Preconditioning for saddle point problems

Jed Brown jed at
Wed Apr 30 05:41:12 CDT 2008

On Tue 2008-04-29 11:03, Matthew Knepley wrote:
> 1) I believe the Wathen-Elman-Silvester stuff is the best out there of the
>     shelf. I love the review
>      A.C. de Niet and F.W. Wubs "Two preconditioners for saddle point
> problems in fluid flows"
>      Int. J. Num. Meth. Fluids 2007: 54: 355-377

Thanks for pointing this out.

> 3) If you want a mixed system, there is new code in PETSc (PCFieldSplit) to do
> exactly what you want, and it works automatically with DAs. If you do it by
> hand, you provide explicitly the IS for each field.

This looks like it works only as long as the preconditioner is block diagonal.
The preconditioner I am using is an approximate block LU decomposition of the
original problem so can't be made block diagonal.  Since most of my matrices are
MatShell I'll always have to write the pieces individually, just providing index
sets won't work.  However, decomposing the mixed global vectors into each
component requires a lot of boilerplate (and maybe always will in my case due to
removing constrained degrees of freedom).

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