[Dune] hanging node detection

[Bernd Flemisch]

Hey Carsten, hey Dune,

thank you for your hints. I implemented it and it seems to 
work. However, I came across another issue: I try to 
construct a macro triangulation with hanging nodes via a 
DGF file, see e.g. the attached file. Both ALU and UG 
create a boundary along the interface containing the 
hanging node, so it is not possible to get to the neighbor 
via the intersection. Does that mean that for ALU and UG, 
it is only possible to construct conforming macrogrids 
with correct neighbor information? Or is there some other 
way?

Thank you. Kind regards
Bernd

On Thu, 13 Oct 2011 22:21:42 +0200
  Carsten Gräser <graeser at math.fu-berlin.de> wrote:
> Am 13.10.2011 17:29, schrieb Bernd Flemisch:
>> Hey Carsten,
>> 
>> that does not sound so bad, I will try that.
> Just a few hints for the implementation:
> 
> * If you want to use local finite elements you need to
>  wrap a single local basis functions of one element
>  to take local coordinated wrt the other. This
>  requires to compute x_Alocal -> x_global -> x_Blocal
>  while x_Alocal -> x_intersection_local -> x_Blocal
>  does not work.
> 
> * You might want to implement caching since one cannot
>  implement a single local basis function at once.
> 
> * If you really only want to know if a node is
>  hanging the following does essentially the same
>  but seems to be much simpler:
> 
>  For each vertex of element A compute the local
>  coordinates and barycentric coordinates in B.
>  Then the node is hanging if any of these
>  coordinates is in (0,1). The barycentric
>  coordinates can be computed using the P1
>  local fe.
> 
> Best,
> Carsten
> 
>> 
>> Thank you for your fast answer. Kind regards
>> Bernd
>> 
>> On Thu, 13 Oct 2011 17:05:22 +0200
>>  Carsten Gräser <graeser at math.fu-berlin.de> wrote:
>>> Hello Bernd,
>>>
>>> Am 13.10.2011 16:18, schrieb Bernd Flemisch:
>>>> Dear Dune,
>>>>
>>>> can you recommend a way of detecting whether a node is 
>>>>hanging or not?
>>>> It's easy if the neighboring elements are on different 
>>>>levels, but let's
>>>> assume they are on the same. I can think of comparing
>>>> intersection.geometryInInside and 
>>>>intersection.geometryInOutside, but
>>>> maybe there is something nicer?
>>>
>>> in dune-fufem we construct conforming fe spaces on grids 
>>>with
>>> hanging nodes in the following way:
>>>
>>> For each pair of neighboring elements we evaluate the 
>>>local
>>> interpolation on one element for all local basis 
>>>functions
>>> of the other. This gives you the weights you need to 
>>>construct
>>> the conforming composite basis function. This does at 
>>>least
>>> work for Pk,Qk, and RefinedP1 local finite elements on 
>>>grids
>>> with conforming level grids.
>>>
>>> If level grids are not conforming you can still use
>>> this approach with P1/Q1 elements to find the hanging 
>>>nodes
>>> which are just the ones associated to all weights in 
>>>(0,1).
>>> Of coarse you must check this with some epsilon. However 
>>>this
>>> is safe for all reasonable grids.
>>>
>>> This approach does essentially wrap all coordinate 
>>>computations
>>> in a nice way. There might be faster ways to check this, 
>>>however
>>> you cannot avoid to do some coordinate computations 
>>>because this
>>> is the only way to check if a vertex is contained in a 
>>>face if
>>> it is not a node (or copy of one) of the face.
>>>
>>> Best,
>>> Carsten

___________________________________________________________

Bernd Flemisch                     phone: +49 711 685 
69162
IWS, Universitaet Stuttgart          fax: +49 711 685 
67020
Pfaffenwaldring 61        email: 
bernd at iws.uni-stuttgart.de
D-70569 Stuttgart        url: 
www.hydrosys.uni-stuttgart.de
___________________________________________________________
-------------- next part --------------
A non-text attachment was scrubbed...
Name: test_1p_2d.dgf
Type: application/octet-stream
Size: 279 bytes
Desc: not available
URL: <https://lists.dune-project.org/pipermail/dune/attachments/20111018/a3182f46/attachment.obj>