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

[Jed Brown]

On Tue, Nov 15, 2011 at 12:03, Brandt Belson <bbelson at princeton.edu> wrote:

> I'm not sure what you mean by the sign of the shift, but the equations are
> roughly of the form:
>
> (I dt/Re - L) u = f
>
> where dt~0.1, Re~1000, and L is the Laplacian in 3D,
>

The time step size is in the numerator? (It's more commonly the other way.)

In any case, this is a positive shift, so you always have a positive
definite operator. Multigrid should work very well, so you shouldn't need
to bother with direct solvers.


> so once it is Fourier transformed each x-y plane has equations like this:
>
> (I dt/Re + I k_z^2 - L_{k_z}) \hat{u}_{k_z} = \hat{f}_{k_z}
>
> I'm not sure which wavenumber you mean, but k_z goes as nz.
>

It arises for frequency-domain problems where the shift is in the other
direction (producing an indefinite operator).
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