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<html>
<head>
<title>
TETRAHEDRON_ARBQ_RULE - Quadrature Rules for Tetrahedrons.
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TETRAHEDRON_ARBQ_RULE <br> Quadrature Rules for Tetrahedrons.
</h1>
<hr>
<p>
<b>TETRAHEDRON_ARBQ_RULE</b>
is a C++ library which
returns quadrature rules,
with exactness up to total degree 15,
over the interior of a tetrahedron in 3D,
by Hong Xiao and Zydrunas Gimbutas.
</p>
<p>
The original source code, from which this library was developed,
is available from the Courant Mathematics and Computing Laboratory, at
<a href = "http://www.cims.nyu.edu/cmcl/quadratures/quadratures.html">
http://www.cims.nyu.edu/cmcl/quadratures/quadratures.html </a>,
</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>TETRAHEDRON_ARBQ_RULE</b> is available in
<a href = "../../c_src/tetrahedron_arbq_rule/tetrahedron_arbq_rule.html">a C version</a> and
<a href = "../../cpp_src/tetrahedron_arbq_rule/tetrahedron_arbq_rule.html">a C++ version</a> and
<a href = "../../f77_src/tetrahedron_arbq_rule/tetrahedron_arbq_rule.html">a FORTRAN77 version</a> and
<a href = "../../f_src/tetrahedron_arbq_rule/tetrahedron_arbq_rule.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tetrahedron_arbq_rule/tetrahedron_arbq_rule.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/cube_arbq_rule/cube_arbq_rule.html">
CUBE_ARBQ_RULE</a>,
a C++ library which
returns quadrature rules,
with exactness up to total degree 15,
over the interior of the symmetric cube in 3D,
by Hong Xiao and Zydrunas Gimbutas.
</p>
<p>
<a href = "../../cpp_src/cube_felippa_rule/cube_felippa_rule.html">
CUBE_FELIPPA_RULE</a>,
a C++ library which
returns the points and weights of a Felippa quadrature rule
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
</p>
<p>
<a href = "../../cpp_src/pyramid_felippa_rule/pyramid_felippa_rule.html">
PYRAMID_FELIPPA_RULE</a>,
a C++ library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a pyramid in 3D.
</p>
<p>
<a href = "../../cpp_src/simplex_gm_rule/simplex_gm_rule.html">
SIMPLEX_GM_RULE</a>,
a C++ library which
defines Grundmann-Moeller quadrature rules
over the interior of a simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/square_arbq_rule/square_arbq_rule.html">
SQUARE_ARBQ_RULE</a>,
a C++ library which
returns quadrature rules,
with exactness up to total degree 20,
over the interior of the symmetric square in 2D,
by Hong Xiao and Zydrunas Gimbutas.
</p>
<p>
<a href = "../../cpp_src/square_felippa_rule/square_felippa_rule.html">
SQUARE_FELIPPA_RULE</a>,
a C++ library which
returns the points and weights of a Felippa quadrature rule
over the interior of a square in 2D.
</p>
<p>
<a href = "../../cpp_src/square_symq_rule/square_symq_rule.html">
SQUARE_SYMQ_RULE</a>,
a C++ library which
returns symmetric quadrature rules,
with exactness up to total degree 20,
over the interior of the symmetric square in 2D,
by Hong Xiao and Zydrunas Gimbutas.
</p>
<p>
<a href = "../../cpp_src/stroud/stroud.html">
STROUD</a>,
a C++ library which
defines quadrature rules for a variety of M-dimensional regions,
including the interior of the square, cube and hypercube, the pyramid,
cone and ellipse, the hexagon, the M-dimensional octahedron,
the circle, sphere and hypersphere, the triangle, tetrahedron and simplex,
and the surface of the circle, sphere and hypersphere.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_felippa_rule/tetrahedron_felippa_rule.html">
TETRAHEDRON_FELIPPA_RULE</a>,
a C++ library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_integrals/tetrahedron_integrals.html">
TETRAHEDRON_INTEGRALS</a>,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate the integral of a function
over the interior of the unit tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/triangle_fekete_rule/triangle_fekete_rule.html">
TRIANGLE_FEKETE_RULE</a>,
a C++ library which
defines Fekete rules for interpolation or quadrature
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/triangle_felippa_rule/triangle_felippa_rule.html">
TRIANGLE_FELIPPA_RULE</a>,
a C++ library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/triangle_symq_rule/triangle_symq_rule.html">
TRIANGLE_SYMQ_RULE</a>,
a C++ library which
returns efficient symmetric quadrature rules,
with exactness up to total degree 50,
over the interior of an arbitrary triangle in 2D,
by Hong Xiao and Zydrunas Gimbutas.
</p>
<p>
<a href = "../../cpp_src/wedge_felippa_rule/wedge_felippa_rule.html">
WEDGE_FELIPPA_RULE</a>,
a C++ library which
returns quadratures rules for approximating integrals
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Hong Xiao, Zydrunas Gimbutas, <br>
A numerical algorithm for the construction of efficient quadrature
rules in two and higher dimensions,<br>
Computers and Mathematics with Applications,<br>
Volume 59, 2010, pages 663-676.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "tetrahedron_arbq_rule.cpp">tetrahedron_arbq_rule.cpp</a>, the source code.
</li>
<li>
<a href = "tetrahedron_arbq_rule.hpp">tetrahedron_arbq_rule.hpp</a>, the source code.
</li>
<li>
<a href = "tetrahedron_arbq_rule.sh">tetrahedron_arbq_rule.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "tetrahedron_arbq_rule_prb.cpp">tetrahedron_arbq_rule_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "tetrahedron_arbq_rule_prb.sh">tetrahedron_arbq_rule_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "tetrahedron_arbq_rule_prb_output.txt">tetrahedron_arbq_rule_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
TETRAHEDRON08 is a degree 8 rule in the reference tetrahedron.
<ul>
<li>
<a href = "tetrahedron08.txt">tetrahedron08.txt</a>,
the node coordinates and weights.
</li>
<li>
<a href = "tetrahedron08_commands.txt">tetrahedron08_commands.txt</a>,
gnuplot commands to create a plot.
</li>
<li>
<a href = "tetrahedron08_nodes.txt">tetrahedron08_nodes.txt</a>,
the node coordinates.
</li>
<li>
<a href = "tetrahedron08_vertices.txt">tetrahedron08_vertices.txt</a>,
the vertices.
</li>
<li>
<a href = "tetrahedron08.png">tetrahedron08.png</a>,
the PNG image of the point locations.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>KJACOYPOLS3</b> evaluates modified Jacobi polynomials.
</li>
<li>
<b>KLEGEYPOLS</b> evaluates scaled Legendre polynomials.
</li>
<li>
<b>ORTHO3EVA</b> evaluates polynomials orthogonal in the reference triangle.
</li>
<li>
<b>R8MAT_ROW_COPY</b> copies a vector into a row of an R8MAT.
</li>
<li>
<b>R8VEC_COPY</b> copies an R8VEC.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_SUM</b> returns the sum of the entries of an R8VEC.
</li>
<li>
<b>REF_TO_KOORN</b> maps points from the reference to Koornwinder's tetrahedron.
</li>
<li>
<b>RULE01</b> returns the rule of degree 1.
</li>
<li>
<b>RULE02</b> returns the rule of degree 2.
</li>
<li>
<b>RULE03</b> returns the rule of degree 3.
</li>
<li>
<b>RULE04</b> returns the rule of degree 4.
</li>
<li>
<b>RULE05</b> returns the rule of degree 5.
</li>
<li>
<b>RULE06</b> returns the rule of degree 6.
</li>
<li>
<b>RULE07</b> returns the rule of degree 7.
</li>
<li>
<b>RULE08</b> returns the rule of degree 8.
</li>
<li>
<b>RULE09</b> returns the rule of degree 9.
</li>
<li>
<b>RULE10</b> returns the rule of degree 10.
</li>
<li>
<b>RULE11</b> returns the rule of degree 11.
</li>
<li>
<b>RULE12</b> returns the rule of degree 12.
</li>
<li>
<b>RULE13</b> returns the rule of degree 13.
</li>
<li>
<b>RULE14</b> returns the rule of degree 14.
</li>
<li>
<b>RULE15</b> returns the rule of degree 15.
</li>
<li>
<b>TETRAHEDRON_ARBQ</b> returns a quadrature rule for a tetrahedron.
</li>
<li>
<b>TETRAHEDRON_ARBQ_GNUPLOT:</b> plot of a quadrature rule in the tetrahedron.
</li>
<li>
<b>TETRAHEDRON_ARBQ_SIZE</b> returns the size of quadrature rule for a tetrahedron.
</li>
<li>
<b>TETRAHEDRON_REF</b> returns the vertices of the reference tetrahedron.
</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 11 July 2014.
</i>
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