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

[Jed Brown]

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
Helmholtz.
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