[dune-pdelab] some problems in dune

[Markus Blatt]

Hi,

On Fri, Oct 31, 2014 at 02:08:50PM +0100, Rebecca de Cuveland wrote:
> why did you change the coarsentarget parameter? The default is
> somewhere at 1000 nodes, and it seems you have 1? That is certainly
> not a reasonable choice. (You have only one unknown on your coarsest
> level).
> 
> I also see in your code that you do not use Superlu as solver on the
> coarsest level (usesuperlu = false). As the warning that you
> explicitly supress with this flag states: Use superlu, sometimes
> this has a drastic impact on the solution.
> 
> Does something change, when you use superlu and a coarsentarget of
> at least 100 (or even more)?
> 
> One last thing, we spoke about AMG in combination with Q2 today in
> our group meeting:
> Nobody has really used this in pdelab, and we are not sure if the
> implementation in istl is also valid for Q2. Perhaps Markus can say
> something about that?
> 

I never used the vanilla AMG  with higher order discretization. Given
that our interpolation is piecewise constant, I would not expect good results
here. (IMHO  even geometric multigrid  would need/use special
interpolation operators for this.) The problem probably is the
interpolation between the two finest levels. To test this you could try to
use SuperLU as coarse level solver and set the maxLevel parameter to 1 to
get a two level method. If I am right you should experience a similar
convergence behaviour as for your tests.

You might be able to increase the convergence slightly by increasing the number
of post-smoothing steps. But that will probably not give you
h-independant convergence.

As you realized in one of your other emails, the solver cannot see
that you are using higher order elements just from the input
matrix. Ergo the solver as it is will not give you optimal results. To
get these you might have to adjust it similar to the way that Peter
and me have done for discontinuous Galerkin methods in
dune/pdelab/backend/istl/ovlp_amg_dg_backend.hh. That approach take
into account the basis functions.

Markus


-- 
Do you need more support with DUNE or HPC in general? 

Dr. Markus Blatt - HPC-Simulation-Software & Services http://www.dr-blatt.de
Hans-Bunte-Str. 8-10, 69123 Heidelberg, Germany
Tel.: +49 (0) 160 97590858
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