rheolef::hexahedron Namespace Reference

Variables
const size_t	dimension = 3
	hexahedron - Hexaedron reference element
const Float	measure = 8
const size_t	n_vertex = 8
const Float	vertex [n_vertex][dimension]
const size_t	n_face = 6
const size_t	face [n_face][4]
const size_t	n_edge = 12
const size_t	edge [n_edge][2]

Variable Documentation

const size_t rheolef::hexahedron::dimension = 3

hexahedron - Hexaedron reference element

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

^ z
|
4----------7  
|\\         |\\ 
| \\        | \\ 
|  \\       |  \\ 
|   5------+---6 
|   |      |   |
0---+------3 - | ---> y    
 \\  |       \\  |
  \\ |        \\ |
   \\|         \\|
    1----------2
     \\
      x

Curved high order Pk hexaedra (k >= 1) in 3d geometries are supported. These hexaedra 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 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 command).

Definition at line 62 of file reference_element.cc.

const Float rheolef::hexahedron::measure = 8

Definition at line 63 of file reference_element.cc.

const size_t rheolef::hexahedron::n_vertex = 8

Definition at line 64 of file reference_element.cc.

const Float rheolef::hexahedron::vertex[n_vertex][dimension]

Initial value:

 {
        {-1,-1,-1 },
        { 1,-1,-1 },
        { 1, 1,-1 },
        {-1, 1,-1 },
        {-1,-1, 1 },
        { 1,-1, 1 },
        { 1, 1, 1 },
        {-1, 1, 1 } }

Definition at line 65 of file reference_element.cc.

const size_t rheolef::hexahedron::n_face = 6

Definition at line 74 of file reference_element.cc.

const size_t rheolef::hexahedron::face[n_face][4]

Initial value:

 {
        {0, 3, 2, 1 },
        {0, 4, 7, 3 },
        {0, 1, 5, 4 },
        {4, 5, 6, 7 },
        {1, 2, 6, 5 },
        {2, 3, 7, 6 } }

Definition at line 75 of file reference_element.cc.

const size_t rheolef::hexahedron::n_edge = 12

Definition at line 82 of file reference_element.cc.

const size_t rheolef::hexahedron::edge[n_edge][2]

Initial value:

 {
        {0, 1 },
        {1, 2 },
        {2, 3 },
        {3, 0 },
        {0, 4 },
        {1, 5 },
        {2, 6 },
        {3, 7 },
        {4, 5 },
        {5, 6 },
        {6, 7 },
        {7, 4 } }

Definition at line 83 of file reference_element.cc.