W dniu wtorek, 26 września 2017 18:42:33 UTC+2 użytkownik Wolfgang Bangerth
napisał:
>
> On 09/26/2017 09:42 AM, Michał Wichrowski wrote:
> >
> > 3) Is there a way to use multigrid on one block? For example I would
> > like to compute approximation of A^-1 using multigrid.
>
> This might be the way to go since applying multigrid on the whole
> saddle-point problem is difficult (but feasible).
>
> step-22 shows how to create a preconditioner that involves A^{-1} --
> take a particular look at the "Possibilities for extensions" section. I
> think one of the Stokes or Navier-Stokes equation problems (54? 55? 56?
> 57?) may even implement something that applies multigrid already to the
> A block of the Stokes system. You may then want to replace that
> multigrid method by a matrix-free version. I'll let others comment on
> how this can best be done.
>
> My approach is different, I'm using B-S method that I mentioned in my
post. The smoother works on whole problem (not on blocks), the smoothing
operation is done by applying inverse of following matrix:
(S{A} B^T
B 0)
Where S(A) is some simple preconditioner for A (e.g. SSOR, Jaccobi etc).
I've already tested it for standard matrices and it works surprisingly well
for standard Stokes equation. The only problem with doing it in matrix-free
way is multiplication by block.
However in mine application slightly modified Stokes equation appears and I
will need to do some multigid for blocks inside multigrid.
>
> Yours is a case that I think a lot of people would be interested in,
> myself included. If you get it to work, could I interest you in thinking
> about whether your program could be made into either a tutorial program
> or a contribution to the code gallery?
>
I'm probably going to publish my method. Since I do not have mathematica
proof for it I'm thinking of publishing source code.
>
> Best
> W.
>
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