hexahedron(7rheolef) [debian man page]

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)

Check Out this Related Man Page

geo_element(7rheolef)						    rheolef-6.1 					     geo_element(7rheolef)

NAME

       geo_element - element of a mesh

DESCRIPTION

       Defines	geometrical elements and sides as a set of vertice and edge indexes.  This element is obtained after a Piola transformation from a
       reference element (see reference_element(2)).  Indexes are related to arrays of edges and vertices.   These  arrays  are  included  in  the
       description of the mesh.  Thus, this class is related of a given mesh instance (see geo(2)).

EXAMPLE

       This is the test of geo_element:

	   geo_element_auto<> K;
	   K.set_name('t') ;
	   cout << "n_vertices: " << K.size()	   << endl
		<< "n_edges   : " << K.n_edges()   << endl
		<< "dimension : " << K.dimension() << endl << endl;
	   for(geo_element::size_type i = 0; i < K.size(); i++)
	       K[i] = i*10 ;
	   for(geo_element::size_type i = 0; i < K.n_edges(); i++)
	       K.set_edge(i, i*10+5) ;
	   cout << "vertices: local -> global" << endl;
	   for (geo_element::size_type vloc = 0; vloc < K.size(); vloc++)
	       cout << vloc << "-> " << K[vloc] << endl;
	   cout << endl
		<< "edges: local -> global" << endl;
	   for (geo_element::size_type eloc = 0; eloc < K.n_edges(); eloc++) {
	       geo_element::size_type vloc1 = subgeo_local_vertex(1, eloc, 0);
	       geo_element::size_type vloc2 = subgeo_local_vertex(1, eloc, 1);
	       cout << eloc << "-> " << K.edge(eloc) << endl
		    << "local_vertex_from_edge(" << eloc
		    << ") -> (" << vloc1 << ", " << vloc2 << ")" << endl;
	   }

SEE ALSO

       reference_element(2), geo(2)

rheolef-6.1							    rheolef-6.1 					     geo_element(7rheolef)

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hexahedron(7rheolef) [debian man page]

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