[dune-functions] Parallelization of GlobalBasis

[Simon Praetorius]

While the GlobalGridView seems to work (what ever this means), some
other parts of the MR are more experimental and, e.g., the parallel
poisson equation does not work correctly. Also, it is quiet inefficient,
since the same communication needs to be performed multiple time to
build up the parallel indexset. Essentially, to build up the
GlobalIndexSet we need at least two communications over the grid and
then the same communications again on the ParallelIndexSet and
RemoteIndices. This is not very efficient. If the GlobalIndexSet is just
used to identy uniquely all DOFs, it is not worth building this up. A
better approach is something that can be computed locally, to have a
global indentification of all DOFs, e.g. a global ID-Set for basis
functions.

With just the globalIndexSet one cannot directly build any parallel
linear algebra. One needs more information about the overlap of DOFs and
who has to communicate with whom. This is not encoded in the
GlobalIndexSet, but in the RemoteIndices. A ScalarProduct also needs the
information whether the local DOF should be added up to the global value
or not.

There are a lot of open questions. I do not have answers for all of them.

Am 11.11.21 um 08:12 schrieb Oliver Sander:
>
> Hi Simon,
>
>> So far so good. [The GlobalGridView] works fine and is implemented in
>> the branch
>> feature/parallel-grid-view. 
>
> thank you!  I recently realized that this is what I need to replace
> a lot of hand-written goo in a central part of my code.  Would you
> be able to open a merge request to make code review easier?
>
> Best,
> Oliver
>
>
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-- 
Dr. Simon Praetorius
Institut für Wissenschaftliches Rechnen
Fakultät Mathematik
Technische Universität Dresden
Tel.: TUD-34432
Mail: simon.praetorius at tu-dresden.de
Web: https://tu-dresden.de/mn/math/wir/das-institut/beschaeftigte/simon-praetorius

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