1.0 0.0e+00 0.0e+00 0.0e+00 1 1 0 0 0 1 1 0 0 0 962<br>VecAssemblyBegin 6 1.0 3.6338e-0212.1 0.00e+00 0.0 0.0e+00 0.0e+00 1.8e+01 0 0 0 0 0 0 0 0 0 0 0<br>
VecAssemblyEnd 6 1.0 7.2002e-05 1.4 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<br>VecPointwiseMult 2996 1.0 9.7892e+00 2.4 2.21e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 360<br>
VecScatterBegin 2995 1.0 4.0570e+00 5.5 0.00e+00 0.0 1.1e+05 1.8e+05 0.0e+00 1 0100100 0 1 0100100 0 0<br>VecScatterEnd 2995 1.0 1.7309e+0251.3 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 22 0 0 0 0 22 0 0 0 0 0<br>
KSPSetup 1 1.0 1.3058e-02 2.2 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<br>KSPSolve 1 1.0 3.2641e+02 1.0 3.96e+10 1.1 1.1e+05 1.8e+05 4.5e+03 92100100100 99 92100100100 99 1893<br>
PCSetUp 1 1.0 8.1062e-06 1.6 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<br>PCApply 2996 1.0 9.8336e+00 2.4 2.21e+08 1.0 0.0e+00 0.0e+00 0.0e+00 2 1 0 0 0 2 1 0 0 0 359<br>
------------------------------------------------------------------------------------------------------------------------<br><br>Memory usage is given in bytes:<br><br>Object Type Creations Destructions Memory Descendants' Mem.<br>
Reports information only for process 0.<br><br>--- Event Stage 0: Main Stage<br><br> Matrix 3 3 42424600 0<br> Vec 18 18 7924896 0<br> Vec Scatter 2 2 1736 0<br>
Index Set 4 4 247632 0<br> Krylov Solver 1 1 832 0<br> Preconditioner 1 1 872 0<br> Viewer 1 1 544 0<br>
========================================================================================================================<br>Average time to get PetscTime(): 6.10352e-06<br>Average time for MPI_Barrier(): 0.000129986<br>Average time for zero size MPI_Send(): 2.08169e-05<br>
#PETSc Option Table entries:<br>-ksp_type bicg<br>-log_summary<br>-pc_type jacobi<br>#End of PETSc Option Table entries<br>Compiled without FORTRAN kernels<br>Compiled with full precision matrices (default)<br>sizeof(short) 2 sizeof(int) 4 sizeof(long) 8 sizeof(void*) 8 sizeof(PetscScalar) 8<br>
Configure run at: Tue Nov 23 15:54:45 2010<br>Configure options: --known-level1-dcache-size=65536 --known-level1-dcache-linesize=64 --known-level1-dcache-assoc=2 --known-memcmp-ok=1 --known-sizeof-char=1 --known-sizeof-void-p=8 --known-sizeof-short=2 --known-sizeof-int=4 --known-sizeof-long=8 --known-sizeof-long-long=8 --known-sizeof-float=4 --known-sizeof-double=8 --known-sizeof-size_t=8 --known-bits-per-byte=8 --known-sizeof-MPI_Comm=4 --known-sizeof-MPI_Fint=4 --known-mpi-long-double=1 --with-cc=gcc --with-cxx=g++ --with-F77=ifort --with-FC=ifort --download-f-blas-lapack=1 --download-superlu-dist=1 --download-hypre=1 --download-trilinos=1 --download-parmetis=1 --download-mumps=1 --download-scalapack=1 --download-blacs=1 --download-mpich=1 --with-debugging=0 --with-batch --known-mpi-shared=1<br>
-----------------------------------------<br><br><br><br><br><div class="gmail_quote">On Mon, Dec 20, 2010 at 6:06 PM, Matthew Knepley <span dir="ltr"><<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;"><div class="im">On Mon, Dec 20, 2010 at 8:46 AM, Yongjun Chen <span dir="ltr"><<a href="mailto:yjxd.chen@gmail.com" target="_blank">yjxd.chen@gmail.com</a>></span> wrote:<br>
</div><div class="gmail_quote"><div class="im"><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
<br>
<p class="MsoNormal"><span lang="DE">Hi everyone,</span></p><p class="MsoNormal"><span lang="DE"><br></span></p>
<p class="MsoNormal"><span lang="DE">I use PETSC
(version 3.1-p5) to solve a linear problem Ax=b. The matrix A and right hand
vector b are read from files. The dimension of A is 1.2Million*1.2Million. I am
pretty sure the matrix A and vector b have been read correctly. </span></p>
<p class="MsoNormal"><span lang="DE">I compiled the
program with optimized version (--with-debugging=0), tested the speed up
performance on two servers, and I have found that the performance is very poor.</span></p>
<p class="MsoNormal"><span lang="DE">For the two
servers, one is 4 cpus * 4 cores per cpu, i.e., with a total 16 cores. And the
other one is 4 cpus * 12 cores per cpu, with a total 48 cores.</span></p>
<p class="MsoNormal"><span lang="DE">On each of them, with
the increasing of computing cores k from 1 to 8 (mpiexec –n k ./Solver_MPI -pc_type jacobi -ksp-type gmres), the speed
up will increase from 1 to 6, but when the computing cores k increase from 9 to
16(for the first server) or 48 (for the second server), the speed up decrease firstly
and then remains a constant value 5.0 (for the first server) or 4.5(for the second
server).</span></p></blockquote><div><br></div></div><div>We cannot say anything at all without -log_summary data for your runs.</div><div><br></div><div> Matt</div><div class="im"><div> </div><blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE">Actually, the
program LAMMPS speed up excellently on these two servers.</span></p>
<p class="MsoNormal"><span lang="DE">Any comments are
very appreciated! Thanks!<br></span></p>
<p class="MsoNormal"><span lang="DE"> </span></p><p class="MsoNormal"><span lang="DE">--------------------------------------------------------------------------------------------------------------------------<br>
</span></p>
<p class="MsoNormal"><span lang="DE">PS: the related
codes are as following,</span></p>
<p class="MsoNormal"><span lang="DE"><br></span></p><p class="MsoNormal"><span lang="DE">//firstly read A and b from
files</span></p>
<p class="MsoNormal"><span lang="DE">...</span></p><p class="MsoNormal"><span lang="DE">//then<br></span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = VecAssemblyBegin(b); CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = VecAssemblyEnd(b); CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE); CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = MatGetRowUpperTriangular(A); CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr =
KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = KSPGetSolution(ksp, &x);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = VecAssemblyBegin(x);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE"><span> </span><span>
</span>ierr = VecAssemblyEnd(x);CHKERRQ(ierr);</span></p>
<p class="MsoNormal"><span lang="DE">...</span></p>
<p class="MsoNormal"><span lang="DE"> </span></p>
<br>
</blockquote></div></div><font color="#888888"><br><br clear="all"><br>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<br>
</font></blockquote></div><br><br clear="all"><br>-- <br>Dr.Yongjun Chen<br>Room 2507, Building M<br>Institute of Materials Science and Technology<br>Technical University of Hamburg-Harburg<br>Eißendorfer Straße 42, 21073 Hamburg, Germany.<br>
Tel: +49 (0)40-42878-4386<br>Fax: +49 (0)40-42878-4070<br>E-mail: <a href="mailto:yjxd.chen@gmail.com">yjxd.chen@gmail.com</a><br><br>