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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 C++ program which
computes the reverse
Cuthill-McKee 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 (input);
</li>
<li>
<i>prefix</i><b>_elements.txt</b>, the element definitions (input).
</li>
<li>
<i>prefix</i><b>_rcm_nodes.txt</b>, the reordered node coordinates (output);
</li>
<li>
<i>prefix</i><b>_rcm_elements.txt</b>, the reordered element definitions (output).
</li>
</ul>
</p>
<p>
The element definition file will list node indices. In C++, it may be
more natural to use 0-based indices. This program will accept an element
definition file that is 0-based or 1-based, and will convert a 1-based
input file so that it becomes 0-based internal to the program. The detection
of 1-based data is determined by the absence of the use of a 0 index, and
the use of an index equal to the number of nodes. This is an implicit
and fallible, but reasonable, way to handle this problem.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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 = "../../cpp_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a C++ 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 = "../../cpp_src/quad_mesh_rcm/quad_mesh_rcm.html">
QUAD_MESH_RCM</a>,
a C++ program which
computes the reverse Cuthill-McKee (RCM) reordering for nodes in a mesh of 4-node
quadrilaterals.
</p>
<p>
<a href = "../../cpp_src/rcm/rcm.html">
RCM</a>,
a C++ 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 = "../../cpp_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a C++ library which
works with tet meshes.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_boundary/tet_mesh_boundary.html">
TET_MESH_BOUNDARY</a>,
a C++ 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 = "../../cpp_src/tet_mesh_l2q/tet_mesh_l2q.html">
TET_MESH_L2Q</a>,
a C++ 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 = "../../cpp_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a C++ program which
converts a quadratic (10-node) to linear (4-node) tetrahedral mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a C++ program which
computes the quality of a tetrahedral mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_refine/tet_mesh_refine.html">
TET_MESH_REFINE</a>,
a C++ program which
can refine a tet mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a C++ program which
computes the tetrahedron-to-tetrahedron
adjacency information.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_volumes/tet_mesh_volumes.html">
TET_MESH_VOLUMES</a>,
a C++ program which
computes the volume of each tetrahedron in a tet mesh;
</p>
<p>
<a href = "../../cpp_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a C++ 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.cpp">tet_mesh_rcm.cpp</a>, the source code.
</li>
<li>
<a href = "tet_mesh_rcm.sh">tet_mesh_rcm.sh</a>,
commands to compile 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 element 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 element file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TET_MESH_RCM.
</li>
<li>
<b>ADJ_BANDWIDTH</b> computes the bandwidth of an adjacency matrix.
</li>
<li>
<b>ADJ_PERM_BANDWIDTH</b> computes the bandwidth of a permuted adjacency matrix.
</li>
<li>
<b>ADJ_PRINT</b> prints adjacency information.
</li>
<li>
<b>ADJ_PRINT_SOME</b> prints some adjacency information.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is true if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DEGREE</b> computes the degrees of the nodes in the connected component.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the columns in the first line of a file.
</li>
<li>
<b>FILE_EXIST</b> reports whether a file exists.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GENRCM</b> finds the reverse Cuthill-Mckee ordering for a general graph.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_SWAP</b> switches two I4's.
</li>
<li>
<b>I4COL_COMPARE</b> compares columns I and J of an I4COL.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts the columns of an I4COL.
</li>
<li>
<b>I4COL_SORT2_A</b> ascending sorts the elements of each column of an I4COL.
</li>
<li>
<b>I4COL_SORTED_UNIQUE_COUNT</b> counts unique elements in an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps two columns of an I4COL.
</li>
<li>
<b>I4MAT_DATA_READ</b> reads data from an I4MAT file.
</li>
<li>
<b>I4MAT_HEADER_READ</b> reads the header from an I4MAT file.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an I4MAT, transposed.
</li>
<li>
<b>I4MAT_WRITE</b> writes an I4MAT file with no header.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_REVERSE</b> reverses the elements of an I4VEC.
</li>
<li>
<b>LEVEL_SET</b> generates the connected level structure rooted at a given node.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_INVERSE3</b> produces the inverse of a given permutation.
</li>
<li>
<b>R8COL_PERMUTE</b> permutes an R8COL in place.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads the data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file with no header.
</li>
<li>
<b>RCM</b> renumbers a connected component by the reverse Cuthill McKee algorithm.
</li>
<li>
<b>ROOT_FIND</b> finds a pseudo-peripheral node.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an I4VEC from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TET_MESH_BASE_ZERO</b> ensures that the element definition is zero-based.
</li>
<li>
<b>TET_MESH_ORDER4_ADJ_COUNT</b> counts the number of nodal adjacencies.
</li>
<li>
<b>TET_MESH_ORDER4_ADJ_SET</b> sets the nodal adjacency matrix.
</li>
<li>
<b>TET_MESH_ORDER10_ADJ_COUNT</b> counts the number of nodal adjacencies.
</li>
<li>
<b>TET_MESH_ORDER10_ADJ_SET</b> sets the nodal adjacency matrix.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 08 March 2013.
</i>
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