[Dune] BCRS matrix and matrix operations

[Oliver Sander]

Hi Arne!
You are right, BCRSMatrix does not support matrix-matrix-multiplication.
The reason is that such a multiplication cannot be implemented efficiently
with compressed row storage, and it is recommended to avoid it.

In many Schur-complement methods you don't actually need the matrix S.
If, for example, you want to use a cg method to solve Sq=r, all you need is
to be able to compute matrix-vector products with S.  You can do that
without ever actually computing S.

Now if you really really need S computed I'm afraid you'll have to code
the multiplication yourself.

best wishes,
Oliver

Arne Rekdal schrieb:
> Hello,
>
> I have this system of equations: (where ' denotes the transpose of the  
> matrix)
> |	B	-C'	D'	|	v		f
> |	C  	0	0	|	p	=	0
> |	D	0	0	|	q		g
>
> I have chosen to use BCRS-matrices to represent the matrix blocks B, C  
> and D, since these have few non-zero element. This system is  
> indefinite, so by applying Schur-complement reduction twice, I achieve  
> the following positive definite system
>
> Sq=	r
>
> where S is some product of the matrices B^(-1), C and D. (B is  
> diagonal so it is trivial to invert)
>
> My question is, how can this be done with the BCRS matrix in DUNE? My  
> problem is that it seems the BCRS-matrix lacks the Matrix-Matrix  
> product, and also the transpose operation, so I am not able to  
> generate the matrix S.
>
>
> Thank you!
>
>
> Best regards
> Arne Rekdal
>
> _______________________________________________
> Dune mailing list
> Dune at dune-project.org
> http://lists.dune-project.org/mailman/listinfo/dune
>   


-- 
************************************************************************
* Oliver Sander                ** email: sander at mi.fu-berlin.de        *
* Freie Universität Berlin     ** phone: + 49 (30) 838 75348           *
* Institut für Mathematik      ** URL  : page.mi.fu-berlin.de/~sander  *
* Arnimallee 6                 ** -------------------------------------*
* 14195 Berlin, Germany        ** Member of MATHEON (www.matheon.de)   *
************************************************************************