[Dune] Reference hexahedron

[Oliver Sander]

Hallo!
Ob der vielen neuen Entwicklung hätte ich doch _bitte_ bald
mal wieder ein Gesamttreffen.  Bin ich denn der einzige,
der daran Interesse hat?  Zu diskutieren gibt es ja wohl
genug.

Grüße,
Oliver

************************************************************************
* Oliver Sander                **                                      *
* Freie Universität Berlin     ** email: sander at math.fu-berlin.de      *
* Institut für Mathematik II   ** phone: + 49 (30) 838 75217           *
* Arnimallee 2-6               ** fax  : + 49 (30) 838 54977           *
* 14195 Berlin, Germany        ** URL  : www.math.fu-berlin.de/~sander *
************************************************************************

On Wed, 4 May 2005, Peter Bastian wrote:

> Adrian Burri schrieb:
>> Hi everyone!
>> 
>> I've got a question regarding the reference element for a hexahedron: is 
>> there a convention for the local numbering of the vertices on the faces of 
>> the hexahedron? (Say, I want to write something like 
>> hexa.myvertex(hexaFaceIndex, vertexIndex), hexaFaceIndex \in {0, 5}, 
>> vertexIndex \in {0, 3}, which is the corresponding index hexaVertexIndex 
>> \in {0, 7} of the hexahedron?)
>> 
>> Another question: is the face numbering of the hexahedron on the Dune 
>> homepage indeed correct? (Shouldn't be 2 at the front and 4 at the bottom?)
>> 
> I have written an interface for reference elements that includes also the 
> numbering of all subentities and it is algorithmically generated:
>
>  //! This is the abstract base class for reference elements
>  template<typename ctype, int dim>
>  class ReferenceElement
>  {
>  public:
>
> 	// compile time sizes
> 	enum { d=dim };    // maps from R^d
>
> 	// export types
> 	typedef ctype CoordType;
>
> 	//! number of entities of codim c
> 	virtual int size (int c) const = 0;
> 		//! number of subentities of codim cc of entitity (i,c)
> 	virtual int size (int i, int c, int cc) const = 0;
> 		//! number of ii'th subentity with codim cc of (i,c)
> 	virtual int subentity (int i, int c, int ii, int cc) const = 0;
>
> 	//! position of entity (i,c)
> 	virtual const FieldVector<ctype,dim>& position (int i, int c) const = 
> 0;
>
> 	//! type of (i,c)
> 	virtual GeometryType type (int i, int c) const = 0;
>
> 	//! volume of the reference element
> 	virtual double volume () const = 0;
>
> 	//! virtual destructor
> 	virtual ~ReferenceElement ()
> 	{}
>  };
>
>
>
> You can look at it by checking out dune-dd. It is implemented for cubes of 
> all dimensions and Sreejith is currently doing the simplices, the pyramid and 
> the prism. With this class I wrote P2 shape functions without any implicit 
> knowledge about the local numbering of the entities.
>
> I could check in all that we did. Whats the opinion of the others?
>
> Cheers,
>
> -- Peter
> ------------------------------------------------------------------
> Peter Bastian, IWR,Uni Heidelberg, INF 348,R 020, 69120 Heidelberg
> email: Peter.Bastian at iwr.uni-heidelberg.de   Tel: +49 6221 54 4984
> WWW: http://www.iwr.uni-heidelberg.de/~Peter.Bastian Fax: ... 8860
>
>
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