[petsc-users] SNES convergence failure (line search) for Neumann boundary condition

[Matthew Knepley]

On Wed, Aug 10, 2011 at 12:39 PM, Graf, Peter <Peter.Graf at nrel.gov> wrote:

> Dear Petsc-Users,
> I am implementing a 1D solution of the (drift/diffusion) semiconductor
> equations.  The case of Dirichlet boundaries works fine.  The case of
> Neumann boundaries (i.e. current boundary conditions such as occur at
> semiconductor/metal contacts) does not.   In sorting this out, I have
> modified one of your examples to recreate the problem:
>
> The (modified) example seeks to solve
> u`` + u^{2} = f
> on [0,1] with
> u'(0) = U0
> u(1) = 1
>
> With U0 = 0, the SNES solver converges.  With U0=-2 (for example) it does
> not:
>

Just to be clear, both of these are Neumann conditions.


>  11 SNES Function norm 5.018284941187e+00
> Nonlinear solve did not converge due to DIVERGED_LS_FAILURE
>

When asking about convergence, please send the entire output of -snes_view
-snes_monitor -ksp_monitor -snes_converged_reason

Since the Jacobian becomes more ill-conditioned, its possible the linear
solver is not converging. When testing, its best to always use
-ksp_type preonly -pc_type lu so that the solves are exact to start out.

  Thanks,

      Matt


> (interestingly, it still comes up with roughly good solutions, e.g. at
> least visually, which suggests to me my discretization is not _total_
> garbage)
>
> Along the way (with -info) I get messages of the form:
> SNESLSCheckResidual_Private(): ||J^T(F-Ax)||/||F-AX|| 208.031 near zero
> implies inconsistent rhs
>
> At the end, I get:
> [0] SNESLSCheckLocalMin_Private(): || J^T F|| 80.3 near zero implies found
> a local minimum
>
> I have used -snes_type test to verify that my Jacobian is accurate.
> I have also dumped the Jacobians to a file and examined their condition
> numbers.  The nonconverged cases have condition numbers around 10^7, whereas
> the converged cases have condition numbers around 10^3.  This seems like a
> clue, but I'm not sure what to do about it.
>
> All this is completely analogous to the real case of interest (in that
> case, my condition numbers go to 10^13 or more, and there is similar visual
> evidence that the solver is "trying" to do the right thing).
> I would love to have help getting this to work.  Specifically, what does
> the message about the "inconsistent rhs" tell me I'm doing wrong?  What is
> the evidence of the condition number telling me?  Do I have an error
> somewhere, or do I have a legitimately ill-conditioned Jacobian (in which
> case, what should I do about that?)?
>
> Thank you very much for any advice,
>
> Peter Graf
> NREL Scientific Computing Center
> Golden, CO
>



-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20110810/ddc73c93/attachment-0001.htm>