[Dune] The subentity numbering again...

[Sven Marnach]

Hi all,

last week I had a long phone call with Martin.  Among other things, we
discussed again the possibilities of changing the subentity numbering.

After discussion among the people in Heidelberg, we suggest the
follwoing changes to the current generic numbering:

 1. The old 2D simplex numbering is recovered by special-casing.  This
    special case is used as a basis for recursively building higher
    dimension simplices.  These will be numbered generically according
    to the rules in 2.

 2. When recursively building the higher dimension simplex E° from a
    simplex E, the subentities are numbered in the following way:

      * First, all subentities of E° which are not part of E get the
        numbers of the subentities of E which they are based on.

      * Then the subentities of E° which are contained in E are
        numbered consecutively in the same ordering as they were
        numbered before.

    This will recover opposite-vertex numbering for the faces of a
    simplex of any dimension, except for the 1D simplex (but in the
    case of 1D simplces, opposite-vertex numbering would mean that a
    vertex should get a different number when the vertex is considered
    as a face).

 3. The cubes will retain their current generic numbering (i.e. the
    one introduced by Martin and Andreas).

 4. The numberings of prisms and pyramids change according to the
    rules in 2.

This numbering has the following advantages:

 1. The numbering in 2D will be completely the same as before.  Many
    people only have 2D codes, which will essentially work unchanged
    (of course, method calls have to be changed to the new method
    names).

 2. In 3D, the old numbering of vertices and faces is preserved for
    cubes and simplices.  Only the edge numbering of simplices and
    cubes will change.  This will not affect as many people as
    renumbering faces.

 3. Simplices will retain opposite-vertex numbering.  This is what
    most people expect because it is already used in school.  It is
    also more intuitive for P1 finite elements.  (People _really_
    expect this.  We were already asked why on earth we adopted a
    numbering which does not have opposite-vertex numbering.)

 4. The faces of 2D simplices will be numbered anticlockwise, which
    again is what most people expect.

Martin thinks that these changes would be possible whith some minor
changes to the current code.

What is the opinion of the DUNE developers on this topic?  Who is in
favor of adopting this proposal?

Regards from Heidelberg,
    Sven