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## Re: [Libmesh-users] arc-length method

 Re: [Libmesh-users] arc-length method From: John Peterson - 2010-10-19 14:34:15 ```On Tue, Oct 19, 2010 at 8:41 AM, Roy Stogner 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 ```

 [Libmesh-users] arc-length method From: yunfei zhu - 2010-10-19 08:59:21 ```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 ```
 Re: [Libmesh-users] arc-length method From: Roy Stogner - 2010-10-19 13:41:16 ```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 ```
 Re: [Libmesh-users] arc-length method From: John Peterson - 2010-10-19 14:34:15 ```On Tue, Oct 19, 2010 at 8:41 AM, Roy Stogner 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 ```