Hi Jed,<br>Thank you very much for the suggestion and providing the reference and examples.<br><br>I have tried the grid sequencing, but with little luck on that.<br><br>I will try the approach 1 for the explicit form of the conservation system. <br>
<br>Yan<br><br><br><div class="gmail_quote">On Tue, Jan 26, 2010 at 5:49 AM, Jed Brown <span dir="ltr"><<a href="mailto:jed@59a2.org">jed@59a2.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div class="im">On Mon, 25 Jan 2010 22:03:57 -0500, Ryan Yan <<a href="mailto:vyan2000@gmail.com">vyan2000@gmail.com</a>> wrote:<br>
> I am solving a nonlinear BVP(steady-states) extracted from a time-dependent<br>
> problem by setting d/dt=0.<br>
<br>
</div>Globalization of steady-state problems is notoriously difficult, it's<br>
very likely that you will need to perform a continuation, of which there<br>
are at least two kinds to consider.<br>
<br>
1. Pseudotransient continuation, I like this paper<br>
<br>
<a href="http://www.cs.odu.edu/%7Ekeyes/papers/ptc03.pdf" target="_blank">http://www.cs.odu.edu/~keyes/papers/ptc03.pdf</a><br>
<br>
which explains snes/examples/tutorials/ex27.c.<br>
<br>
This can be done with TSPSEUDO, but not currently for differential<br>
algebraic systems. If you would like it to work with DAEs, or ODEs<br>
written in implicit form (f(t,x,x')=0 instead of x' = f(t,x)), let me<br>
know and I'll add such support to PETSc-dev.<br>
<br>
2. Grid sequencing: solve the problem on coarser grids to get an initial<br>
guess on the finer grids. If you use DMMG, this is -dmmg_grid_sequence.<br>
<div class="im"><br>
> So, do I have to solve the time-dependent problem after a long time stepping<br>
> to get a steady solution? Or is there any better way of finding a good<br>
> initial guess?<br>
<br>
</div>Pseudotransient continuation is somewhat like this, but does it in a<br>
clever and adaptive way.<br>
<font color="#888888"><br>
Jed<br>
</font></blockquote></div><br>