[petsc-users] approaches to reduce computing time
Roc Wang
pengxwang at hotmail.com
Tue Nov 12 14:14:47 CST 2013
Thanks Jed,
I have questions about load balance and PC type below.
> From: jedbrown at mcs.anl.gov
> To: pengxwang at hotmail.com; petsc-users at mcs.anl.gov
> Subject: Re: [petsc-users] approaches to reduce computing time
> Date: Sun, 10 Nov 2013 12:20:18 -0700
>
> Roc Wang <pengxwang at hotmail.com> writes:
>
> > Hi all,
> >
> > I am trying to minimize the computing time to solve a large sparse matrix. The matrix dimension is with m=321 n=321 and p=321. I am trying to reduce the computing time from two directions: 1 finding a Pre-conditioner to reduce the number of iterations which reduces the time numerically, 2 requesting more cores.
> >
> > ----For the first method, I tried several methods:
> > 1 default KSP and PC,
> > 2 -ksp_type fgmres -ksp_gmres_restart 30 -pc_type ksp -ksp_pc_type jacobi,
> > 3 -ksp_type lgmres -ksp_gmres_restart 40 -ksp_lgmres_augment 10,
> > 4 -ksp_type lgmres -ksp_gmres_restart 50 -ksp_lgmres_augment 10,
> > 5 -ksp_type lgmres -ksp_gmres_restart 40 -ksp_lgmres_augment 10 -pc_type asm (PCASM)
> >
> > The iterations and timing is like the following with 128 cores requested:
> > case# iter timing (s)
> > 1 1436 816
> > 2 3 12658
> > 3 1069 669.64
> > 4 872 768.12
> > 5 927 513.14
> >
> > It can be seen that change -ksp_gmres_restart and -ksp_lgmres_augment can help to reduce the iterations but not the timing (comparing case 3 and 4). Second, the PCASM helps a lot. Although the second option is able to reduce iterations, the timing increases very much. Is it because more operations are needed in the PC?
> >
> > My questions here are: 1. Which direction should I take to select
> > -ksp_gmres_restart and -ksp_lgmres_augment? For example, if larger
> > restart with large augment is better or larger restart with smaller
> > augment is better?
>
> Look at the -log_summary. By increasing the restart, the work in
> KSPGMRESOrthog will increase linearly, but the number of iterations
> might decrease enough to compensate. There is no general rule here
> since it depends on the relative expense of operations for your problem
> on your machine.
>
> > ----For the second method, I tried with -ksp_type lgmres -ksp_gmres_restart 40 -ksp_lgmres_augment 10 -pc_type asm with different number of cores. I found the speedup ratio increases slowly when more than 32 to 64 cores are requested. I searched the milling list archives and found that I am very likely running into the memory bandwidth bottleneck. http://www.mail-archive.com/petsc-users@mcs.anl.gov/msg19152.html:
> >
> > # of cores iter timing
> > 1 923 19541.83
> > 4 929 5897.06
> > 8 932 4854.72
> > 16 924 1494.33
> > 32 924 1480.88
> > 64 928 686.89
> > 128 927 627.33
> > 256 926 552.93
>
> The bandwidth issue has more to do with using multiple cores within a
> node rather than between nodes. Likely the above is a load balancing
> problem or bad communication.
I use DM to manage the distributed data. The DM was created by calling DMDACreate3d() and let PETSc decide the local number of nodes in each direction. To my understand the load of each core is determined at this stage. If the load balance is done when DMDACreate3d() is called and use PETSC_DECIDE option? Or how should make the load balanced after DM is created?
>
> > My question here is: Is there any other PC can help on both reducing iterations and increasing scalability? Thanks.
>
> Always send -log_summary with questions like this, but algebraic multigrid is a good place to start.
Please take a look at the attached log file, they are for 128 cores and 256 cores, respectively. Based on the log files, what should be done to increase the scalability? Thanks.
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