[petsc-users] nonlinear eigenvalue problem with structured mesh

[Matthew Knepley]

On Sat, Jul 25, 2015 at 2:56 PM, Gideon Simpson <gideon.simpson at gmail.com>
wrote:

> Are there any tools for constructing the Jacobian of a function when using
> DMComposite and DMRedundant?
>

No good ones right now, since it would be a sparse Jacobian + a low rank
update. We have talked about putting
this in forever, but no one was screaming for it.

   Matt


> -gideon
>
> On Jul 13, 2015, at 8:25 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>
>  You can use a DMCOMPOSITE with a DMDA and a DMREDUNDANT see
> src/snes/examples/tutorials/ex21.c  It is intended for this type of
> situation.
>
>  Barry
>
>
> On Jul 13, 2015, at 4:05 PM, Gideon Simpson <gideon.simpson at gmail.com>
> wrote:
>
> Thanks for the suggestions.  Suppose though that I wanted to avoid using a
> self-consistent approach and just attack the full nonlinear problem.  Is
> there a “smart” way to handle my data where the Vec q, which stores both
> the function on the mesh, and the eigenvalue parameter.  Suppose the
> eigenvalue parameter was in the last entry of the q vector, and the N-1
> entries represnted the solution.  Is there a way to mask this sub-vector so
> it can be manipulated with a da?
>
> -gideon
>
> On Jul 7, 2015, at 10:38 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Tue, Jul 7, 2015 at 2:06 AM, Jose E. Roman <jroman at dsic.upv.es> wrote:
>
> El 07/07/2015, a las 03:34, Matthew Knepley escribió:
>
> On Mon, Jul 6, 2015 at 7:43 PM, Gideon Simpson <gideon.simpson at gmail.com>
> wrote:
> I have a nonlinear eigenvalue problem for a system of equations, of the
> form,
>
> -Delta u + f(u) = E * u,
>
> where E is my nonlinear eigenvalue parameter, and u and f are vector
> valued.
>
> I thus have the following two things to contend with:
>
> 1.  E is a scalar which needs to be distributed across all the processes
> when the right hand side is formed
>
> 2.  I would like to be able to use a da to manage the spatial and
> multicomponent nature of u
>
> Obviously the Vec that my nonlinear solver is going to search for has to
> store both bits of data.  Is there a clever petsc way to handle this, or
> will I need to do all the indexing and broadcasting by hand?
>
> My first suggestion would be to investigate SLEPc, which does have some
> support for nonlinear
> eigenvalue problems. Failing that, E normally comes out of the algorithm
> as the result of some
> vector algebra which automatically distributes the constant (like VecDot).
>
>
> Nonlinear eigenvalue problems can be generally classified in two groups:
> those that depend nonlinearly on the eigenvalue parameter T(lambda)*x=0,
> and those that are nonlinear with respect to the eigenvector
> H(X)*X=X*Lambda. It seems that Gideon's problem belongs to the seocond type.
>
> Currently, SLEPc provides solvers for the first type only. We do not
> foresee to have solvers for the latter type anytime soon.
>
> I guess what Gideon needs to do is compute E from an initial guess of u,
> then use SNES to update u, and iterate until a self-consistent state is
> reached.
>
> Thanks for the clarification, Jose. I think what you could do is to use
> SLEPc as the subsolver for each
> eigenproblem with frozen coefficients (so this would be a type of 'Picard'
> method according to Jed or
> an Inexact Newton Method according to me) and then update using SNES,
> exactly as Jose says above.
> Even if you do not know the actual Jacobian, you can do the obvious thing
> in your FormJacobian, which
> is to just reassemble the matrix with the latest 'u' and you will get
> linear convergence if its contractive. This
> also allows you to try out the nice line searches.
>
>  Thanks,
>
>     Matt
>
> Jose
>
>
>
>  Thanks,
>
>     Matt
>
> -gideon
>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
>
>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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