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mesh_bandwidth.html
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<html>
<head>
<title>
MESH_BANDWIDTH - Geometric Bandwidth of a Mesh
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MESH_BANDWIDTH <br> Geometric Bandwidth of a Mesh
</h1>
<hr>
<p>
<b>MESH_BANDWIDTH</b>
is a FORTRAN90 program which
computes the geometric bandwidth of a mesh.
</p>
<p>
The user specifies an element file, containing the indices of the
nodes that make up each element. Examples of such a file include
the order 3 and order 6 triangulation files, but any order of element
may be used.
</p>
<p>
Not only may any element type be used, but the geometric region
may be of any spatial dimension.
</p>
<p>
The program reads the element information and computes the
geometric bandwidth <b>M</b> as
<blockquote><b>
M = ML + 1 + MU
</b></blockquote>
where <b>ML</b> is the lower bandwidth, namely, the maximum value
over all nodes <b>I</b> of the difference <b>(I-J)</b>, taken over
all nodes <b>J</b> that share an element with node <b>I</b>.
The upper bandwidth is the maximum value of <b>(J-I)</b> under
the same conditions.
</p>
<p>
The geometric bandwidth <b>M</b> is the linear algebraic bandwidth
of the adjacency matrix of the mesh, where <b>I</b> and <b>J</b>
are considered to be adjacent if there is some element that includes
both nodes.
</p>
<p>
The geometric bandwidth is of interest since it is the bandwidth
of the finite element matrix associated with the mesh, when a
scalar quantity is being approximated and there is a single
unknown for every node, and the unknowns have the same numbering
as the nodes.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>mesh_bandwidth</b> <i>element_file</i>
</blockquote>
where
<ul>
<li>
<i>element_file</i> contains a list of the node indices that
form each triangle of the triangulation,
</li>
</ul>
computes and prints the geometric bandwidth.
</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>MESH_BANDWIDTH</b> is available in
<a href = "../../c_src/mesh_bandwidth/mesh_bandwidth.html">a C version</a> and
<a href = "../../cpp_src/mesh_bandwidth/mesh_bandwidth.html">a C++ version</a> and
<a href = "../../f77_src/mesh_bandwidth/mesh_bandwidth.html">a FORTRAN77 version</a> and
<a href = "../../f_src/mesh_bandwidth/mesh_bandwidth.html">a FORTRAN90 version</a> and
<a href = "../../m_src/mesh_bandwidth/mesh_bandwidth.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
triangulates a set of nodes whose coordinates are stored in a file.
</p>
<p>
<a href = "../../f_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a FORTRAN90 program which
applies the reverse Cuthill-McKee reordering to a tetrahedral
mesh of nodes in 3D.
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image
using Open GL.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a data directory which
contains a description and
examples of order 3 triangulations.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a data directory which
contains a description and
examples of order 6 triangulations.
</p>
<p>
<a href = "../../f_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a FORTRAN90 program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Alan George, Joseph Liu,<br>
Computer Solution of Large Sparse Positive Definite Matrices,<br>
Prentice Hall, 1981,<br>
QA 188.G46
</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, pages 236-250, 1976.
</li>
<li>
Norman Gibbs,<br>
Algorithm 509: A Hybrid Profile Reduction Algorithm,<br>
ACM Transactions on Mathematical Software,<br>
Volume 2, Issue 4, pages 378-387, 1976.
</li>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Cambridge University Press,<br>
Second Edition, 1998.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "mesh_bandwidth.f90">mesh_bandwidth.f90</a>,
the source code.
</li>
<li>
<a href = "mesh_bandwidth.sh">mesh_bandwidth.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "mesh_bandwidth_prb.sh">mesh_bandwidth_prb.sh</a>,
a script that runs the program on a number of meshes.
</li>
<li>
<a href = "mesh_bandwidth_prb_output.txt">mesh_bandwidth_prb_output.txt</a>,
the resulting output.
</li>
</ul>
</p>
<p>
Some sample mesh files include:
<ul>
<li>
<a href = "../../data/polygonal_surface/sphere_q4_elements.txt">
sphere_q4_elements.txt</a>
</li>
<li>
<a href = "../../data/polygonal_surface/sphere_t3_elements.txt">
sphere_t3_elements.txt</a>
</li>
<li>
<a href = "../../data/tet_mesh_order4/cube_order4_tetras.txt">
cube_order4_tetras.txt</a>
</li>
<li>
<a href = "../../data/tet_mesh_order4/twenty_order4_tetras.txt">
twenty_order4_tetras.txt</a>
</li>
<li>
<a href = "../../data/tet_mesh_order10/cube_order10_tetras.txt">
cube_order10_tetras.txt</a>
</li>
<li>
<a href = "../../data/tet_mesh_order10/oneoneeight_order10_tetras.txt">
oneoneeight_order10_tetras.txt</a>
</li>
<li>
<a href = "../../data/triangulation_order3/ell_tri3.txt">
ell_tri3.txt</a>
</li>
<li>
<a href = "../../data/triangulation_order3/hex_cvt_tri3.txt">
hex_cvt_tri3.txt</a>
</li>
<li>
<a href = "../../data/triangulation_order3/hex_triangle_tri3.txt">
hex_triangle_tri3.txt</a>
</li>
<li>
<a href = "../../data/triangulation_order3/hot_pipe_tri3.txt">
hot_pipe_tri3.txt</a>
</li>
<li>
<a href = "../../data/triangulation_order6/ell_tri6.txt">
ell_tri6.txt</a>
</li>
<li>
<a href = "../../data/triangulation_order6/hex_jeff_tri6.txt">
hex_jeff_tri6.txt</a>
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for MESH_BANDWIDTH.
</li>
<li>
<b>BANDWIDTH</b> determines the bandwidth associated with the finite element mesh.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>ITABLE_DATA_READ</b> reads data from an integer table file.
</li>
<li>
<b>ITABLE_HEADER_READ</b> reads the header from an integer table file.
</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_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 02 September 2006.
</i>
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