[dune-functions] Parallelization of GlobalBasis

[Simon Praetorius]

Hi,

as discussed in the dune-functions meeting, I started the first attempt
to implement a parallelization of the global bases. The idea is:

- Implement a GlobalGridView that wraps an existing gridView and
provides the GlobalIndexSet from dune/grid/utility instead of its own
IndexSet
- Construct two bases, one with the local GridView, the other one with
the parallel global GridView
- Compute a local-to-global mapping by traversing the local grid

So far so good. This works fine and is implemented in the branch
feature/parallel-grid-view. However, the parallel GlobalGridView is
probably not very efficient. The GlobalIndexSet must be constructed
separately for each codimension. This means multiple communication steps
when constructing an IndexSet for all codimensions. One could reduce
this to only construct those codimensions that are needed to build the
Basis and to bind its LocalView.

Now, I wanted to construct a ParallelIndexSet from dune-common and a
OwnerOverlapCopyCommunication from dune-istl using this pair of global
bases. But there some additional information is missing. We need to know
which DOF belongs to which partition and whether it is "owned" by a
processor. So, we have to find a way to assign one of the three
attributes "owner", "overlap", and "copy" to all DOFs. The computation
of these flags probably requires some additional knowledge and
communication. Essentially the computation of this is as expensive as
the build-up of the GlobalIndexSet and requires a lot code shared with
the indexset implementation.

Maybe do you have an idea how to retrieve the attributes from the
local-to-global mapping?

Best,
Simon

-- 
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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