[petsc-users] Problems about Picard and NolinearGS

[Yingjie Wu]

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). 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.

Thanks,
Yingjie
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