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

[Matthew Knepley]

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/>
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