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.simp...@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 <knep...@gmail.com> wrote: >> >> On Tue, Jul 7, 2015 at 2:06 AM, Jose E. Roman <jro...@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.simp...@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 >
