[petsc-users] help needed for -snes_mf_operator

[Matthew Knepley]

On Fri, Apr 27, 2012 at 2:12 AM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Fri, Apr 27, 2012 at 01:00, Dominik Szczerba <dominik at itis.ethz.ch>wrote:
>
>> I have
>> properly converging non-trivial cases with the Newton solver using
>> analytically derived Jacobian. I want to reproduce these results
>> WITHOUT using my Jacobian at all with the secant method (i.e. F'(x)
>> approximated with finite differences)). You say my Jacobian is wrong,
>> and maybe you are right and maybe not. But it does not matter: I do
>> not want to use my Jacobian anyway, hoping for the petsc's secant
>> method to approximate it. Does petsc have a secant method and does
>> -snes_mf_operator option enables it? Or it only works as a
>> preconditioner, requiring the Jacobian in any case?
>>
>
> -snes_mf_operator is NOT the secant method. Secant is actually only a 1D
> method, the generalizations to multiple dimensions are usually referred to
> as quasi-Newton, of which BFGS is perhaps the most popular. Those are
> -snes_type qn, most of that work is new in petsc-dev.
>
> -snes_mf_operator is Newton, but with the *operator* applied using
> matrix-free finite differences. It uses whatever you provide as the
> preconditioning matrix.
>
> As for what is going wrong, some of the symptoms you report often occur
> when the original system is poorly scaled. What units are you using for
> state variables and residuals? This has lots of useful tips
>

I disagree here. I think what is wrong is

  You are screwing up providing the preconditioner matrix. There is no
other way to explain the GMRES performance.

Try using -snes_mf and it will converge, just slowly. This is a simple
thing of correcting an error in providing that matrix I think.

    Matt


>
> http://scicomp.stackexchange.com/questions/30/why-is-newtons-method-not-converging
>
> See these entries relating to inaccurate finite differencing
>
> * Run with -snes_type test -snes_test_display to see if the Jacobian you
> are using is wrong. Compare the output when you add -mat_fd_type ds to see
> if the result is sensitive to the choice of differencing parameter.
> * Run with -snes_mf_operator -pc_type lu to see if the Jacobian you are
> using is wrong. If the problem is too large for a direct solve, try
> -snes_mf_operator -pc_type ksp -ksp_ksp_rtol 1e-12. Compare the output when
> you add -mat_mffd_type ds to see if the result is sensitive to choice of
> differencing parameter.
> * Run with quad precision (./configure --with-precision=__float128
> --download-f2cblaslapack with PETSc 3.2 and later, needs version 4.6 or
> later GNU compilers)
> * Change the units (nondimensionalization), boundary condition scaling, or
> formulation so that the Jacobian is better conditioned.
>



-- 
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
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