[petsc-users] Poor multigrid convergence in parallel

[Jed Brown]

Lawrence Mitchell <lawrence.mitchell at imperial.ac.uk> writes:
> So my coarse space is spanned by the fine one, so I copy coarse dofs to the corresponding fine ones and then linearly interpolate to get the coefficient value at the missing fine dofs.  

Good, and is restriction the transpose?

Some people mistakenly use nodal injection and not surprisingly see poor
convergence because the restriction operator aliases high frequencies at
full amplitude and the prolongation is accurate for neither high or low
frequencies.  (HPCG does this, for example.)

>> It's odd for the estimates to require that many iterations unless the
>> RHS is somehow degenerate.  I was hoping that a random right hand side
>> would excite the higher mode sooner.
>
> I had another look and it turns out this does work, I was driving the
> options database incorrectly the first time round.  I needed to run
> with both estimate_eigenvalues and estimate_eigenvalues_random.
>
> If I run with:
>
> -pc_type mg -ksp_max_it 6 -pc_mg_levels 2 -ksp_monitor -mg_levels_1_ksp_chebyshev_estimate_eigenvalues_random -mg_levels_1_ksp_chebyshev_estimate_eigenvalues
>
> Then I get decent estimation of the higher modes and good convergence.

Excellent.
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