> On Aug 26, 2017, at 5:56 PM, zakaryah . <[email protected]> wrote:
>
> I'm using PETSc's SNES methods to solve PDEs which result from Euler-Lagrange
> equations for the strain energy of a 3D displacement field. There is an
> additional term in the Lagrangian which describes external forces which arise
> from various data sets, and that term contains nonlinearities (field terms
> higher than linear). The grid has about 1.6e6 elements, and the displacement
> field has 3 components at each grid element.
>
> I'm trying to solve a sequence of successively more complicated equations,
> and the latest equation is failing to converge on some data sets. In
> particular, the methods were successful for the infinitesimal bulk strain
> (compression) energy, as well as the full infinitesimal strain energy (bulk +
> shear), but I'm now trying to generalize to the finite strain, as certain
> data sets are known to result from displacement fields for which the
> infinitesimal strain is a poor approximation.
>
> I'm using a DMDA, closely following example 48, and my preferred solver is
> L-BFGS.
So you are using ?
-snes_type qn -snes_qn_type lbfgs
>
> I have read the FAQs "Why is Newton's method not converging?" and "Why is my
> iterative linear solver not converging?" which have raised a number of
> questions:
Quasi Newton methods either don't use Jacobians or use only the initial
Jacobian (the idea behind quasi-Newton methods is to approximate Jacobian
information from previous iterations without having the user compute a Jacobian
at each iteration). With PETSc's qn it only uses the Jacobian if you use the
option
-snes_qn_scale_type Jacobian
otherwise the Jacobian is never computed or used
>
> Is there documentation for the DMDA/SNES methods somewhere? I don't
> understand these very well. For example, I am not allocating any matrix for
> the global Jacobian, and I believe this prevents me from changing the line
> search. If I'm mistaken I would love to see an example of changing the line
> search type while using DMDA/SNES.
Whether you provide a Jacobian or not is orthogonal to the line search.
You should be able to change the line search with
-snes_linesearch_type bt or nleqerr or basic or l2 or cp
not all of them may work with qn
>
> I don't know how to interpret the linesearch monitor. Even for problems
> which are converging properly, the linesearch monitor reports "lssucceed=0"
> on every iteration. Is this a problem?
It returns a 0 if the line search does not believe it has achieved
"sufficient decrease" in the function norm (or possibly some other measure of
decrease) you should run -snes_linesearch_monitor also with the option
-snes_monitor to see what is happening to the function norm
For qn you can add the option
-snes_qn_monitor
to get more detailed monitoring
>
> I'm also having trouble understanding the methods for troubleshooting. I
> suspect that I've made an error in the analytical Jacobian, which has a
> rather large number of non-zero elements, but I have no idea how to use
> -snes_type test -snes_test_display. The FAQs mention that some
> troubleshooting tools are more useful for small test problems. How small is
> small?
Tiny, at most a few dozen rows and columns in the Jacobin.
You should run without the -snes_test_display information, what does it say?
Does it indicate the Jacobian or report there is likely a problem?
With DMDA you can also use -snes_fd_color to have PETSc compute the
Jacobian for you instead of using your analytical form. If it works with this,
but not your Jacobian then your Jacobian is wrong.
> When I try to run the program with -snes_type test -snes_test_display, I get
> errors like:
>
> [0]PETSC ERROR: Argument out of range [0]PETSC ERROR: Local index 1076396032
> too large 4979879 (max) at 0
>
> The second size is 1 less than the number of field elements, while the first
> number seems too large for any aspect of the problem - the Jacobian has at
> most 59 non-zero columns per row.
>
> Because I suspect a possible error in the Jacobian, I ran with
> -snes_mf_operator -pc_type ksp -ksp_ksp_rtol 1e-12 and observed very similar
> failure to converge (diverging residual) as with the explicit Jacobian.
What do you get with -ksp_monitor -ksp_ksp_monitor it sounds like the true
Jacobian is either very ill-conditioned or your function evaluation is wrong.
> Do I need to set an SNES method which is somehow compatible with the
> "matrix-free" approach? If I instead use -snes_mf, the problem seems to
> converge, but horrendously slowly (true residual relative decrease by about
> 1e-5 per iteration). I suppose this supports my suspicion that the Jacobian
> is incorrect but doesn't really suggest a solution.
>
> Is it possible that the analytical Jacobian is correct, but somehow
> pathological, which causes the SNES to diverge?
Yes
> Neither the Jacobian nor the function have singularities.
>
> Thanks for any help you can provide!
Try really hard to set up a small problem (like just use a very coarse
grid) to experiment with as you try to get convergence. Using a big problem for
debugging convergence is a recipe for pain.
Also since you have a Jacobian I would start with -snes_fd_color -snes_type
ls -snes_monitor -snes_linesearch_monitor -ksp_monitor -pc_type lu (not on a
huge problem), what happens? Send the output
Barry
