[petsc-users] Newton methods that converge all the time

[Matthew Knepley]

On Tue, Nov 7, 2017 at 4:19 AM, Buesing, Henrik <
hbuesing at eonerc.rwth-aachen.de> wrote:

> Dear all,
>
>
>
> I am solving a system of nonlinear, transient PDEs. I am using Newton’s
> method in every time step to solve the nonlinear algebraic equations. Of
> course, Newton’s method only converges if the initial guess is sufficiently
> close to the solution.
>
> This is often not the case and Newton’s method diverges. Then, I reduce
> the time step and try again. This can become prohibitively costly, if the
> time steps get very small. I am thus looking for variants of Newton’s
> method, which have a bigger convergence radius or ideally converge all the
> time.
>
>
>
> I tried out the pseudo-timestepping described in
> http://www.mcs.anl.gov/petsc/petsc-current/src/ts/examples/
> tutorials/ex1f.F.html.
>
>
>
> However, this does converge even worse. I am seeing breakdown when I have
> phase changes (e.g. liquid to two-phase).
>
>
>
> I was under the impression that pseudo-timestepping should converge
> better. Thus, my question:
>
> Am I doing something wrong or is it possible that Newton’s method
> converges and pseudo-timestepping does not?
>
> Thank you for any insight on this.
>

Hi Hendrik,

I would try using NGMRES as a nonlinear preconditioner. I have an example
in my tutorial slides for using it with SNES ex19.
I hope this will work because I suspect that around the phase boundary
Newton directions are noisy, since sometimes you
step into the other phase. NGMRES takes a few directions (you set the m)
and then picks the best one.

  Hopefully this helps,

     Matt


> Henrik
>
>
>
>
>
>
> --
>
> Dipl.-Math. Henrik Büsing
>
> Institute for Applied Geophysics and Geothermal Energy
>
> E.ON Energy Research Center
>
> RWTH Aachen University
>
> ------------------------------------------------------
>
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> ------------------------------------------------------
>
> http://www.eonerc.rwth-aachen.de/GGE
>
> hbuesing at eonerc.rwth-aachen.de
>
> ------------------------------------------------------
>
>
>



-- 
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.caam.rice.edu/~mk51/>
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