rheolef  6.3
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.