hexahedron(7rheolef)						    rheolef-6.1 					      hexahedron(7rheolef)

NAME

       hexahedron - Hexaedron reference element

DESCRIPTION

       The hexahedron reference element is [-1,1]^3.

	    ^ z
	    |
	    4----------7
	    |	       |
	    |         | 
	    |         |  
	    |	5------+---6
	    |	|      |   |
	    0---+------3 - | ---> y
	     	|	  |
	       |	  |
	       |	  |
		1----------2
		 
		  x

       Curved  high order Pk hexaedra (k >= 1) in 3d geometries are supported.	These hexaedra 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 hexaedron lattice.  See below for edges and faces numbering and orioenta-
       tion.

	    4----19----7
	    |	       |
	    |16    23  | 18
	   12   21    15 
	    |	5----17+---6
	    |22 |  26  | 25|
	    0---+-11---3   |
	      13    24   14
	      8 |  20	 10|
	       |	  |
		1-----9----2
		    P2

NUMBERING

       The orientation is such that triedra (01, 03, 04) 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 = 8;
       const size_t n_vertex = 8;
       const Float vertex [n_vertex][dimension] = {
	       {-1,-1,-1 },
	       { 1,-1,-1 },
	       { 1, 1,-1 },
	       {-1, 1,-1 },
	       {-1,-1, 1 },
	       { 1,-1, 1 },
	       { 1, 1, 1 },
	       {-1, 1, 1 } };
       const size_t  n_face = 6;
       const size_t face [n_face][4] = {
	       {0, 3, 2, 1 },
	       {0, 4, 7, 3 },
	       {0, 1, 5, 4 },
	       {4, 5, 6, 7 },
	       {1, 2, 6, 5 },
	       {2, 3, 7, 6 } };
       const size_t  n_edge = 12;
       const size_t edge [n_edge][2] = {
	       {0, 1 },
	       {1, 2 },
	       {2, 3 },
	       {3, 0 },
	       {0, 4 },
	       {1, 5 },
	       {2, 6 },
	       {3, 7 },
	       {4, 5 },
	       {5, 6 },
	       {6, 7 },
	       {7, 4 } };

SEE ALSO

       msh2geo(1)

rheolef-6.1							    rheolef-6.1 					      hexahedron(7rheolef)