triangle(7rheolef) [debian man page]

triangle(7rheolef)						    rheolef-6.1 						triangle(7rheolef)

NAME

       triangle - Triangle reference element

DESCRIPTION

       The triangle reference element is

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

NUMBERING

	     y

	     2
	     | +
	     |	 +
	     |	   +
	     |	     +
	     0---------1   x

       Curved high order Pk triangles (k >= 1), in 2d or 3d geometries, are supported.	These triangles have additional edge-nodes and face-nodes.

THESE NODES ARE NUMBERED AS

	first  vertex, then edge-node, following the edge numbering order and orientation, and finally the face internal nodes, following the tri-
       angle lattice.  See below for edge numbering and orientation.

	     2		     2		     2
	     | +	     | +	     | +
	     |	 +	     7	 6	     9	 8
	     5	   4	     |	   +	    10 14  7
	     |	     +	     8	 9   5	    11 12 13 6
	     |	       +     |	       +     |	       +
	     0-----3-----1   0---3---4---1   0--3--4--5--1
		   P2		   P3		   P4

IMPLEMENTATION

       const size_t dimension = 2;
       const Float  measure = 0.5;
       const size_t n_vertex = 3;
       const Float vertex [n_vertex][dimension] = {
	       { 0, 0 },
	       { 1, 0 },
	       { 0, 1 } };
       const size_t  n_edge = 3;
       const size_t edge [n_edge][2] = {
	       { 0, 1 },
	       { 1, 2 },
	       { 2, 0 } };

rheolef-6.1							    rheolef-6.1 						triangle(7rheolef)

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)