[petsc-users] How to investigate the reason for slow convergence rate?

Sun Jul 22 07:16:07 CDT 2012

Please send -log_summary output with performance questions.

On Sun, Jul 22, 2012 at 4:01 AM, Bao Kai <paeanball at gmail.com> wrote:

> Hi, Matt,
>
> I tried ML6.2 with petsc3.3 with default parameters by only specifying
> the preconditioner to be PCML.  The KSP solver is gmres.
>
> The convergence rate is much faster, while it still took much longer
> time in total.
>
> For example, for the problem with 500^3 mesh ( 125 million unknowns )
> with 512nodes(4 processors per node) on bluegene/P , it tooks about
> ten iterations to get convergent while the total time used is about
> 400 seconds.
>
>     506   the KSP type is gmres
>     507   the PC type is ml
>     508  KSP rtol =  0.100000000000000008E-04  abstol =
> 0.100000000000000001E-49  dtol =  10000.0000000000000  maxit =  10000
>     509  SNES rtol =  0.100000000000000002E-07  abstol =
> 0.100000000000000001E-49  stol =  0.100000000000000002E-07  maxit =
> 50  maxf=  10000
>     510   0 SNES Function norm 5.859593121800e+02
>     511     0 KSP Residual norm 8.340827070202e+06
>     512     1 KSP Residual norm 7.980806572332e+05
>     513     2 KSP Residual norm 1.870896731234e+05
>     514     3 KSP Residual norm 6.790580947452e+04
>     515     4 KSP Residual norm 2.665552335248e+04
>     516     5 KSP Residual norm 1.130212349885e+04
>     517     6 KSP Residual norm 4.053599972292e+03
>     518     7 KSP Residual norm 1.786770710693e+03
>     519     8 KSP Residual norm 7.313571654931e+02
>     520     9 KSP Residual norm 3.205683714450e+02
>     521    10 KSP Residual norm 1.263243312734e+02
>     522    11 KSP Residual norm 3.945082815178e+01
>     523   1 SNES Function norm 9.378772067642e-02
>     524     0 KSP Residual norm 5.413489711800e+01
>     525     1 KSP Residual norm 1.442598710609e+01
>     526     2 KSP Residual norm 4.073537172140e+00
>     527     3 KSP Residual norm 1.157455598705e+00
>     528     4 KSP Residual norm 3.509855901968e-01
>     529     5 KSP Residual norm 1.160625342728e-01
>     530     6 KSP Residual norm 3.209351890216e-02
>     531     7 KSP Residual norm 7.780869881329e-03
>     532     8 KSP Residual norm 1.820828886636e-03
>     533     9 KSP Residual norm 4.172544590190e-04
>     534   2 SNES Function norm 6.747963806680e-07
>     535  Number of KSP iteration is  9
>     536  SNES solve takes time  406.724867261176314
>
> But with bcgs and bjacobi, it tooks about 550 KSP iterations ( 2 snes
> iterations ) and 69 seconds to get the result.
>
> For much smaller problems, benefiting from the fast convergence, it
> did takes less time to get the result. It seems that the ml can not be
> scaled, or I used it in a wrong way.
>
> Best Regards,
> Kai
>
>
> > Message: 2
> > Date: Sat, 21 Jul 2012 08:47:10 -0500
> > From: Matthew Knepley <knepley at gmail.com>
> > To: PETSc users list <petsc-users at mcs.anl.gov>
> > Subject: Re: [petsc-users] How to investigate the reason for slow
> >       convergence rate?
> > Message-ID:
> >       <
> CAMYG4GkfV6kmTFEKXUadOv+2CrKHk9hRY7UR-cFWf+vcRxCv5g at mail.gmail.com>
> > Content-Type: text/plain; charset="iso-8859-1"
> >
> > On Sat, Jul 21, 2012 at 4:30 AM, Bao Kai <paeanball at gmail.com> wrote:
> >
> >>
> >>> HI, all,
> >>
> >> I am still suffering from the slow convergence rate of the KSP solution.
> >>
> >> I changed the code to use Petsc3.3 and then try the gamg precoditioner,
> >> the convergence rate is better, while it took more total time because it
> >> took much more time for each iteration and some extra time for
> >> pre-processing.
> >>
> >
> > Try ML to see if it has better defaults for your problem. If not, you
> will
> > have to start experimenting with the solver
> > parameters.
> >
> >
> >> I am wondering if there are some ways that can help me to investigate
> the
> >> slow convergence rate for KSP solution so that I can do some
> improvement.
> >>  Is DMMG will be a good solution?
> >>
> >
> > No.
> >
> >     Matt
> >
> >
> >> Thank you very much.
> >>
> >> Best Regards,
> >> Kai
> >>
> >>>
> >>> Message: 2
> >>> Date: Wed, 11 Jul 2012 15:17:15 -0500
> >>> From: Matthew Knepley <knepley at gmail.com>
> >>> To: PETSc users list <petsc-users at mcs.anl.gov>
> >>> Subject: Re: [petsc-users] Does this mean the matrix is
> >>>         ill-conditioned?
> >>> Message-ID:
> >>>         <CAMYG4Gk7T=
> >>> q+w1PKO7G_TW07iDzux90Sncbv9K7d0FD-MDrLRg at mail.gmail.com>
> >>> Content-Type: text/plain; charset="iso-8859-1"
> >>>
> >>> On Wed, Jul 11, 2012 at 12:40 PM, Bao Kai <paeanball at gmail.com> wrote:
> >>>
> >>> > Hi, all,
> >>> >
> >>> > The following is the output from the solution of a Poisson equation
> >>> > from Darcy's law.
> >>> >
> >>> > To compute the condition number of matrix, I did not use PC and use
> >>> > GMRES KSP to do the test.
> >>> >
> >>> > It seems like that the condition number keep increasing during the
> >>> > iterative solution. Does this mean the matrix is ill-conditioned?
> >>> >
> >>>
> >>> Generally yes. Krylov methods take a long time to resolve the smallest
> >>> eigenvalues, so this approximation is not great.
> >>>
> >>>
> >>> > For this test, it did not achieve convergence with 10000 iterations.
> >>> >
> >>> > When I use BJOCABI PC and BICGSTAB KSP, it generally takes about 600
> >>> > times iteration to get the iteration convergent.
> >>> >
> >>> > Any suggestion for improving the convergence rate will be much
> >>> > appreciated.  The solution of this equation has been the bottleneck
> of
> >>> > my code, it takes more than 90% of the total time.
> >>> >
> >>>
> >>> Try ML or GAMG.
> >>>
> >>>     Matt
> >>>
> >>>
> >>> > Thank you very much.
> >>> >
> >>> > Best Regards,
> >>> > Kai
> >>> >
> >>>
> >>>
> >>>
> >
> >
> > --
> > 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
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