.\"
.de Id
..
.de Sp
.if n .sp
.if t .sp 0.4
..
.TH hexahedron 7rheolef "rheolef-6.7" "rheolef-6.7" "rheolef-6.7"
.\" label: /*Class:hexa
.SH NAME
\fBhexahedron\fP - Hexaedron reference element
.\" skip: @cindex hexaedron
.\" skip: @cindex reference element
.\" skip: @pindex gmsh
.\" skip: @pindex msh2geo
.SH DESCRIPTION

The hexahedron reference element is [-1,1]^3.
.\" begin_example
.Sp
.nf
     ^ z
     |
     4----------7
     |\\         |\\
     | \\        | \\
     |  \\       |  \\
     |   5------+---6
     |   |      |   |
     0---+------3 - | ---> y
      \\  |       \\  |
       \\ |        \\ |
        \\|         \\|
         1----------2
          \\
           x
.Sp
.fi
.\" end_example
Curved high order Pk hexaedra (k >= 1) in 3d geometries are supported.
These hexaedra have additional edge-nodes, face-nodes
and internal volume-nodes.
.SH 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 orioentation.
.\" begin_example
.Sp
.nf
     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
.Sp
.fi
.\" end_example
.SH 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 \fBgmsh\fP mesh generator when using high-order elements.
This difference is handled by the \fBmsh2geo\fP mesh file converter (see msh2geo(1)).
.\" END
.SH IMPLEMENTATION
.\" begin_example
.Sp
.nf
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 } };
.Sp
.fi
.\" end_example

.\" LENGTH = 1
.SH SEE ALSO
msh2geo(1)