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<html>
<head>
<title>
TET_MESH_RCM - Reverse Cuthill-McKee Node Reordering
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TET_MESH_RCM <br> Reverse Cuthill-McKee Node Reordering
</h1>
<hr>
<p>
<b>TET_MESH_RCM</b>
is a MATLAB program which
computes the reverse Cuthill-McKee (RCM) reordering for nodes
in a tetrahedral mesh ("tet mesh").
</p>
<p>
The user supplies a node file and a tetrahedron file, containing
the coordinates of the nodes, and the indices of the nodes that
make up each tetrahedron. Either 4-node or 10-node tetrahedrons may
be used.
</p>
<p>
The program reads the data, computes the adjacency information,
carries out the RCM algorithm to get the permutation, applies
the permutation to the nodes and tetrahedrons, and writes out
new node and tetrahedron files that correspond to the RCM permutation.
</p>
<p>
Note that the node file would normally contain exactly 3 values
on each line, namely the X, Y and Z coordinates of the nodes.
However, this is not necessary. Extra information can be
included on each line, for instance, a "W" coordinate. Each
line should include the same number of items, but all will be
permuted correctly together. The program does not actually
need to know the coordinates of the nodes, so in fact, ANY data
(as long as it is real numeric data) associated with the nodes
can be listed in the node file, and will be correctly permuted.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>tet_mesh_rcm</b> <i>'prefix'</i>
</blockquote>
where <i>'prefix'</i> is the common file prefix:
<ul>
<li>
<i>'prefix'</i><b>_nodes.txt</b>, the node coordinates;
</li>
<li>
<i>'prefix'</i><b>_elements.txt</b>, the element definitions.
</li>
<li>
<i>'prefix'</i><b>_rcm_nodes.txt</b>, the reordered node coordinates;
</li>
<li>
<i>'prefix'</i><b>_rcm_elements.txt</b>, the reordered element definitions.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TET_MESH_RCM</b> is available in
<a href = "../../cpp_src/tet_mesh_rcm/tet_mesh_rcm.html">a C++ version</a> and
<a href = "../../f_src/tet_mesh_rcm/tet_mesh_rcm.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tet_mesh_rcm/tet_mesh_rcm.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt_tet_mesh/cvt_tet_mesh.html">
CVT_TET_MESH</a>,
a FORTRAN90 program which
uses CVT techniques to compute a tet mesh in a region.
</p>
<p>
<a href = "../../m_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a MATLAB program which
returns the geometric bandwidth associated with a mesh of
elements of any order and in a space of arbitrary dimension.
</p>
<p>
<a href = "../../m_src/quad_mesh_rcm/quad_mesh_rcm.html">
QUAD_MESH_RCM</a>,
a MATLAB program which
computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node
quadrilaterals.
</p>
<p>
<a href = "../../m_src/rcm/rcm.html">
RCM</a>,
a MATLAB library which
carries out reverse Cuthill-McKee computations.
</p>
<p>
<a href = "../../f_src/table_tet_mesh/table_tet_mesh.html">
TABLE_TET_MESH</a>,
a FORTRAN90 program which
can compute a tet mesh of a given set of points.
</p>
<p>
<a href = "../../f_src/test_tet_mesh/test_tet_mesh.html">
TEST_TET_MESH</a>,
a FORTRAN90 library which
defines regions for which
a tet mesh is desired.
</p>
<p>
<a href = "../../m_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a MATLAB library which
works with tet meshes.
</p>
<p>
<a href = "../../m_src/tet_mesh_boundary/tet_mesh_boundary.html">
TET_MESH_BOUNDARY</a>,
a MATLAB program which
returns the nodes and faces of the boundary of a tetrahedral mesh,
which themselves form a 3D triangular mesh or "TRI_SURFACE".
</p>
<p>
<a href = "../../m_src/tet_mesh_display/tet_mesh_display.html">
TET_MESH_DISPLAY</a>,
a MATLAB program which
can read in the node and tetra files defining a tet mesh and display a wireframe
image.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_display_opengl/tet_mesh_display_opengl.html">
TET_MESH_DISPLAY_OPENGL</a>,
a C++ program which
reads a tet mesh and displays the
nodes and edges using OpenGL.
</p>
<p>
<a href = "../../m_src/tet_mesh_l2q/tet_mesh_l2q.html">
TET_MESH_L2Q</a>,
a MATLAB program which
converts a linear to quadratic tet mesh.
</p>
<p>
<a href = "../../data/tet_mesh_order4/tet_mesh_order4.html">
TET_MESH_ORDER4</a>,
a directory which
contains a description and examples of a tet mesh using order 4 elements.
</p>
<p>
<a href = "../../data/tet_mesh_order10/tet_mesh_order10.html">
TET_MESH_ORDER10</a>,
a directory which
contains a description and examples of a tet mesh using order 10 elements.
</p>
<p>
<a href = "../../m_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a MATLAB program which
converts a quadratic (10-node) to linear (4-node) tetrahedral mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a MATLAB program which
computes the quality of a tetrahedral mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_refine/tet_mesh_refine.html">
TET_MESH_REFINE</a>,
a MATLAB program which
can refine a tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a MATLAB program which
computes the tetrahedron-to-tetrahedron
adjacency information.
</p>
<p>
<a href = "../../m_src/tet_mesh_volumes/tet_mesh_volumes.html">
TET_MESH_VOLUMES</a>,
a MATLAB program which
computes the volume of each tetrahedron in a tet mesh;
</p>
<p>
<a href = "../../m_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a MATLAB program which
applies the reverse Cuthill-McKee reordering to a triangulation of 2D data.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
HL Crane, Norman Gibbs, William Poole, Paul Stockmeyer,<br>
Algorithm 508:
Matrix Bandwidth and Profile Reduction,<br>
ACM Transactions on Mathematical Software,<br>
Volume 2, Number 4, December 1976, pages 375-377.
</li>
<li>
Herbert Edelsbrunner,<br>
Geometry and Topology for Mesh Generation,<br>
Cambridge, 2001,<br>
ISBN: 0-521-79309-2,<br>
LC: QA377.E36.
</li>
<li>
Alan George, Joseph Liu,<br>
Computer Solution of Large Sparse Positive Definite Matrices,<br>
Prentice Hall, 1981,<br>
ISBN: 0131652745,<br>
LC: QA188.G46
</li>
<li>
Norman Gibbs,<br>
Algorithm 509:
A Hybrid Profile Reduction Algorithm,<br>
ACM Transactions on Mathematical Software,<br>
Volume 2, Number 4, December 1976, pages 378-387.
</li>
<li>
Norman Gibbs, William Poole, Paul Stockmeyer,<br>
An Algorithm for Reducing the Bandwidth
and Profile of a Sparse Matrix,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 13, Number 2, April 1976, pages 236-250.
</li>
<li>
Barry Joe,<br>
GEOMPACK - a software package for the generation of meshes
using geometric algorithms,<br>
Advances in Engineering Software,<br>
Volume 13, 1991, pages 325-331.
</li>
<li>
Per-Olof Persson, Gilbert Strang,<br>
A Simple Mesh Generator in MATLAB,<br>
SIAM Review,<br>
Volume 46, Number 2, June 2004, pages 329-345.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "tet_mesh_rcm.m">tet_mesh_rcm.m</a>,
is the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>CUBE4</b> is an order 4 tet mesh of a cube:
<ul>
<li>
<a href = "cube4_output.txt">cube4_output.txt</a>,
the printed output from the command <br>
"tet_mesh_rcm cube4_nodes.txt cube4_tetras.txt"
</li>
<li>
<a href = "cube4_nodes.txt">cube4_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "cube4_elements.txt">cube4_elements.txt</a>,
the tetrahedron file.
</li>
<li>
<a href = "cube4_rcm_nodes.txt">cube4_rcm_nodes.txt</a>,
the RCM reordered node file.
</li>
<li>
<a href = "cube4_rcm_elements.txt">cube4_rcm_elements.txt</a>,
the RCM reordered tetrahedron file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 29 September 2009.
</i>
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