Matrix free example snes/ex20.c

[Barry Smith]

On Dec 30, 2007, at 12:44 PM, Vijay M wrote:

> Matt,
>
> Thanks for the reply. What you suggested makes sense and so to start  
> from a
> common ground, I used no preconditioner at all in both the J-free and
> analytical Jacobian cases. But now, interestingly, the analytical  
> Jacobian
> takes around twice the number of linear iterations.
>
> mpirun -np 1 ex20 -ksp_type gmres -snes_monitor -pc_type none
> Number of Newton iterations = 6
> Number of Linear iterations = 112
> Average Linear its / Newton = 1.866667e+01
>
> mpirun -np 1 ex20 -ksp_type gmres -snes_monitor -snes_mf -pc_type none
> Number of Newton iterations = 6
> Number of Linear iterations = 54
> Average Linear its / Newton = 9.000000e+00
>
> I understand that both the methods will not give me the same number  
> of total
> linear iterations but a factor of 2 seems a little odd to me.

    Yes, this is surprising.

    Run with -ksp_monitor how are the linear convergence different?

> This leads to
> another question whether the user can actually change the epsilon  
> used for
> computing the perturbation in J-free scheme or is this fixed in  
> PETSc ?

    Yes, see the manual page for MatMFFDSetFromOptions() and related  
manual
pages.

>
>
> If not, then what do you think is the reason for this ?

    Bug in your analytic Jacobian? Run with -snes_monitor and - 
ksp_monitor and
send all output.

    Barry

> Do let me know your
> comments when you get some time. Thanks.
>
> Vijay
>
> -----Original Message-----
> From: owner-petsc-users at mcs.anl.gov [mailto:owner-petsc-users at mcs.anl.gov 
> ]
> On Behalf Of Matthew Knepley
> Sent: Saturday, December 29, 2007 9:05 PM
> To: petsc-users at mcs.anl.gov
> Subject: Re: Matrix free example snes/ex20.c
>
> On Dec 29, 2007 8:07 PM, Vijay M <vijay.m at gmail.com> wrote:
>> Hi all,
>>
>> I was trying to compile and run the ex20.c example code in the  
>> tutorial
>> section of SNES. Although it does not explicitly specify that - 
>> snes_mf
>> option can be used, my understanding is that as long as a nonlinear
> residual
>> function is written correctly, PETSc will calculate via finite  
>> difference
>> the action of the Jacobian on a given vector. Is that correct ?
>
> Yes.
>
>> Now if that is the case, then please observe the discrepancy in the  
>> number
>> of linear iterations taken with an analytical Jacobian and matrix- 
>> free
>> option. What puzzles me is that the SNES function norm are quite  
>> close for
>> both the methods but the linear iterations differ by a factor of 3.  
>> Why
>> exactly is this ?
>
> There is no PC when using -snes_mf whereas the default is ILU for the
> analytic
> Jacobian.
>
>   Matt
>
>> Here's the output to make this clearer.
>>
>> vijay :mpirun -np 1 ex20 -ksp_type gmres -snes_monitor
>>
>>  0 SNES Function norm 2.271442542876e-01
>>
>>  1 SNES Function norm 6.881516100891e-02
>>
>>  2 SNES Function norm 1.813939751552e-02
>>
>>  3 SNES Function norm 2.354176462207e-03
>>
>>  4 SNES Function norm 3.063728077362e-05
>>
>>  5 SNES Function norm 3.106106268946e-08
>>
>>  6 SNES Function norm 5.344742712545e-12
>>
>>  0 SNES Function norm 2.271442542876e-01
>>
>>  1 SNES Function norm 6.881516100891e-02
>>
>>  2 SNES Function norm 1.813939751552e-02
>>
>>  3 SNES Function norm 2.354176462207e-03
>>
>>  4 SNES Function norm 3.063728077362e-05
>>
>>  5 SNES Function norm 3.106106268946e-08
>>
>>  6 SNES Function norm 5.344742712545e-12
>>
>> Number of Newton iterations = 6
>>
>> Number of Linear iterations = 18
>>
>> Average Linear its / Newton = 3.000000e+00
>>
>>
>>
>> vijay :mpirun -np 1 ex20 -ksp_type gmres -snes_monitor -snes_mf
>>
>>  0 SNES Function norm 2.271442542876e-01
>>
>>  1 SNES Function norm 6.870629867542e-02
>>
>>  2 SNES Function norm 1.804335379848e-02
>>
>>  3 SNES Function norm 2.290074339682e-03
>>
>>  4 SNES Function norm 3.082384186373e-05
>>
>>  5 SNES Function norm 3.926396277038e-09
>>
>>  6 SNES Function norm 3.754922566585e-16
>>
>>  0 SNES Function norm 2.271442542876e-01
>>
>>  1 SNES Function norm 6.870629867542e-02
>>
>>  2 SNES Function norm 1.804335379848e-02
>>
>>  3 SNES Function norm 2.290074339682e-03
>>
>>  4 SNES Function norm 3.082384186373e-05
>>
>>  5 SNES Function norm 3.926396277038e-09
>>
>>  6 SNES Function norm 3.754922566585e-16
>>
>> Number of Newton iterations = 6
>>
>> Number of Linear iterations = 54
>>
>> Average Linear its / Newton = 9.000000e+00
>>
>>
>>
>> Thanks,
>>
>> Vijay
>>
>>
>
>
>
> -- 
> 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
>