[petsc-users] Convergence of AMG

[Mark Adams]

* 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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