[petsc-users] Matrix-free vs finite differenced Jacobian approximation

[Matthew Knepley]

On Tue, Dec 12, 2017 at 12:26 PM, Alexander Lindsay <
alexlindsay239 at gmail.com> wrote:

> Ok, I'm going to go back on my original statement...the physics being run
> here is a sub-set of a much larger set of physics; for the current set the
> hand-coded Jacobian actually appears to be quite good.
>
> With hand-coded Jacobian, -pc_type lu, the convergence is perfect:
>
>  0 Nonlinear |R| = 2.259203e-02
>       0 Linear |R| = 2.259203e-02
>       1 Linear |R| = 1.129089e-10
>  1 Nonlinear |R| = 6.295583e-11
>
> So yea I guess at this point I'm just curious about the different behavior
> between `-snes_fd` and `-snes_fd -snes_mf_operator`. Does the hand-coded
> result change your opinion Matt that the rules for FormFunction/Jacobian
> might be being violated?
>
> I understand that a finite difference approximation of the true Jacobian *is
> an approximation. *However, in the absence of possible complications like
> Matt suggested where an on-the-fly calculation might stand a better chance
> of capturing the behavior, I would expect both `-snes_mf_operator -snes_fd`
> and `-snes_fd` to suffer from the same approximations, right?
>

There are too many things that do not make sense:

1) How could LU be working with -snes_mf_operator?

     What operator are you using here. The hand-coded Jacobian?

2) How can LU take more than one iterate?

0 Nonlinear |R| = 2.259203e-02
      0 Linear |R| = 2.259203e-02
      1 Linear |R| = 2.258733e-02
      2 Linear |R| = 3.103342e-06
      3 Linear |R| = 6.779865e-12

That seems to say that we are not solving a linear system for some reason.

 3) Why would -snes_fd be different from a hand-coded Jacobian?

  Did you try -snes_type test?

  Matt

On Tue, Dec 12, 2017 at 9:43 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Tue, Dec 12, 2017 at 11:30 AM, Alexander Lindsay <
>> alexlindsay239 at gmail.com> wrote:
>>
>>> I'm not using any hand-coded Jacobians.
>>>
>>
>> This looks to me like the rules for FormFunction/Jacobian() are being
>> broken. If the residual function
>> depends on some third variable, and it changes between calls independent
>> of the solution U, then
>> the stored Jacobian could look wrong, but one done every time on the fly
>> might converge.
>>
>>    Matt
>>
>>
>>> Case 1 options: -snes_fd -pc_type lu
>>>
>>> 0 Nonlinear |R| = 2.259203e-02
>>>       0 Linear |R| = 2.259203e-02
>>>       1 Linear |R| = 7.821248e-11
>>>  1 Nonlinear |R| = 2.258733e-02
>>>       0 Linear |R| = 2.258733e-02
>>>       1 Linear |R| = 5.277296e-11
>>>  2 Nonlinear |R| = 2.258733e-02
>>>       0 Linear |R| = 2.258733e-02
>>>       1 Linear |R| = 5.993971e-11
>>> Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 2
>>>
>>> Case 2 options: -snes_fd -snes_mf_operator -pc_type lu
>>>
>>>  0 Nonlinear |R| = 2.259203e-02
>>>       0 Linear |R| = 2.259203e-02
>>>       1 Linear |R| = 2.258733e-02
>>>       2 Linear |R| = 3.103342e-06
>>>       3 Linear |R| = 6.779865e-12
>>>  1 Nonlinear |R| = 7.497740e-06
>>>       0 Linear |R| = 7.497740e-06
>>>       1 Linear |R| = 8.265413e-12
>>>  2 Nonlinear |R| = 7.993729e-12
>>> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 2
>>>
>>> On Tue, Dec 12, 2017 at 9:12 AM, zakaryah . <zakaryah at gmail.com> wrote:
>>>
>>>> When you say "Jacobians are bad" and "debugging the Jacobians", do you
>>>> mean that the hand-coded Jacobian is wrong?  In that case, why would you be
>>>> surprised that the finite difference Jacobians, which are "correct" to
>>>> approximation error, perform better?  Otherwise, what does "Jacobians are
>>>> bad" mean - ill-conditioned?  Singular?  Not symmetric?  Not positive
>>>> definite?
>>>>
>>>
>>>
>>
>>
>> --
>> 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
>>
>> https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
>>
>
>


-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
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