On Tue, Nov 7, 2017 at 4:19 AM, Buesing, Henrik < [email protected]> 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 > > ------------------------------------------------------ > > Mathieustr. 10 > <https://maps.google.com/?q=Mathieustr.+10&entry=gmail&source=g> > | Tel +49 (0)241 80 49907 <+49%20241%208049907> > > 52074 Aachen, Germany | Fax +49 (0)241 80 49889 > <+49%20241%208049889> > > ------------------------------------------------------ > > http://www.eonerc.rwth-aachen.de/GGE > > [email protected] > > ------------------------------------------------------ > > > -- 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/>
