NAME

       hexahedron - reference element (rheolef-7.2)

DESCRIPTION

       The edge reference_element(6) is K = [-1,1].

            x2
            4----------7
            |\\         |\\
            | \\        | \\
            |  \\       |  \\
            |   5------+---6
            |   |      |   |
            0---+------3 - | ---> x1
             \\  |       \\  |
              \\ |        \\ |
               \\|         \\|
                1----------2
                 \\
                  x0

        The orientation is such that triedra (01, 03, 04) is direct and all faces, see from exterior, are in the
       direct sens. See

           P. L. Georges,
           Generation automatique de maillages,
           page 24, coll RMA, 16, Masson, 1994.

        This three-dimensional reference_element(6) is then transformed, after the Piola geometrical
       application, as a hexahedron in a 3D physical space, as a geo_element(6).

       Curved high order Pk hexahedra (k >= 1) in 3D geometries are supported. These hexahedra 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 hexahedron lattice.

            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

        Notice that the edge-nodes and face-nodes numbering slightly differ from those used in the gmsh mesh
       generator when using high-order elements. This difference is handled by the msh2geo_1 mesh file
       converter.

IMPLEMENTATION

       This documentation has been generated from file fem/geo_element/hexahedron.icc

       const size_t dimension = 3;
       const Float  measure = 8;
       const size_t n_vertex = 8;
       const point vertex [n_vertex] = {
               point(-1,-1,-1 ),
               point( 1,-1,-1 ),
               point( 1, 1,-1 ),
               point(-1, 1,-1 ),
               point(-1,-1, 1 ),
               point( 1,-1, 1 ),
               point( 1, 1, 1 ),
               point(-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 } };

AUTHOR

       Pierre  Saramito  <Pierre.Saramito@imag.fr>

COPYRIGHT

       Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or
       later  <http://gnu.org/licenses/gpl.html>.  This  is  free  software:  you  are free to change and
       redistribute it.  There is NO WARRANTY, to the extent permitted by law.