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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 MATLAB 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 sets of node indices;
each set of node indices describes a single element.
</li>
</ul>
The program reads the element file and prints out the geometric
mesh 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 = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
computes a triangulation of a geometric region.
</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 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 directory which
contains a description and
examples of order 6 triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a MATLAB 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.m">mesh_bandwidth.m</a>,
the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "mesh_bandwidth_test_output.txt">mesh_bandwidth_test_output.txt</a>,
the output file.
</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_elements.txt">
cube_elements.txt</a>
</li>
<li>
<a href = "../../datasets/tet_mesh_order4/twenty_elements.txt">
twenty_elements.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>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 06 August 2009.
</i>
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