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

Ryan Yan vyan2000 at gmail.com
Mon Feb 1 16:14:36 CST 2010

```Hi all,
I just realized that I do need to work with the implicit form of the  DAE.
For instance, if I need to add a following tendency term "rho(x)*x' ":

rho* x' = - f(t,x))

My question is:

> In order to solve the above system by dmmg, is it suffice to multiply the
line p380-384 in snes/examples/tutorials/ex27.c, namely, multiply a "rho(x)"
term to each of the right hand side of the line  p380-384? Or is there
invisible barrier that I should beware of.

Thank you very much,

Yan

On Tue, Jan 26, 2010 at 11:27 AM, Ryan Yan <vyan2000 at gmail.com> wrote:

> 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