Re: [Libmesh-users] arc-length method

[John Peterson <peterson@cf...>]

On Tue, Oct 19, 2010 at 8:41 AM, Roy Stogner <roystgnr@...> wrote:
>
> On Tue, 19 Oct 2010, yunfei zhu wrote:
>
>> I am trying to use arc-length method to track the post-buckling equilibrium
>> path. I need to add another parameter and another additional equation to the
>> system.
>> Has anyone got experience on using arc-length together with libmesh and
>> petsc.
>> Is there any Class in libmesh that I can use directly? Thanks.
>
> There's a ContinuationSystem class to do exactly that.  I think John
> Peterson is the only expert with it; we'll see if he chimes in.

Yes, it's been a while since I've touched it, but the
ContinuationSystem class can be used for this purpose.

This particular implementation takes a different approach from the
SCALAR.  It solves two linear systems per Newton iteration using the
decomposition method of Keller, rather than a single system with an
additional dense row and column.  This has the benefit of working with
an existing matrix assembly routine for a non-continuation solve, but
has the drawback of requiring two solves.

H. B. Keller. Numerical solution of bifurcation and nonlinear eigenvalue
problems. In Applications of Bifurcation Theory, P. H. Rabinowitz (ed.),
pages 359–389. Academic Press, 1977.

I have an electronic copy of the above but it's a bit too large to
email, let me know if you would like a copy.

-- 
John

Re: [Libmesh-users] arc-length method

[Roy Stogner <roystgnr@ic...>]

On Tue, 19 Oct 2010, yunfei zhu wrote:

> I am trying to use arc-length method to track the post-buckling equilibrium
> path. I need to add another parameter and another additional equation to the
> system.
> Has anyone got experience on using arc-length together with libmesh and
> petsc.
> Is there any Class in libmesh that I can use directly? Thanks.

There's a ContinuationSystem class to do exactly that.  I think John
Peterson is the only expert with it; we'll see if he chimes in.

If you want to add an additional scalar equation, coupled to all the
others, by hand, then the SCALAR variable type is now the best way to
do that.
---
Roy

[Libmesh-users] arc-length method

[yunfei zhu <yzhu2009@go...>]

Hi
I am trying to use arc-length method to track the post-buckling equilibrium
path. I need to add another parameter and another additional equation to the
system.
Has anyone got experience on using arc-length together with libmesh and
petsc.
 Is there any Class in libmesh that I can use directly? Thanks.
Best wishes,
yunfei