[petsc-users] Matrix-free vs finite differenced Jacobian approximation
Matthew Knepley
knepley at gmail.com
Tue Dec 12 15:49:43 CST 2017
On Tue, Dec 12, 2017 at 3:19 PM, Alexander Lindsay <alexlindsay239 at gmail.com
> wrote:
> I'm helping debug the finite strain models in the TensorMechanics module
> in MOOSE, so unfortunately I don't have a nice small PetSc code I can hand
> you guys :-(
>
> Hmm, interesting, if I run with `-snes_mf_operator -snes_fd -mat_mffd_type
> ds`, I get DIVERGED_BREAKDOWN during the initial linear solve.
>
So the MF operator always converges. The FD operator does not always
converge, and factorization also can fail (DIVERGED_BREAKDOWN)
so it seems that the FD operator is incorrect. Usually we have bugs with
coloring, but I do not think coloring is used by -snes_fd. What happens
if you get the coloring version by just deleting the FormJacobian pointer?
Thanks,
Matt
> If I run with `-snes_fd -mat_fd_type ds`, then the solve converges.
>
> So summary:
>
> - J = B = finite-differenced, differencing type = wp : Solve fails due to
> DIVERGED_LINE_SEARCH
>
> - J = B = finite-differenced, differencing type = ds : Solve converges in
> 3 non-linear iterations
> 0 Nonlinear |R| = 2.259203e-02
> 0 Linear |R| = 2.259203e-02
> 1 Linear |R| = 6.084393e-11
> 1 Nonlinear |R| = 4.780691e-03
> 0 Linear |R| = 4.780691e-03
> 1 Linear |R| = 8.580132e-19
> 2 Nonlinear |R| = 4.806625e-09
> 0 Linear |R| = 4.806625e-09
> 1 Linear |R| = 1.650725e-24
> 3 Nonlinear |R| = 9.603678e-12
>
> - J = matrix-free, B = finite-differenced, mat_mffd_type = mat_fd_type =
> wp: Solve converges in 2 non-linear iterations
> 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
>
> - J = matrix-free, B = finite-differenced, mat_mffd_type = ds, mat_fd_type
> = wp: DIVERGED_BREAKDOWN in linear solve
>
> - J = matrix-free, B = finite-differenced, mat_mffd_type = wp, mat_fd_type
> = ds: Solve converges in 2 non-linear iterations
> 0 Nonlinear |R| = 2.259203e-02
> 0 Linear |R| = 2.259203e-02
> 1 Linear |R| = 4.635397e-03
> 2 Linear |R| = 5.413676e-11
> 1 Nonlinear |R| = 1.068626e-05
> 0 Linear |R| = 1.068626e-05
> 1 Linear |R| = 7.942385e-12
> 2 Nonlinear |R| = 5.444448e-11
>
> - J = matrix-free, B = finite-differenced, mat_mffd_type = mat_fd_type =
> ds: Solves converges in 3 non-linear iterations:
> 0 Nonlinear |R| = 2.259203e-02
> 0 Linear |R| = 2.259203e-02
> 1 Linear |R| = 1.312921e-06
> 2 Linear |R| = 7.714018e-09
> 1 Nonlinear |R| = 4.780690e-03
> 0 Linear |R| = 4.780690e-03
> 1 Linear |R| = 7.773053e-09
> 2 Nonlinear |R| = 1.226836e-08
> 0 Linear |R| = 1.226836e-08
> 1 Linear |R| = 1.546288e-14
> 3 Nonlinear |R| = 1.295982e-10
>
>
>
>
> On Tue, Dec 12, 2017 at 12:33 PM, Smith, Barry F. <bsmith at mcs.anl.gov>
> wrote:
>
>>
>>
>> > On Dec 12, 2017, at 11:26 AM, 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`.
>>
>> Now that you have provided the exact options you are using, yes it is
>> very unexpected behavior. Is there any chance you can send us the code that
>> reproduces this?
>>
>> The code that does the differencing in -snes_fd is similar to the code
>> that does the differencing for -snes_mf_operator so normally one expects
>> similar behavior but there are a couple of options you can try. Run with
>> -snes_mf_operator and -help | grep mat_mffd and this will show options to
>> control the differencing for the matrix free. For -snes_fd you have the
>> option -mat_fd_type wp or ds
>>
>>
>> > 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?
>> >
>> > 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/
>> >
>>
>>
>
--
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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