[Dune] GridPaper...

[Andreas Dedner]

Hi all,
Robert and myself have sat down and tried to insert a
suitable grid definition into the paper. Unfortunately this
work was done at same time as the revisions from Oliver so that
there is some conflict. For better comparison we have only
attached our suggestion.

The basic concepts behind our revision is the following:
1) For a fixed set of verticies we define all possible entities E
   - no changes here...
2) Then relations $ and F are defined
These definitions are done starting from codim c=d down to c=0
3) Now we define a hierarchic tessilation of a domain $Omega$
   This is a starting point for a grid but basically it is
   just a subset of all entities fulfilling some properties.
Starting from this definition all the following definitions follow
the concept: start at codim c=0 and go up to c=d. This is close to
the philosophy in DUNE.
4) Now we define leaf/level tessilations and the domain Theta_j
   as used before. In the original version these were always defined
   based on all possible entities E now these definitions are based
   on a given hierarchic tessilation.
5) Now we have intersions and geometries
Now we define a data decompostion based on a hierarchic tessilation of
a domain Omega.
The actual definition of a grid is somewhat trivial but could
now include all things a DUNE grid knows about.

Section 6 is still in the original form...

Some remarks:
1) should we include the father relation on codim>0 entities.
   This relation is not modeled in DUNE
   (actually subentities are not even part of the interface at the
   moment).
2) There is some confusion concerning the level II at interior
   level boundaries. Should the II stop in this case and what is
   boundary(), neighbour()... (boundary=neighbor=false?)
   The DUNE documentation seems to say that the II stops in this
   case but the values of boundary() and neighbor() are not mentioned.
   The paper says that no intersection is generated...
3) The leaf definition is simpler than before prehaps we have missed
   some problem here? Instead of some sarcastic remark a real
   explanation would be welcomed - if both Robert and myself do not
   see the importants of the original definition than a external
   reader would probably have similar problems...

Have fun
Robert and Andreas


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