[petsc-users] How to find a good initial guess for a BVP

[Ryan Yan]

Hi Jed,
Thank you very much for the suggestion and providing the reference and
examples.

I have tried the grid sequencing, but with little luck on that.

I will try the approach 1 for the explicit form of the conservation system.

Yan


On Tue, Jan 26, 2010 at 5:49 AM, Jed Brown <jed at 59a2.org> wrote:

> On Mon, 25 Jan 2010 22:03:57 -0500, Ryan Yan <vyan2000 at gmail.com> wrote:
> > I am solving a nonlinear BVP(steady-states) extracted from a
> time-dependent
> > problem by setting d/dt=0.
>
> Globalization of steady-state problems is notoriously difficult, it's
> very likely that you will need to perform a continuation, of which there
> are at least two kinds to consider.
>
> 1. Pseudotransient continuation, I like this paper
>
>  http://www.cs.odu.edu/~keyes/papers/ptc03.pdf<http://www.cs.odu.edu/%7Ekeyes/papers/ptc03.pdf>
>
> which explains snes/examples/tutorials/ex27.c.
>
> This can be done with TSPSEUDO, but not currently for differential
> algebraic systems.  If you would like it to work with DAEs, or ODEs
> written in implicit form (f(t,x,x')=0 instead of x' = f(t,x)), let me
> know and I'll add such support to PETSc-dev.
>
> 2. Grid sequencing: solve the problem on coarser grids to get an initial
> guess on the finer grids.  If you use DMMG, this is -dmmg_grid_sequence.
>
> > So, do I have to solve the time-dependent problem after a long time
> stepping
> > to get a steady solution? Or is there any better way of finding a good
> > initial guess?
>
> Pseudotransient continuation is somewhat like this, but does it in a
> clever and adaptive way.
>
> Jed
>
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