[petsc-users] Convergence of AMG

[Mark Adams]

Nicolas,

Smoothed aggregation is fine with shells. see the original SA paper (
https://link.springer.com/article/10.1007/BF02238511).

The rotational modes, which are the non-trivial modes that must be
supplied, are used in the interpolation.

Mark

On Tue, Oct 30, 2018 at 5:22 AM Karin&NiKo <niko.karin at gmail.com> wrote:

> Manav,
>
> How are interpolated the rotational degrees of freedom? AFAIK, when using
> smoothed aggregation, the interpolation process tries to mimic linear
> interpolation, which can be OK for the displacement DOF but is not for the
> rotational DOF using some plate and shell formulations.
> This can explain poor convergence of a multilevel approach, which needs to
> restrict and extrapolate the unknowns. In order to check this hypothesis,
> you can try a test case with zero rotations.
>
> Nicolas
>
> Le lun. 29 oct. 2018 à 22:13, Mark Adams via petsc-users <
> petsc-users at mcs.anl.gov> a écrit :
>
>> * the two level results tell us that MG is not doing well on the coarse
>> grids. So the coarse grids are the problem.
>>
>> * Do not worry about timing now. Get the math correct. The two level
>> solve is not meant to be a solution just a diagnostic so don't try to
>> optimize it by squaring the graph. Use -pc_gamg_square_graph 0.
>>
>> * It looks like you don't need 4 smoothing steps but lets keep it and we
>> can dial it back later.
>>
>> * This table is interesting. First, you had about 12 iterations earlier
>> and I think your rtol was tighter than the default (so the iteration could
>> should go down not up). Do you know what change here?
>>
>> Note, even though -mg_levels_ksp_max_it is not in the ksp_view it does
>> work. It is syntactic sugar to just add it to all levels like you did
>> manually.
>>
>> Anyway, these number look reasonable. It is interesting that 3 levels ran
>> well but the 4th level ran poorly. This implies we want to slow down
>> coarsening on these levels, but ...
>>
>> First can you please rerun this experiment with -pc_gamg_square_graph 0.
>>
>> Also, please run with -info. This is very noisy but you can grep on
>> "GAMG" and send that output to us (about 15 lines).
>>
>> Thanks,
>> Mark
>>
>>
>>
>> On Mon, Oct 29, 2018 at 3:34 PM Manav Bhatia <bhatiamanav at gmail.com>
>> wrote:
>>
>>> Barry,
>>>
>>>    Here are some quick numbers with the following options on 4 CPUs and
>>> 543,606 dofs:
>>>
>>> -mg_levels_ksp_max_it 4 -pc_gamg_square_graph 1 -pc_gamg_threshold 0.
>>>
>>>  #levels   |    #KSP Iters
>>> ———————————
>>>      2        |       18
>>>      3        |       18
>>>      4        |       40
>>>      5        |       59
>>>
>>> -Manav
>>>
>>>
>>> On Oct 29, 2018, at 2:06 PM, Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
>>>
>>>
>>>  Exactly how much does it increase with number of levels? Send a chart
>>> number of levels and number of iterations. With say -mg_levels_ksp_maxit 4
>>>
>>>   Thanks
>>>
>>>   Barry
>>>
>>>
>>>
>>>
>>> On Oct 29, 2018, at 12:59 PM, Manav Bhatia <bhatiamanav at gmail.com>
>>> wrote:
>>>
>>> Thanks for the clarification.
>>>
>>> I also observed that the number of KSP iterations increases with an
>>> increase in the levels of AMG. Is this true, in general, for all/most
>>> applications?
>>>
>>> -Manav
>>>
>>> On Oct 29, 2018, at 12:53 PM, Jed Brown <jed at jedbrown.org> wrote:
>>>
>>> Manav Bhatia <bhatiamanav at gmail.com> writes:
>>>
>>> Thanks, Jed.
>>>
>>> The description says: “ Square the graph, ie. compute A'*A before
>>> aggregating it"
>>>
>>> What is A here?
>>>
>>>
>>> The original matrix, or its "graph" (your 6x6 blocks condensed to
>>> scalars).
>>>
>>> What is the impact of setting this to 0, which led to a very significant
>>> increase in the CPU time in my case?
>>>
>>>
>>> The aggregates are formed on the connectivity of your original matrix,
>>> so root nodes are aggregated only with their first neighbors, resulting
>>> in slower coarsening.
>>>
>>>
>>>
>>>
>>>
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