> On Aug 26, 2017, at 10:43 PM, zakaryah . <[email protected]> wrote: > > Hi Barry - many thanks for taking the time to understand my many problems and > providing so much help. > > The reason I was concerned that I could not alter the linesearch was when I > tried to use bt instead of the L-BFGS default, cp, the code crashed with an > error like "Could not get Jacobian". Maybe this is an incompatibility like > you say, since L-BFGS only uses the initial Jacobian and I never tried > setting the scale type. > > I took your advice and tried to shrink the problem. First I tried shrinking > by a factor 1000 but this converged very quickly with all test data I could > provide, including the data which was problematic with the large grid. So I > settled for a reduction in size by a factor 125. The grid size is 13,230. > This is a decent test case because the solver fails to converge with the > options I was using before, and it is small enough that I can run it with the > options you suggested (-snes_fd_color -snes_type newtonls -snes_monitor > -snes_linesearch_monitor -ksp_monitor -pc_type lu). > > The output is 1800 lines long - how shall I share it?
Just email it, that is small enough for email. Barry > > > > > On Sat, Aug 26, 2017 at 7:38 PM, Barry Smith <[email protected]> wrote: > > > 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 > > >
