# [petsc-users] DIVERGED_INDEFINITE_PC in algebraic multigrid

Jed Brown jed at jedbrown.org
Mon May 19 17:30:06 CDT 2014

```Michele Rosso <mrosso at uci.edu> writes:

> Jed,
>
> By using the options you suggested, namely /-mg_levels_ksp_type
> richardson -mg_levels_pc_type sor/, I was able to
> solve without bumping into the DIVERGED_INDEFINITE_PC message.
> Nevertheless, the number of iterations increases drastically as the
> simulation progresses.

What about SOR with Chebyshev?  (A little weird, but sometimes it's a
good choice.)  If the solve is expensive, you can add a few more
iterations for eigenvalue estimation.

> The Poisson's equation I am solving arises from a variable-density
> projection method for incompressible multi-phase flows.
> At each time step the system matrix coefficients change as a consequence
> of the change in location of the heavier phase; the rhs changes
> in time because of the change in the velocity field. Usually the
> black-box multigrid or the deflated conjugate gradient method are used
> to solve efficiently this type of problem: it is my understanding -
> please correct me if I am wrong - that AMG is a generalization of the
> former.

Dendy's "black-box MG" is a semi-geometric method for cell-centered
discretizations.  AMG is not a superset or subset of those methods.

> The only source term acting is gravity; the hydrostatic pressure is
> removed from the governing equation in order to accommodate periodic
> boundary conditions: this is more a hack than a clean solution. Could it
> be the reason behind the poor performances/ DIVERGED_INDEFINITE_PC
> problem I am experiencing?

If you have periodic boundary conditions, then you also have a pressure
null space.  Have you removed the null space from the RHS and supplied
the null space to the solver?
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