NAME¶

hexahedron - Hexaedron reference element

DESCRIPTION¶

The hexahedron reference element is [-1,1]^3.

     ^ z


     |


     4----------7


     |\         |\


     | \        | \


     |  \       |  \


     |   5------+---6


     |   |      |   |


     0---+------3 - | ---> y


      \  |       \  |


       \ |        \ |


        \|         \|


         1----------2


          \


           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 hexaedron lattice. See below for edges and faces numbering and orioentation.

     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

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 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 = 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 } };

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.