[petsc-users] Can I use the direct solver without providing the analytical Jacobian?

Wed Mar 23 12:04:13 CDT 2011

Dear Matt,

Thanks very much for your reply.

I add "snes_fd" in the option, but get

*********************************************
   0 SNES Function norm 6.064004119408e-01
Linear solve converged due to CONVERGED_RTOL iterations 2
Nonlinear solve did not converge due to DIVERGED_FUNCTION_COUNT
*********************************************

which is worse than the default Newton-Krylov solver as

*********************************************
   0 SNES Function norm 6.064004119408e-01
Linear solve converged due to CONVERGED_RTOL iterations 2
   1 SNES Function norm 7.917252729980e-02
Linear solve converged due to CONVERGED_RTOL iterations 2
   2 SNES Function norm 6.967390244191e-03
Linear solve converged due to CONVERGED_RTOL iterations 10
   3 SNES Function norm 4.863622639964e-03
Linear solve converged due to CONVERGED_RTOL iterations 5
   4 SNES Function norm 3.696117297933e-03
Linear solve converged due to CONVERGED_RTOL iterations 1
   5 SNES Function norm 1.755926765314e-03
Linear solve converged due to CONVERGED_RTOL iterations 4
   6 SNES Function norm 1.206810772164e-03
Linear solve converged due to CONVERGED_RTOL iterations 1
   7 SNES Function norm 2.339140575778e-04
Linear solve converged due to CONVERGED_RTOL iterations 7
   8 SNES Function norm 1.676689222401e-04
Linear solve converged due to CONVERGED_RTOL iterations 1
   9 SNES Function norm 6.032645773400e-05
Linear solve converged due to CONVERGED_RTOL iterations 5
  10 SNES Function norm 4.747680518253e-05
Linear solve converged due to CONVERGED_RTOL iterations 1
  11 SNES Function norm 1.650301627011e-05
Linear solve converged due to CONVERGED_RTOL iterations 2
  12 SNES Function norm 6.030736960845e-06
Linear solve converged due to CONVERGED_RTOL iterations 5
  13 SNES Function norm 3.278948607849e-06
Linear solve converged due to CONVERGED_RTOL iterations 5
  14 SNES Function norm 2.488486141044e-06
Linear solve converged due to CONVERGED_RTOL iterations 1
  15 SNES Function norm 6.689684826529e-07
Linear solve converged due to CONVERGED_RTOL iterations 3
  16 SNES Function norm 2.543676285453e-07
Linear solve converged due to CONVERGED_RTOL iterations 7
  17 SNES Function norm 1.671616367100e-07
Linear solve converged due to CONVERGED_RTOL iterations 1
  18 SNES Function norm 7.228647551356e-08
Linear solve converged due to CONVERGED_RTOL iterations 7
  19 SNES Function norm 5.812218130475e-08
Linear solve converged due to CONVERGED_RTOL iterations 1
  20 SNES Function norm 2.883628165794e-08
Linear solve converged due to CONVERGED_RTOL iterations 3
  21 SNES Function norm 2.291142576313e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  22 SNES Function norm 2.291142573122e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  23 SNES Function norm 2.291142569390e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  24 SNES Function norm 2.291142565808e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  25 SNES Function norm 2.291142562249e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  26 SNES Function norm 2.291142558929e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  27 SNES Function norm 2.291142555415e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  28 SNES Function norm 2.291142554381e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  29 SNES Function norm 2.291142550392e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  30 SNES Function norm 2.291142549609e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  31 SNES Function norm 2.291142546087e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  32 SNES Function norm 2.291142544510e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  33 SNES Function norm 2.291142542335e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  34 SNES Function norm 2.291142541222e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  35 SNES Function norm 2.291142540142e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  36 SNES Function norm 2.291142539388e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  37 SNES Function norm 2.291142535647e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  38 SNES Function norm 2.291142532336e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  39 SNES Function norm 2.291142528666e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  40 SNES Function norm 2.291142526471e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  41 SNES Function norm 2.291142526200e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  42 SNES Function norm 2.291142526187e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  43 SNES Function norm 2.291142522689e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  44 SNES Function norm 2.291142518799e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  45 SNES Function norm 2.291142517718e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  46 SNES Function norm 2.291142517238e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  47 SNES Function norm 2.291142515991e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  48 SNES Function norm 2.291142512095e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  49 SNES Function norm 2.291142508630e-08
Linear solve converged due to CONVERGED_RTOL iterations 2
  50 SNES Function norm 2.291142507169e-08
Nonlinear solve did not converge due to DIVERGED_MAX_IT
*********************************************

When I see this residual history, I would like to make some  
improvement on the solver, any suggestions on it?

The options for the Newton-Krylov run are

-pc_type asm
-snes_ksp_ew true

for np=1.

Thanks again for your kind help!

Cheers,

Rebecca

Quoting Matthew Knepley <knepley at gmail.com>:

> On Wed, Mar 23, 2011 at 11:46 AM, Rebecca Xuefei Yuan
> <xy2102 at columbia.edu>wrote:
>
>> Hi,
>>
>> If the nonlinear system is evaluated at F(u) = 0 in "FormFunction()", but
>> the symbolic Jacobian is not provided. Is there any options that I can call
>> to solve the corresponding linear system by direct solver?
>>
>
> -snes_fd, which is very slow.
>
>   Matt
>
>
>> Thanks very much!
>>
>> Best regards,
>>
>> Rebecca
>>
>>
>>
>
>
> --
> 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
>

Rebecca Xuefei YUAN
Department of Applied Physics and Applied Mathematics
Columbia University
Tel:917-399-8032
www.columbia.edu/~xy2102