[petsc-users] GAMG and near-null-space when applying Dirichlet Conditions

[Mark Adams]

On Fri, Feb 26, 2016 at 12:19 PM, Manav Bhatia <bhatiamanav at gmail.com>
wrote:

> I have now experimented with different AMG solvers (gamg, ML, hypre )
>  through petsc, and have a mixed bag of results. I have used
> -pc_gamg_threshold 0.1 for all cases.
>

This should be -pc_gamg_agg_threshold X, and 0.1 is way too high.  a
negative number keeps all entries that you add in the matrix, zero drops
only zero entries, > 0 drops stuff.  0.05 is at the high end of what is
probably useful, but you can check.  This is a very problem dependant
parameter.



>
> The problem is that of plate-bending that is clamped on all ends, and has
> a uniformly distributed load.
>
> The problem has 6 dofs per node: {u, v, w, tx, ty, tz}.  u, v are the
> in-plane deformations related to membrane action. w, tx, ty get the
> stiffness from the Mandlin first-order shear deformation theory. tz doesn’t
> really do anything in the problem, and the stiffness matrix has small
> diagonal values to avoid singularity problems.
>
>
> I have tested AMG solvers for number of unknowns from a few hundred to
> about 1.5e6.
>
> First off, I am absolutely thrilled to be able to solve that large a
> system of equations coming from a bending operator on my laptop! So a big
> thanks to the petsc team for giving us the tools!
>
> I have not done a very thorough convergence study, but following are some
> general observations:
>
> — Without providing the near null space, all three solvers work.
>
> — The convergence of the solvers is significantly better when the near
> null space is provided. There are 6 near-null space modes provided: 3
> rigid-body translations and 3-rigid body rotations.
>
> — With the near null space provided, both hypre and ML work without
> problems, but GAMG quits the error of zero-pivot in LU decomposition. I am
> guessing this happens for the coarsest level. I was able to get around this
> with -mg_levels_pc_type jacobi . (I saw some earlier discussion on the
> mailing list about this, and got the sense that this may be a
> non-deterministic issue (?) ).
>
> — With -pc_gamg_threshold 0.1 and -pc_mg_type full, I get the fastest
> convergence from ML.
>
> — GAMG seems to take about twice the amount of memory than ML.
>
>
> I am now keen to play around with various parameters to see how to
> influence the convergence.
>
> Any comments would be greatly appreciated.
>
> Regards,
> Manav
>
>
>
> On Feb 25, 2016, at 6:21 AM, Mark Adams <mfadams at lbl.gov> wrote:
>
> I added ", which is often the null space of the operator without boundary
> conditions" to the web page doc for MatSetNearNullSpace.
>
> On Wed, Feb 24, 2016 at 10:57 AM, Matthew Knepley <knepley at gmail.com>
> wrote:
>
>> On Wed, Feb 24, 2016 at 9:45 AM, Manav Bhatia <bhatiamanav at gmail.com>
>> wrote:
>>
>>> Hi,
>>>
>>>     I typically apply Dirichlet BCs by modifying the Jacobin and rhs:
>>> zero constrained rows of matrix with 1.0 at diagonal, and zero
>>> corresponding rows of rhs.
>>>
>>>     While using GAMG, is it still recommended to provide the near-null
>>> space (given that the zero-eigenvalues have been removed by specification
>>> of DIrichlet BCs)?
>>>
>>
>> Yes.
>>
>>
>>>     If that information is still needed, should the vectors be modified
>>> in any manner to be consistent with the Dirichlet BCs?
>>>
>>
>> No. You can see that if you take a small piece of the domain, apart from
>> the boundary, it will have this as a null space.
>>
>>   Matt
>>
>>
>>> Thanks,
>>> Manav
>>>
>>>
>>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>
>
>
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