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

[Carsten Gräser]

Am 07.06.2010 20:24, schrieb 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).
Just to specify 'most': Any grid implementation with conforming level
grids satisfies this. This is especially true for the ALUGrid variants
and UG (conforming and nonconforming).

Regards
Carsten

> 
> 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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>>    
> 
> 
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Carsten Gräser           | phone: +49-30 / 838-75349
Freie Universität Berlin | fax  : +49-30 / 838-54977
Institut für Mathematik  | email: graeser at math.fu-berlin.de
Arnimallee 6             |
14195 Berlin, Germany    | URL  : http://page.mi.fu-berlin.de/graeser
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