[petsc-users] matrix-free preconditionning of FGMRES

[Barry Smith]

On Jan 16, 2011, at 5:59 PM, Darcoux Christine wrote:

> I am new to PETSc and I am interested to use the nonlinear solver in a CFD code for low speed compressible fluid.
> 
> According to some papers, it seems that GMRES (or any other Krylov method) could be used to precondition FGMRES in a way that is completely matrix-free. Is it something possible with the fgmres implementation provided by PETSc ?

   Yes, but like anything with "matrix-free" is the question how you provide a decent preconditioner without forming any matrices. If you can do that then you are all set.

 KSPSetOperators(ksp,A,B,...)   or SNESSetJacobian(snes,A,B, ....)  where A is a a MATSHELL that does matrix vector products or use MatCreateMFFD()

-ksp_type fgmres -pc_type ksp -ksp_ksp_type gmres  -ksp_view

  If B is some approximate representation of A then B will be used to construct the preconditioner, if you never have a matrix-representation but have a function/subroutine that is supposedly a good preconditioner then you would use PCSHELL to provide it. So there are several possibilities depending on what you have and what you want to do.

  Barry

> Christine
>