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tetrahedron(7rheolef) [debian man page]

tetrahedron(7rheolef)						    rheolef-6.1 					     tetrahedron(7rheolef)

NAME

       tetrahedron - Tetraedron reference element

DESCRIPTION

       The tetrahedron reference element is

	       K = { 0 < x < 1 and 0 < y < 1-x and 0 < z < 1-x-y }

			      z
			    .
			  ,/
			 /
		       3
		     ,/|`
		   ,/  |  `
		 ,/    '.   `
	       ,/	|     `
	     ,/ 	|	`
	    0-----------'.--------2 --> y
	     `.	 |	,/
		`.	 |    ,/
		   `.	 '. ,/
		      `. |/
			 `1
			    `.
			      ` x

       Curved  high  order  Pk	tetrahedra  (k	>= 1) in 3d geometries are supported.  These tetrahedra have additional edge-nodes, face-nodes and
       internal volume-nodes.

THESE NODES ARE NUMBERED AS

	first vertex, then edge-node, following the edge numbering order and orientation, then face-nodes following the face numbering	order  and
       orientation, and finally the face internal nodes, following the tetrahedron lattice.  See below for edges and faces numbering and orioenta-
       tion.

		       3
		     ,/|`
		   ,/  |  `
		 ,7    '.   `9
	       ,/	|     `
	     ,/ 	8	`
	    0--------6--'.--------2
	     `.	 |	,/
		`.	 |    ,5
		   `4.	 '. ,/
		      `. |/
			 `1
		      P2

NUMBERING

       The orientation is such that triedra (01, 02, 03) is direct, and all faces, see from exterior, are in the direct sens.  References:  P.	L.
       Georges,  "Generation automatique de maillages", page 24-, coll RMA, 16, Masson, 1994.  Notice that the edge-nodes and face-nodes numbering
       slighly differ from those used in the gmsh mesh generator when using high-order elements.  This difference is handled by the  msh2geo  mesh
       file converter (see msh2geo(1)).

IMPLEMENTATION

       const size_t dimension = 3;
       const Float  measure = Float(1.)/Float(6.);
       const size_t n_vertex = 4;
       const Float vertex [n_vertex][dimension] = {
	       { 0, 0, 0 },
	       { 1, 0, 0 },
	       { 0, 1, 0 },
	       { 0, 0, 1 } };
       const size_t  n_face = 4;
       const size_t face [n_face][3] = {
	       { 0, 2, 1 },
	       { 0, 3, 2 },
	       { 0, 1, 3 },
	       { 1, 2, 3 } };
       const size_t  n_edge = 6;
       const size_t edge [n_edge][2] = {
	       { 0, 1 },
	       { 1, 2 },
	       { 2, 0 },
	       { 0, 3 },
	       { 1, 3 },
	       { 2, 3 } };

SEE ALSO

       msh2geo(1)

rheolef-6.1							    rheolef-6.1 					     tetrahedron(7rheolef)

Check Out this Related Man Page

basis(7rheolef) 						    rheolef-6.1 						   basis(7rheolef)

NAME

       basis - polynomial basis

SYNOPSYS

       The basis class defines functions that evaluates a polynomial basis and its derivatives on a point. The polynomial basis is designated by a
       string, e.g. "P0", "P1", "P2", "bubble",...  indicating the basis. The basis depends also  of  the  reference  element:	triangle,  square,
       tetrahedron (see reference_element(2)).	For instance, on a square, the "P1" string designates the common Q1 four-nodes basis on the refer-
       ence square.

       The nodes associated to the Lagrange polynomial basis are also available by its associated accessor.

IMPLEMENTATION NOTE

       The basis class is a see smart_pointer(2)) class on a basis_rep class that is a pure virtual base class for effective bases, e.g. basis_P1,
       basis_P1, etc.

IMPLEMENTATION

       template<class T>
       class basis_basic : public smart_pointer<basis_rep<T> > {
       public:

       // typedefs:

	   typedef basis_rep<T> 			  rep;
	   typedef smart_pointer<rep>			  base;
	   typedef typename basis_rep<T>::size_type	  size_type;

       // allocators:

	   basis_basic (std::string name = "");

       // accessors:

	   std::string name() const;
	   size_type   degree() const;
	   size_type   size (reference_element hat_K) const;

	   void hat_node(
	       reference_element	      hat_K,
	       std::vector<point_basic<T> >&  hat_node) const;

	   void eval(
	       reference_element    hat_K,
	       const point_basic<T>&	     hat_x,
	       std::vector<T>&	values) const;

	   void grad_eval(
	       reference_element    hat_K,
	       const point_basic<T>&	     hat_x,
	       std::vector<point_basic<T> >&  values) const;
       };
       typedef basis_basic<Float> basis;

SEE ALSO

       reference_element(2), smart_pointer(2)

rheolef-6.1							    rheolef-6.1 						   basis(7rheolef)
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