hexahedron(7rheolef)
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
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(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)
Opportunity
Personal Opportunity - Free software gives you access to billions of dollars of software at no cost. Use this software for your business, personal use or to develop a profitable skill. Access to source code provides access to a level of capabilities/information that companies protect though copyrights. Open source is a core component of the Internet and it is available to you. Leverage the billions of dollars in resources and capabilities to build a career, establish a business or change the world. The potential is endless for those who understand the opportunity.
Business Opportunity - Goldman Sachs, IBM and countless large corporations are leveraging open source to reduce costs, develop products and increase their bottom lines. Learn what these companies know about open source and how open source can give you the advantage.
Free Software
Free Software provides computer programs and capabilities at no cost but more importantly, it provides the freedom to run, edit, contribute to, and share the software. The importance of free software is a matter of access, not price. Software at no cost is a benefit but ownership rights to the software and source code is far more significant.
Free Office Software - The Libre Office suite provides top desktop productivity tools for free. This includes, a word processor, spreadsheet, presentation engine, drawing and flowcharting, database and math applications. Libre Office is available for Linux or Windows.
Free Books
The Free Books Library is a collection of thousands of the most popular public domain books in an online readable format. The collection includes great classical literature and more recent works where the U.S. copyright has expired. These books are yours to read and use without restrictions.
Source Code - Want to change a program or know how it works? Open Source provides the source code for its programs so that anyone can use, modify or learn how to write those programs themselves. Visit the GNU source code repositories to download the source.
Education
Study at Harvard, Stanford or MIT - Open edX provides free online courses from Harvard, MIT, Columbia, UC Berkeley and other top Universities. Hundreds of courses for almost all major subjects and course levels. Open edx also offers some paid courses and selected certifications.
Linux Manual Pages - A man or manual page is a form of software documentation found on Linux/Unix operating systems. Topics covered include computer programs (including library and system calls), formal standards and conventions, and even abstract concepts.
