Okay, I did a similar benchmark now with PETSc's event logging: UMFPACK 16p: Local solve 350 1.0 2.3025e+01 1.1 5.00e+04 1.0 0.0e+00 0.0e+00 7.0e+02 63 0 0 0 52 63 0 0 0 51 0 64p: Local solve 350 1.0 2.3208e+01 1.1 5.00e+04 1.0 0.0e+00 0.0e+00 7.0e+02 60 0 0 0 52 60 0 0 0 51 0 256p: Local solve 350 1.0 2.3373e+01 1.1 5.00e+04 1.0 0.0e+00 0.0e+00 7.0e+02 49 0 0 0 52 49 0 0 0 51 1
MUMPS 16p: Local solve 350 1.0 4.7183e+01 1.1 5.00e+04 1.0 0.0e+00 0.0e+00 7.0e+02 75 0 0 0 52 75 0 0 0 51 0 64p: Local solve 350 1.0 7.1409e+01 1.1 5.00e+04 1.0 0.0e+00 0.0e+00 7.0e+02 78 0 0 0 52 78 0 0 0 51 0 256p: Local solve 350 1.0 2.6079e+02 1.1 5.00e+04 1.0 0.0e+00 0.0e+00 7.0e+02 82 0 0 0 52 82 0 0 0 51 0 As you see, the local solves with UMFPACK have nearly constant time with increasing number of subdomains. This is what I expect. The I replace UMFPACK by MUMPS and I see increasing time for local solves. In the last columns, UMFPACK has a decreasing value from 63 to 49, while MUMPS's column increases here from 75 to 82. What does this mean? Thomas Am 21.12.2012 02:19, schrieb Matthew Knepley: > On Thu, Dec 20, 2012 at 3:39 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: > You misunderstand how to use logging. You just put these thing in > separate stages. Stages represent > parts of the code over which events are aggregated. > > Matt > >> 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 >>> >>> >> > > > -- > What most experimenters take for granted before they begin their > experiments is infinitely more interesting than any results to which > their experiments lead. > -- Norbert Wiener
