[petsc-users] pcfieldsplit for a composite dm with multiple subfields

[Matthew Knepley]

On Thu, Aug 27, 2015 at 7:00 PM, Gideon Simpson <gideon.simpson at gmail.com>
wrote:

> I’m working on a problem which, morally, can be posed as a system of
> coupled semi linear elliptic PDEs together with unknown nonlinear
> eigenvalue parameters, loosely, of the form
>
> -\Delta u_1 + f(u_1, u_2) = lam * u1 - mu * du2/dx
> -\Delta u_2 + g(u_1, u_2) = lam * u2 + mu * du1/dx
>
> Currently, I have it set up with a DMComposite with two sub da’s, one for
> the parameters (lam, mu), and one for the vector field (u_1, u_2) on the
> mesh.  I have had success in solving this as a fully coupled system with
> SNES + sparse direct solvers (MUMPS, SuperLU).
>
> Lately, I am finding that, when the mesh resolution gets fine enough
> (i.e.  10^6-10^8 lattice points), my SNES gets stuck with the function norm
> = O(10^{-4}),  eventually returning reason -6 (failed line search).
>
> Perhaps there is another way around the above problem, but one thing I was
> thinking of trying would be to get away from direct solvers, and I was
> hoping to use field split for this.  However, it’s a bit beyond what I’ve
> seen examples for because it has 2 types of variables: scalar parameters
> which appear globally in the system and vector valued field variables.  Any
> suggestions on how to get started?


Barry is right. However, I also really think we should have a nonlinear
fieldsplit. I tried to write one (SNES multiblock), but no one has ever
used it. I would be willing to put some time in if you need it. You would
likely nonlinearly precondition the Newton solve with this, which is
what X. Cai does to great effect in some problems he works on.

   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
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