.TH "tetrahedron" 6rheolef "Version 7.2" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
tetrahedron \- reference element (rheolef-7\&.2)
.PP
  
.SH "DESCRIPTION"
.PP
The edge \fBreference_element(6)\fP is 
.PP
.nf
    K = { 0 < x0 < 1 and 0 < x1 < 1-x0 and 0 < x2 < 1-x0-x1 }

                      x2
                    \&.
                  ,/
                 /
               3        
             ,/|`\\\\
           ,/  |  `\\\\
         ,/    '\&.   `\\\\
       ,/       |     `\\\\
     ,/         |       `\\\\
    0-----------'\&.--------2 --> x1  
     `\\\\\&.         |      ,/        
        `\\\\\&.      |    ,/         
           `\\\\\&.   '\&. ,/          
              `\\\\\&. |/           
                 `1           
                    `\\\\\&.
                      ` x0

.fi
.PP
 The orientation is such that the trihedral (01, 02, 03) 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 tetrahedron in a physical space, as a \fBgeo_element(6)\fP\&.
.PP
Curved high order Pk tetrahedra (k >= 1) in 3D geometries are supported\&. These tetrahedra 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 tetrahedron lattice\&. See below for edges and faces numbering and orientation\&. 
.PP
.nf
               3                
             ,/|`\\\\
           ,/  |  `\\\\
         ,7    '\&.   `9       
       ,/       |     `\\\\
     ,/         8       `\\\\
    0--------6--'\&.--------2
     `\\\\\&.         |      ,/
        `\\\\\&.      |    ,5  
           `4\&.   '\&. ,/   
              `\\\\\&. |/    
                 `1    
              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/tetrahedron\&.icc
.PP
.PP
.nf
const size_t dimension = 3;
const Float  measure = Float(1\&.)/Float(6\&.);
const size_t n_vertex = 4;
const point vertex [n_vertex] = {
        point( 0, 0, 0 ),
        point( 1, 0, 0 ),
        point( 0, 1, 0 ),
        point( 0, 0, 1 ) };
const size_t  n_face = 4;
const size_t face [n_face][3] = {
        { 0, 2, 1 },
        { 0, 3, 2 },
        { 0, 1, 3 },
        { 1, 2, 3 } };
const size_t  n_edge = 6;
const size_t edge [n_edge][2] = {
        { 0, 1 },
        { 1, 2 },
        { 2, 0 },
        { 0, 3 },
        { 1, 3 },
        { 2, 3 } };
.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.