[petsc-users] user defined algorithm for newton solver

[Matthew Knepley]

On Thu, Oct 8, 2015 at 2:41 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>    The easiest way for you to implement this is to simply call your update
> to the solution and then call SNESSolve() again. For example
>
>    while (1) {
>      SNESSolve(snes,x,NULL);
>      SNESGetConvergedReason(snes,&reason);
>      if (reason > 0) break;  /* since snes has converged */
>      change x per your way
>   }
>
> The problem with the code above is that each new call to SNESSolve()
> resets the rtol convergence factor based on the current latest norm of F so
> the code above will "oversolve" the problem. You can call
> SNESSetTolerance() above the while loop with an appropriate atol to get it
> to exit at the point you want to declare it converged.
>
>   It is not worthwhile trying to "weave" your special update code inside
> the Newton method.


Do you know what the non-physical solutions are?

   Matt


>
>    Barry
>
> > On Oct 8, 2015, at 1:05 PM, Michael Povolotskyi <mpovolot at purdue.edu>
> wrote:
> >
> > Thank you.
> > The situation is as follows:
> > The system I need to solve does not have a unique solution, but only one
> makes sense from physical point of view.  I need to compute direction in a
> different way based on the physics.
> >
> > In other words it should be like this:
> >
> > 1. Start with a solution guess
> > 2. Do full Newton step
> > 3. If converged, exit
> >    else if the solution improved go to step 2
> >    otherwise "update_solution_in_my_way" ang go to step 2
> >
> > Is it possible to do this in PETSc?
> > Michael.
> >
> > On 10/08/2015 01:58 PM, Barry Smith wrote:
> >>> On Oct 8, 2015, at 12:26 PM, Michael Povolotskyi <mpovolot at purdue.edu>
> wrote:
> >>>
> >>> Dear Petsc developers and users,
> >>> I'm solving a nonlinear system with PETSc.
> >>> Often simple Newton iterations do not work and I have to use either
> linear search or trust region.
> >>> I would like to use my own algorithm to find a next iteration
> approximation to solution if the Newton step does not improve the residual.
> As far as I can see I have to define my own SNELLineSearch object. Is there
> any example that shows how to do it?
> >>    The line search model is 1) select direction based on approximate
> solution of approximate Jacobian  2) search in THAT direction for a
> decrease in the function evaluation. You state "if the Newton step does not
> improve the residual." so will you be computing the DIRECTION in a
> different way than (1) or will you be using the same direction but trying
> somehow to find a decrease in the function evaluation using a different
> technique then the standard line searchs we provide?
> >>
> >>    Frankly if the line searches we provide don't work that means the
> direction is not good and no "special" line search will recover.  I really
> recommend you go through our suggestions on the FAQ
> http://www.mcs.anl.gov/petsc/documentation/faq.html#newton on trying to
> figure out why Newton is not converging before you think about writing a
> special line search.
> >>
> >>   Barry
> >>
> >>
> >>
> >>> Thank you,
> >>> Michael.
> >>>
> >>> --
> >>> Michael Povolotskyi, PhD
> >>> Research Assistant Professor
> >>> Network for Computational Nanotechnology
> >>> Hall for Discover and Learning Research, Room 441
> >>> West Lafayette, IN 47907
> >>> Phone (765) 4949396
> >>>
> >
> > --
> > Michael Povolotskyi, PhD
> > Research Assistant Professor
> > Network for Computational Nanotechnology
> > Hall for Discover and Learning Research, Room 441
> > West Lafayette, IN 47907
> > Phone (765) 4949396
> >
>
>


-- 
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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