NAME¶

tetrahedron - Tetraedron reference element

DESCRIPTION¶

The tetrahedron reference element is

        K = { 0 < x < 1 and 0 < y < 1-x and 0 < z < 1-x-y }

                       z


                     .


                   ,/


                  /


                3


              ,/|`\


            ,/  |  `\


          ,/    '.   `\


        ,/       |     `\


      ,/         |       `\


     0-----------'.--------2 --> y


      `\.         |      ,/


         `\.      |    ,/


            `\.   '. ,/


               `\. |/


                  `1


                     `\.


                       ` x

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 orioentation.

                3


              ,/|`\


            ,/  |  `\


          ,7    '.   `9


        ,/       |     `\


      ,/         8       `\


     0--------6--'.--------2


      `\.         |      ,/


         `\.      |    ,5


            `4.   '. ,/


               `\. |/


                  `1


               P2

NUMBERING¶

The orientation is such that triedra (01, 02, 03) 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 = 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 } };

SEE ALSO¶

msh2geo(1)

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.