[petsc-users] Compact finite differences

[Matthew Knepley]

On Fri, Jun 22, 2012 at 9:03 AM, Gaetano Esposito <
gaetano at email.virginia.edu> wrote:

> Compact finite differences have been already discussed in this post
> and following responses:
> http://lists.mcs.anl.gov/pipermail/petsc-users/2011-November/011006.html.
>
> If I understand well, the matrix for a 2-D (or 3-D) *implicit* solver
> that makes use of compact FD for the calculation of derivatives is not
> "banded" because of the ordering of the x-y-z variables in the
> solution vector destroys any structure, and the matrix is simply
> sparse (bandwith=sqrt(n)). In that post is actually suggested that a
> sparse dense solver could be more attractive because of that.
>

The blocks are banded, although in 3D these bands are really wide so I
don't think it would make sense anymore to use banded solvers.

   Matt


> However, if the PDE's are solved explicitly in time, the derivatives
> in all directions may be calculated independently by using an
> efficient sequential algorithm (o(n)). I am not familiar with any
> parallel implementations of the banded diagonal algorithm solvers, but
> I was wondering whether this could be efficiently implemented in Petsc
> with the existing MA modules. But at that point, I don't know whether
> there will be any advantage in possibly using an iterative solver that
> converges to the exact solution in N iterations for a well behaved
> matrix as the one deriving from compact FD.
>
> --g
>



-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120622/5ea3c24d/attachment.html>