[petsc-users] DIVERGED_NANORING with PC GAMG

[Jed Brown]

"Appel, Thibaut" <t.appel17 at imperial.ac.uk> writes:

> Jed, Mark,
>
> Attached are the equations I’m solving.
> p is perturbation pressure (unknown)
> \bar{u} is a base flow (KNOWN) that carries the perturbation velocity field we’re solving for too: u (unknown)

This looks like a frequency domain problem associated with
incompressible flow.  The real-valued part alone is a generalized saddle
point problem and not suitable for direct application of algebraic
multigrid.  (It's common to use fieldsplit first.)  The imaginary shift
is not as bad as a negative shift (the undamped case for Helmholtz).

> -> Unknown vector is (p,u,v)^T
>
> The right hand side intervenes at the wall where we apply some forcing.
>
> What do you mean by low-frequency Helmholtz?

The Helmholtz equation is the frequency domain acoustic wave equation.
High frequency usually means that the number of grid points per
wavelength is small, consequently the smallest eigenvalues correspond to
relatively oscillatory eigenvectors -- this makes multigrid-type
approximation difficult in theory and practice.

> (Please re cc’ petsc-users if you wish,
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