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

[Smith, Barry F.]

  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
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> 52074 Aachen, Germany     |    Fax +49 (0)241 80 49889
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> hbuesing at eonerc.rwth-aachen.de
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