[Dune] Bemerkung Gitter und Gitterhierarchie.

[Andreas Dedner]

> I see this like Robert and Mario. In DUNE a grid is a
> container of 
> entities with certain relations. In Olivers words it is
> always a grid hierarchy, or I would say a hierarchical
> grid. I think this is also clear after one has read the
> paper. But Oliver has a point if many people do not
> anticipate a hierarchical structure if the read the word
> "grid". But for those it is sufficient to write a
> sentence in the introduction (and I think it says
> somewhere that grids in Dune are always understood to be
> hierarchical).

I do not realy see that we need a grid to be hierarchical
we just need the following (after we have defined 
entities and subentities):
1) a grid is a container of entities
2) if e is a entity in G then all subentities of e are
   also in G
3) we assume that for two entities e,e' in G we have
   e cut e' not empty -> e subset e' or e' subset e 
4) For each entity<0> e in G we define
   a) C(e)={e' entity<0> in G : e' real subset of e}
   b) F(e)={e' entity<0> in G : e real subset of e'}
5) e = union of C(e)
6) level(e) = |F(e)|
7) father(e) = e' in F(e) with level(e') = level(e)-1
8) Hierarchic iterator : iteration over C(e)  
9) level l view = all entities with level(e) = l
10) leaf view    = all entities with C(e) = empty
I think this defines a grid.
Andreas