KSP solver efficiency

[Yixun Liu]

Matthew Knepley wrote:
> On Fri, Feb 13, 2009 at 4:37 PM, Yixun Liu <enjoywm at cs.wm.edu
> <mailto:enjoywm at cs.wm.edu>> wrote:
>
>     Hi,
>     Assume  Ku=F is  a linear system assembled from element stiffness
>     matrix. I want to use KSP to solve Ku=F. Assume the size of K is
>     100x100
>     and the number of processors is 4.
>     The question is does the efficiency of KSP depend on the structure
>     of K?
>     For example if each process owns 25 rows does the efficiency of the
>     solver depend on the structure of K?
>
>
> 1) Strictly, yes it does.
>
> 2) Practically, not very much. You want to have at least a decent
> partition, but
>     after that the communication load is small since its a PDE, and
> scales well.
>
> 3) Everything depends on the type of PDE. Krylov solvers will not work
> well for
>     everything, but for elliptic things they are good.
>
>   Matt
>  
>
>
>     Thanks.
>
>     Yixun
>
> -- 
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which
> their experiments lead.
> -- Norbert Wiener
If in practice we assume the efficiency of KSP doesn't rely on the
structure of K, do we need to partition?