.TH "hexahedron" 6rheolef "Sat Mar 13 2021" "Version 7.1" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hexahedron \- reference element (rheolef-7\&.1)
.PP
.SH "DESCRIPTION"
.PP
The edge \fBreference_element(6)\fP is \fCK = [-1,1]\fP\&. 
.PP
.nf
     x2
     4----------7  
     |\\         |\\
     | \\        | \\
     |  \\       |  \\
     |   5------+---6 
     |   |      |   |
     0---+------3 - | ---> x1
      \\  |       \\  |
       \\ |        \\ |
        \\|         \\|
         1----------2
          \\
           x0

.fi
.PP
 The orientation is such that triedra (01, 03, 04) is direct and all faces, see from exterior, are in the direct sens\&. See 
.PP
.nf
    P. L. Georges, 
    Generation automatique de maillages,
    page 24, coll RMA, 16, Masson, 1994.

.fi
.PP
 This three-dimensional \fBreference_element(6)\fP is then transformed, after the Piola geometrical application, as a hexahedron in a 3D physical space, as a \fBgeo_element(6)\fP\&.
.PP
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\&. 
.PP
.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

.fi
.PP
 Notice that the edge-nodes and face-nodes numbering slightly differ from those used in the \fCgmsh\fP mesh generator when using high-order elements\&. This difference is handled by the \fBmsh2geo_1\fP mesh file converter\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file fem/geo_element/hexahedron\&.icc
.PP
.PP
.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 } };
.fi
.PP

.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH 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.