[petsc-users] Using petsc for banded matrices and 2D finite differences

Jed Brown jedbrown at mcs.anl.gov
Tue Nov 15 11:12:57 CST 2011

On Tue, Nov 15, 2011 at 10:57, Brandt Belson <bbelson at princeton.edu> wrote:

> The matrix solves in each x-y plane are linear. The matrices depend on the
> z wavenumber and so are different at each x-y slice. The equations are
> basically Helmholtz and Poisson type.

What is the sign of the shift ("good" or "bad" Helmholtz)? If bad, is the
wave number high?

> They are 3D, but when done in Fourier space, they decouple so each x-y
> plane can be solved independently.

> I'd like to run on a few hundred processors, but if possible I'd like it
> to scale to more processors for higher Re. I agree that keeping the
> z-dimension data local is beneficial for FFTs.

That process count still means about 1M dofs per process, so having 500 in
one direction is still fine. It would be nice to avoid a direct solve on
each slice, in which case the partition you describe should be fine. If you
can't avoid it, then you may want to do a parallel "transpose" where you
can solve planar problems on sub-communicators. Jack Poulson (Cc'd) may
have some advice because he has been doing this for high frequency
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