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

[Buesing, Henrik]

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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hbuesing at eonerc.rwth-aachen.de
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