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<html>
<head>
<title>
FEM3D_SAMPLE - Evaluate a Finite Element Function of a 3D Argument
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM3D_SAMPLE <br> Evaluate a Finite Element Function of a 3D Argument
</h1>
<hr>
<p>
<b>FEM3D_SAMPLE</b>
is a MATLAB program which
can evaluate a finite element function of a 3D argument.
</p>
<p>
The current version of the program can only handle tetrahedral finite element
meshes using linear basis functions.
</p>
<p>
The current version of the program uses a NAIVE search algorithm to locate
points within the mesh. It is intended that this search algorithm be replaced
by a Delaunay search.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>fem3d_sample</b> ( <i>'fem_prefix'</i>, <i>'sample_prefix'</i> )
</blockquote>
where <i>'fem_prefix'</i> is the common prefix for the FEM files:
<ul>
<li>
<i>'fem_prefix'</i><b>_nodes.txt</b>, the node coordinates.
</li>
<li>
<i>'fem_prefix'</i><b>_elements.txt</b>, the nodes that make up each element;
</li>
<li>
<i>'fem_prefix'</i><b>_values.txt</b>, the values defined at each node.
</li>
</ul>
and <i>'sample_prefix'</i> is the common prefix for the SAMPLE files,
for which the node file is input, and the values file is created by the program:
<ul>
<li>
<i>'sample_prefix'</i><b>_nodes.txt</b>, the node coordinates where samples are desired.
</li>
<li>
<i>'sample_prefix'</i><b>_values.txt</b>, the values computed at each sample node.
</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>FEM3D_SAMPLE</b> is available in
<a href = "../../cpp_src/fem3d_sample/fem3d_sample.html">a C++ version</a> and
<a href = "../../f77_src/fem3d_sample/fem3d_sample.html">a FORTRAN77 version</a> and
<a href = "../../f_src/fem3d_sample/fem3d_sample.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem3d_sample/fem3d_sample.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/fem_io/fem_io.html">
FEM_IO</a>,
a MATLAB library which
reads or writes node, element and data files defining a finite element model.
</p>
<p>
<a href = "../../m_src/fem1d_sample/fem1d_sample.html">
FEM1D_SAMPLE</a>,
a MATLAB program which
samples a scalar or vector finite element function of one variable,
defined by FEM files,
returning interpolated values at the sample points.
</p>
<p>
<a href = "../../m_src/fem2d_sample/fem2d_sample.html">
FEM2D_SAMPLE</a>,
a MATLAB program which
samples a scalar or vector finite element function of 2 variables
defined by <a href = "../../data/fem/fem.html">FEM files</a>,
returning interpolated values at the sample points.
</p>
<p>
<a href = "../../data/fem3d/fem3d.html">
FEM3D</a>,
a data directory which
contains examples of 3D FEM files,
three text files that describe a 3D finite element geometry;
</p>
<p>
<a href = "../../m_src/fem3d_pack/fem3d_pack.html">
FEM3D_PACK</a>,
a MATLAB library which
contains utilities for 3D finite element calculations.
</p>
<p>
<a href = "../../m_src/fem3d_project/fem3d_project.html">
FEM3D_PROJECT</a>,
a MATLAB program which
projects a function F(X,Y,Z), given as a data, into a given finite element space
of piecewise linear tetrahedral elements.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hans Rudolf Schwarz,<br>
Finite Element Methods,<br>
Academic Press, 1988,<br>
ISBN: 0126330107,<br>
LC: TA347.F5.S3313.
</li>
<li>
Gilbert Strang, George Fix,<br>
An Analysis of the Finite Element Method,<br>
Cambridge, 1973,<br>
ISBN: 096140888X,<br>
LC: TA335.S77.
</li>
<li>
Olgierd Zienkiewicz,<br>
The Finite Element Method,<br>
Sixth Edition,<br>
Butterworth-Heinemann, 2005,<br>
ISBN: 0750663200,<br>
LC: TA640.2.Z54.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fem3d_sample.m">fem3d_sample.m</a>,
the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>SQ</b> is FEM data for the function f(x,y,z)=x^2+2*y^2-z^2, on a 5x5x5 grid
of nodes in the cube [0,4]x[0,4]x[0,4], organized into linear linear tetrahedrons.
The sample data seeks the values of this function on a 4x4x4
evenly spaced grid.
<ul>
<li>
<a href = "fem_sq_nodes.txt">fem_sq_nodes.txt</a>,
defines the FEM nodes.
</li>
<li>
<a href = "fem_sq_elements.txt">fem_sq_elements.txt</a>,
defines the FEM elements.
</li>
<li>
<a href = "fem_sq_values.txt">fem_sq_values.txt</a>,
defines the FEM nodal values.
</li>
<li>
<a href = "sample_sq_nodes.txt">sample_sq_nodes.txt</a>,
defines the sample nodes.
</li>
<li>
<a href = "sample_sq_values.txt">sample_sq_values.txt</a>,
defines the sample nodal values.
</li>
<li>
<a href = "sample_sq_values_exact.txt">sample_sq_values_exact.txt</a>,
the exact values of the function at the sample nodes. This should be
compared with the values determined from the FEM function.
</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 07 August 2009.
</i>
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