[Dune] Non-unique coordinate mappings of Codim(1) entities?

[Andreas Dedner]

Hi,

the map is (at the moment) the only possible solution I think.
I would suggest orderning intersection so that the inside
entity is alsways the one with the lower index - in the conform
case. In the non-conform case the inside entity should be the
one with the higher level (having the ''smaller'' intersection, that
on most grids dees correspond to an codim 1 entity).

The orientation is now also not a problem since you have a unique
(inside,outside) paring and can always take the geometry from the
inside entity, e.g., the one with the higher level or lower index, if
levels are equal.

Best
Andreas

On 06/07/2010 08:13 PM, Christian Waluga wrote:
> Hi,
>
> Am 07.06.2010 um 19:20 schrieb Christian Engwer:
>    
>>> I am trying to implement  a hybrid DG method using DUNE and I have a
>>> problem with the mapping feature of the intersections. In addition
>>> to my element DOFs, I have an additional function living on the
>>> trace of the grid, i.e. I have some DOFs distributed on the faces of
>>> the mesh. The intersections of the elements seem to be associated
>>> with the codim 1 entities of the mesh, but the orientation of their
>>> geometries seems to be not unique in my experiments (using
>>> ALUSimplexGrid<2,2>).
>>>        
>> no, the intersections do not (necessarily) correspond to the codim1
>> entities. Intersections are of codim1, but they are not an entity of
>> the grid.
>>      
> Yes, that's true. I think I see where the problem is, now that you gave an example with a nonmatching mesh. In the nonmatching case, the intersections can map to the inside and outside geometry, but the codim 1 entities e1 and e2 in my example might indeed differ.
>
> My problem now is the following: I need to define finite element functions on the trace (they couple with the element-wise discontinuous functions in the hybrid DG method). But intersections in Dune seemed to me like temporary element-specific objects, so I did not consider to create a map that does an indexing of intersections to compute the local to global mapping of the DOFs. Therefore I defined my DOFs on the codim 1 entities, but this will definitely fail, if the mesh is nonmatching and I'm not very comfortable with my solution.
>
> So, intersections are not entities of the grid, but codim 1 entities are also not the entities I want to define my trace finite element space on. Intersections can also not be easily indexed, as far as I know... My idea to solve this is to create a map that identifies the 'unique' intersection from the pair indices of is.inside() and is.outside(). So e.g. intersection 1 is between elements 2 and 3, intersection 2 is between elements 1 and 2, etc... What remains is the problem with the orientations in the coordinate mappings of the intersection-geometries in the 'inside' and 'outside' element. Or is there a more elegant way to construct a trace finite element space (dofs living on the intersections) like the one I need? I have a feeling that the solution might be easier than I think.
>
> Thanks for any response!
>
> Best, Chris
>
>
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