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

[Buesing, Henrik]

Dear Barry, 

I am using a pressure-enthalpy formulation, which is valid across all phase states, i.e. no variable switching. Nevertheless, I have

1) a truncate function defined with SNESLineSearchSetPreCheck, which keeps pressure and enthalpy values in physical bounds. 
2) I have if statements in my FormFunction and FormJacobian. These test the current enthalpy vs. saturated water and gas enthalpies and determine the state. 

I could discard the SNESLineSearchSetPreCheck. Would this be better for Newton's method? 

Thank you!

Henrik


-- 
Dipl.-Math. Henrik Büsing
Institute for Applied Geophysics and Geothermal Energy
E.ON Energy Research Center
RWTH Aachen University
------------------------------------------------------
Mathieustr. 10            |    Tel +49 (0)241 80 49907
52074 Aachen, Germany     |    Fax +49 (0)241 80 49889
------------------------------------------------------
http://www.eonerc.rwth-aachen.de/GGE
hbuesing at eonerc.rwth-aachen.de
------------------------------------------------------

> -----Ursprüngliche Nachricht-----
> Von: Smith, Barry F. [mailto:bsmith at mcs.anl.gov]
> Gesendet: 10 November 2017 05:09
> An: Buesing, Henrik <hbuesing at eonerc.rwth-aachen.de>
> Cc: petsc-users <petsc-users at mcs.anl.gov>
> Betreff: Re: [petsc-users] Newton methods that converge all the time
> 
> 
>   Henrik,
> 
>    Please describe in some detail how you are handling phase change. If
> you have if () tests of any sort in your FormFunction() or
> FormJacobian() this can kill Newton's method. If you are using "variable
> switching" this WILL kill Newtons' method. Are you monkeying with phase
> definitions in TSPostStep or with SNESLineSearchSetPostCheck(). This
> will also kill Newton's method.
> 
>   Barry
> 
> 
> > On Nov 7, 2017, at 3:19 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.
> >
> > Henrik
> >
> >
> >
> >
> > --
> > Dipl.-Math. Henrik Büsing
> > Institute for Applied Geophysics and Geothermal Energy E.ON Energy
> > Research Center RWTH Aachen University
> > ------------------------------------------------------
> > Mathieustr. 10            |    Tel +49 (0)241 80 49907
> > 52074 Aachen, Germany     |    Fax +49 (0)241 80 49889
> > ------------------------------------------------------
> > http://www.eonerc.rwth-aachen.de/GGE
> > hbuesing at eonerc.rwth-aachen.de
> > ------------------------------------------------------