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

Sun Jul 22 04:01:07 CDT 2012

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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