[petsc-users] Poor multigrid convergence in parallel

[Jed Brown]

Lawrence Mitchell <lawrence.mitchell at imperial.ac.uk> writes:
> Bog-standard P1 on a pretty much regularly meshed square domain (i.e. no reentrant corners or bad elements).

What interpolation is being used?  The finite-element embedding should
work well.

>> 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.

Can you add 

  -ksp_chebyshev_estimate_eigenvalues_random

I wonder if you have a degenerate right hand side that is not exciting
the largest eigenvalues on two processes.  Anyway, try switching from
GMRES to CG for computing the eigenvalue estimates and also using more
iterations.
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