dolfin team mailing list archive

[Nuno David Lopes <ndl@xxxxxxxxxxxxxx>]

> The Stokes problem is indefinite, hence normal preconditioners are not
> expected to work.  Reordering unknowns and diagonal shifts can help, but
> you really want a Schur complement preconditioner or Vanka smoothers for
> multigrid (not conveniently available).  The easiest thing is to
> assemble the matrix
>
>   P1 = (A  B')         or         P2 = (A  0)
>        (0  M )                         (0  M)
>
> (where M is the mass matrix) to precondition the Stokes system
>
>   (A  B') (u)  =  (f)
>   (B  0 ) (p)     (0)
>
> Unfortunately, Dolfin does not have the plumbing in place for separate
> preconditioning matrices so you will need to work with the KSP directly.  

I'm using uzawa methods with hood-taylor (P2-P1) so we don't really deal with 
the complete indefinite system 
           (A B')(u)=(f)
           (B  0)(p)  (0). 

The idea is to work with something like 
Au^n=f+B'p^n            (this is the problematic case in big problems) 
p^(n+1)=p^n-\rho B u 

In the simpliest case, A a comes from -(grad(u),grad(v)), so it should be 
a "good" system to deal with. 
And it works "well" with other preconditioners. 
I just want to improve timmings. 
But as I'said  Multgrid Preconditioners are out of my league.  

-- 
Nuno David Lopes

e-mail:ndl@xxxxxxxxxxxxxx        (FCUL/CMAF)
           nlopes@xxxxxxxxxxxxxxx    (ISEL)
http://ptmat.ptmat.fc.ul.pt/%7Endl/ 

Thu Sep 25 09:26:02 WEST 2008