So I decided to look at the condition number of our matrix, running with `-pc_type svd -pc_svd_monitor` and it was atrocious, roughly on the order of 1e9. After doing some scaling we are down to a condition number of 1e3, and both MF and FD operators now converge, regardless of the differencing types chosen. I would say the problem was definitely on our end!
On Tue, Dec 12, 2017 at 2:49 PM, Matthew Knepley <[email protected]> wrote: > On Tue, Dec 12, 2017 at 3:19 PM, Alexander Lindsay < > [email protected]> 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. <[email protected]> >> wrote: >> >>> >>> >>> > On Dec 12, 2017, at 11:26 AM, Alexander Lindsay < >>> [email protected]> 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 <[email protected]> >>> wrote: >>> > On Tue, Dec 12, 2017 at 11:30 AM, Alexander Lindsay < >>> [email protected]> 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 . <[email protected]> >>> 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/> >
