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<html>
<head>
<title>
FEM3D_PACK - 3D Finite Element Method Utility Library
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM3D_PACK <br> 3D Finite Element Method Utility Library
</h1>
<hr>
<p>
<b>FEM3D_PACK</b>
is a C++ library which
contains utility routines for 3D finite element calculations.
</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_PACK</b> is available in
<a href = "../../cpp_src/fem3d_pack/fem3d_pack.html">a C++ version</a> and
<a href = "../../f_src/fem3d_pack/fem3d_pack.html">a FORTRAN90 version</a> and
<a href = "../../m_src/fem3d_pack/fem3d_pack.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/fem_basis/fem_basis.html">
FEM_BASIS</a>,
a C++ library which
can define and evaluate basis functions for any degree
in an M-dimensional simplex (1D interval, 2D triangle,
3D tetrahedron, and higher dimensional generalizations.)
</p>
<p>
<a href = "../../cpp_src/fem1d_pack/fem1d_pack.html">
FEM1D_PACK</a>,
a C++ library which
contains utilities for 1D finite element calculations.
</p>
<p>
<a href = "../../cpp_src/fem2d_pack/fem2d_pack.html">
FEM2D_PACK</a>,
a C++ library which
contains utilities for finite element calculations.
</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 = "../../cpp_src/fem3d_project/fem3d_project.html">
FEM3D_PROJECT</a>,
a C++ 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>
<p>
<a href = "../../cpp_src/fem3d_sample/fem3d_sample.html">
FEM3D_SAMPLE</a>,
a C++ program which
evaluates a finite element function defined on 3D tetrahedral mesh.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Claudio Rocchini, Paolo Cignoni,<br>
Generating Random Points in a Tetrahedron,<br>
Journal of Graphics Tools,<br>
Volume 5, Number 4, 2000, pages 9-12.
</li>
<li>
Reuven Rubinstein,<br>
Monte Carlo Optimization, Simulation and Sensitivity of
Queueing Networks,<br>
Krieger, 1992,<br>
ISBN: 0894647644,<br>
LC: QA298.R79.
</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_pack.cpp">fem3d_pack.cpp</a>, the source code.
</li>
<li>
<a href = "fem3d_pack.hpp">fem3d_pack.hpp</a>, the include file.
</li>
<li>
<a href = "fem3d_pack.sh">fem3d_pack.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "fem3d_pack_prb.cpp">fem3d_pack_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "fem3d_pack_prb.sh">fem3d_pack_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "fem3d_pack_prb_output.txt">fem3d_pack_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BANDWIDTH_MESH</b> determines the bandwidth of the coefficient matrix.
</li>
<li>
<b>BANDWIDTH_VAR</b> determines the bandwidth for finite element variables.
</li>
<li>
<b>BASIS_BRICK8:</b> BRICK8 basis functions at natural coordinates.
</li>
<li>
<b>BASIS_BRICK8_TEST</b> verifies BASIS_BRICK8.
</li>
<li>
<b>BASIS_BRICK20:</b> BRICK20 basis functions at natural coordinates.
</li>
<li>
<b>BASIS_BRICK20_TEST</b> verifies BASIS_BRICK20.
</li>
<li>
<b>BASIS_BRICK20:</b> BRICK20 basis functions at natural coordinates.
</li>
<li>
<b>BASIS_BRICK27_TEST</b> verifies BASIS_BRICK27.
</li>
<li>
<b>BASIS_MN_TET4:</b> all bases at N points for a TET4 element.
</li>
<li>
<b>BASIS_MN_T4_TEST</b> verifies BASIS_MN_TET4.
</li>
<li>
<b>BASIS_MN_TET10:</b> all bases at N points for a TET10 element.
</li>
<li>
<b>BASIS_MN_TET10_TEST</b> verifies BASIS_MN_TET10.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>NODES_BRICK8</b> returns the natural coordinates of the BRICK8 element.
</li>
<li>
<b>NODES_BRICK20</b> returns the natural coordinates of the BRICK20 element.
</li>
<li>
<b>NODES_BRICK27</b> returns the natural coordinates of the BRICK27 element.
</li>
<li>
<b>PHYSICAL_TO_REFERENCE_TET4</b> maps physical points to reference points.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8GE_FSS</b> factors and solves multiple R8GE systems.
</li>
<li>
<b>R8MAT_COPY_NEW</b> copies one R8MAT to a "new" R8MAT.
</li>
<li>
<b>R8MAT_DET_4D</b> computes the determinant of a 4 by 4 R8MAT.
</li>
<li>
<b>R8MAT_MV</b> multiplies a matrix times a vector.
</li>
<li>
<b>R8MAT_SOLVE</b> uses Gauss-Jordan elimination to solve an N by N linear system.
</li>
<li>
<b>R8MAT_UNIFORM_01_NEW</b> returns a new unit pseudorandom R8MAT.
</li>
<li>
<b>R8VEC_SUM</b> returns the sum of an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a new unit pseudorandom R8VEC.
</li>
<li>
<b>REFERENCE_TET4_SAMPLE:</b> sample points in the reference tetrahedron.
</li>
<li>
<b>REFERENCE_TET4_UNIFORM:</b> uniform sample points in the reference tetrahedron.
</li>
<li>
<b>REFERENCE_TET4_UNIFORM2:</b> uniform sample points in the reference tetrahedron.
</li>
<li>
<b>REFERENCE_TO_PHYSICAL_TET4</b> maps TET4 reference points to physical points.
</li>
<li>
<b>TETRAHEDRON_BARYCENTRIC</b> returns the barycentric coordinates of a point.
</li>
<li>
<b>TETRAHEDRON_VOLUME</b> computes the volume of a tetrahedron in 3D.
</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 02 March 2010.
</i>
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