[petsc-users] Block Preconditioning

[Elias Karabelas]

Dear Members,

I want to solve a Block System arising from the Discretization of a 
stabilized Finite Element Formulation of the Stokes System.

I have the following Block Structure

A     -B^T
B       C

The Preconditioner I intend to use is a block preconditioner of the Form

A    -B^T
         S

where S is an approximation of the Schur Complement. For applying the 
inverse of the schur complement I want to use a Stabilized Least Squares 
Commutator in the form

S^-1 = (B diag(Q)^-1 B^T + C_1)^-1 (B diag(Q)^-1 A diag(Q)^-1 B^T + C_2) 
(B diag(Q)^-1 B^T + C_1)^-1

where Q is the mass matrix and C_1 and C_2 are some additional 
stabilization matrices.

I got from the Manual, that I can use the PCFieldSplit preconditioner 
for generating the general Block preconditioner as indicated above. And 
I also found that I can define some arbitrary PC with PCSHELL. My 
question is, if it is possible to use PCSHELL to define the action of 
S^-1 as indicated above.

Kind Regards
Elias Karabelas

-- 
Elias Karabelas, Ph.D.

Medical University of Graz
Institute of Biophysics
Harrachgasse 21/IV
8010 Graz, Austria

Phone: +43 316 380 7759
Email: elias.karabelas at medunigraz.at
Web  : http://forschung.medunigraz.at/fodok/staff?name=EliasKarabelas