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

Alexander Lindsay alexlindsay239 at gmail.com
Tue Dec 12 14:19:12 CST 2017 

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.

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/
> >
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20171212/dd55bfb9/attachment.html>

More information about the petsc-users mailing list