[petsc-users] Problems about Picard and NolinearGS

[Matthew Knepley]

On Wed, Dec 26, 2018 at 8:50 AM Yingjie Wu via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Dear Petsc developers:
> Hi,
> 1. I tried to use the Picard solver in Petsc, but the program didn't
> converge. My program is still a thermal program that contains multiple
> physical fields, and is a PDEs' problem. The error message is as follows.
> The reason I use Picard is that it can guarantee convergence(though slow
> and expensive).
>

You can only guarantee convergence if your operator is a contraction. It
does not appear to be, or you would not need a line
search at all. The line search is failing. You could try a different line
search.

My guess is that since you have multiple fields, what you really need is a
nonlinear version of PCFIELDSPLIT. I have been meaning
to code this up, but have not done it yet since all the ways I can think of
doing it are really intrusive. You can put this together by hand
by making residual functions for the individual parts.

  Thanks,

   Matt


> I follow the ex15.c, but I don't use DM to organize the solution vector.
> So I try the SNESSetPicard().
> 0 SNES Function norm 2.91302e+08
>     0 KSP Residual norm 5.79907e+08
>     1 KSP Residual norm 1.46843e-05
>   Linear solve converged due to CONVERGED_RTOL iterations 1
>   1 SNES Function norm 2.891e+08
>     0 KSP Residual norm 5.5989e+08
>     1 KSP Residual norm 4.21314e-06
>   Linear solve converged due to CONVERGED_RTOL iterations 1
>   2 SNES Function norm 2.78289e+08
>     0 KSP Residual norm 5.53553e+08
>     1 KSP Residual norm 2.04076e-05
>   Linear solve converged due to CONVERGED_RTOL iterations 1
>   3 SNES Function norm 2.77833e+08
>     0 KSP Residual norm 5.52907e+08
>     1 KSP Residual norm 2.09919e-05
>   Linear solve converged due to CONVERGED_RTOL iterations 1
>   4 SNES Function norm 2.77821e+08
>     0 KSP Residual norm 5.52708e+08
>     1 KSP Residual norm 2.08677e-05
>   Linear solve converged due to CONVERGED_RTOL iterations 1
> Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 4
> SNES Object: 1 MPI processes
>   type: newtonls
>   maximum iterations=50, maximum function evaluations=10000
>   tolerances: relative=1e-08, absolute=1e-50, solution=1e-08
>   total number of linear solver iterations=5
>   total number of function evaluations=34
>   norm schedule ALWAYS
>   SNESLineSearch Object: 1 MPI processes
>     type: bt
>       interpolation: cubic
>       alpha=1.000000e-04
>     maxstep=1.000000e+08, minlambda=1.000000e-12
>     tolerances: relative=1.000000e-08, absolute=1.000000e-15,
> lambda=1.000000e-08
>     maximum iterations=40
>   KSP Object: 1 MPI processes
>     type: gmres
>       restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
>       happy breakdown tolerance 1e-30
>     maximum iterations=10000, initial guess is zero
>     tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
>     left preconditioning
>     using PRECONDITIONED norm type for convergence test
>   PC Object: 1 MPI processes
>     type: lu
>       out-of-place factorization
>       tolerance for zero pivot 2.22045e-14
>       matrix ordering: nd
>       factor fill ratio given 5., needed 5.48356
>         Factored matrix follows:
>           Mat Object: 1 MPI processes
>             type: seqaij
>             rows=11368, cols=11368
>             package used to perform factorization: petsc
>             total: nonzeros=234554, allocated nonzeros=234554
>             total number of mallocs used during MatSetValues calls =0
>               not using I-node routines
>     linear system matrix = precond matrix:
>     Mat Object: 1 MPI processes
>       type: seqaij
>       rows=11368, cols=11368
>       total: nonzeros=42774, allocated nonzeros=56840
>       total number of mallocs used during MatSetValues calls =0
>         not using I-node routines
> Are there any other examples of Picard methods? I'm very interested in
> this method.
>
> 2. I found that in ex15.c and ex19.c use the NonlinearGS. I know it's a
> iterative method. I don't know how to use this method in above examples.
> As for as I know, NonlinearGS is an iterative method parallel to subspace
> method. NonlinearGS should not be required if subspace methods are used.
>

NonlinearGS is really just an optimization. I would start with NASM if you
think this will work.

  Thanks,

    Matt


> Thanks,
> Yingjie
>
>
>

-- 
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.cse.buffalo.edu/~knepley/>
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