adding SNESSetLinearSolve()

[Barry Smith]

  So SNES is actually only "seeing" a system of size n? And you are
NOT using Newton's method on that nonlinear system of size n? Instead
you are solving some other linear system (defined by your solution
process) and pretending it is the Newton solution?

  Barry


On Mon, 29 Oct 2007, Lisandro Dalcin wrote:

> On 10/29/07, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >    This may be an error in our design, we may need a shell KSP. It would be
> > nice not to need it, but ...
> >    You seem to be saying you want something much like a KSP shell?
> 
> Indeed. Perhaps we need one in the end, but I would prefer to avoid that.
> 
> >   What are the operators for this KSP (the A and B?) do you set them in the
> > SNESSetJacobian()? Is b1 the same size (n+1) as b? Is the Eisenstat walker
> > test used on BOTH KSP::solve(b1,x1) and KSP::solve(b2,x2)?
> 
> The operators A and B are the ones computed with the function set in
> SNESSetJacobian(). So both linear solves should be done with the
> matrices, same preconditioner, same tolerances (perhaps determined
> with EW method), etc, but different rhs's.  From those two solves, I
> next determine the actual solution update for SNES, and an additional
> update for an 'internal' scalar dof managed inside my aplication code.
> 
> Imagine a hypothetical formulation of a nonlinear Stokes-like problem,
> were you have exactly one 'pressure' dof in all your mesh, but this
> dof is coupled with all velocity variables (thus generating a dense
> row and column in your Jacobian matrix). Then you can eliminate this
> scalar degree of freedom, and solve your linear problem by using the
> Schur complement. Then you need two linear solves for your 'momentum'
> equations, using the same 'momentum' block of your jacobian matrix.
> 
> 
>