[petsc-users] Poor multigrid convergence in parallel

[Lawrence Mitchell]

On 25 Jul 2014, at 21:28, Jed Brown <jed at jedbrown.org> wrote:

> Sorry about not following up.  I also find these results peculiar.
> 
> Lawrence Mitchell <lawrence.mitchell at imperial.ac.uk> writes:
>> So I'm sort of none-the-wiser.  I'm a little bit at a loss as to why
>> this occurs, but either switching to Richardson+SOR or Cheby/SOR with
>> more that one SOR sweep appears to fix the problems, so I might just
>> punt for now.
> 
> What discretization and mesh is this running on?

Bog-standard P1 on a pretty much regularly meshed square domain (i.e. no reentrant corners or bad elements).

> Is there something special about the decomposition with 2 subdomains?

It doesn't look like it, the two subdomains are about the same size.

> Are the Chebyshev estimates far from converging?

So for the two-level problem, if I compute the extremal eigenvalues of the preconditioned operator being used as a smoother I get (approximately):

1 process:
0.019, 1.0

2 processes:
0.016, 1.4

3 processes:
0.016, 1.36

The eigenvalue estimates (from ksp_view) are:

1 process:
0.09, 1.01

2 processes:
0.09, 1.01

3 processes:
0.13, 1.47


When I bump to more levels, the estimates are only bad on two processes on the finest grid.

So for example running with something like (for a 3 level problem):

-pc_type mg -mg_levels_2_ksp_chebyshev_eigenvalues 0.09,1.4 

gives me good convergence on two processes where the extremal eigenvalues on the finest grid are:

0.016, 1.39


Cheers,

Lawrence
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