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<html>
<head>
<title>
PYRAMID_FELIPPA_RULE - Quadrature Rules for the Pyramid
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PYRAMID_FELIPPA_RULE <br> Quadrature Rules for the Pyramid
</h1>
<hr>
<p>
<b>PYRAMID_FELIPPA_RULE</b>
is a C++ library which
returns Felippa quadrature rules
over the interior of the unit pyramid in 3D.
</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>PYRAMID_FELIPPA_RULE</b> is available in
<a href = "../../c_src/pyramid_felippa_rule/pyramid_felippa_rule.html">a C version</a> and
<a href = "../../cpp_src/pyramid_felippa_rule/pyramid_felippa_rule.html">a C++ version</a> and
<a href = "../../f_src/pyramid_felippa_rule/pyramid_felippa_rule.html">a FORTRAN90 version</a> and
<a href = "../../f77_src/pyramid_felippa_rule/pyramid_felippa_rule.html">a FORTRAN77 version</a> and
<a href = "../../m_src/pyramid_felippa_rule/pyramid_felippa_rule.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<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/pyramid_rule/pyramid_rule.html">
PYRAMID_RULE</a>,
a C++ program which
computes a quadrature rule
over the interior of the unit 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_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/stroud/stroud.html">
STROUD</a>,
a C++ library which
defines quadrature rules for a variety of unusual areas, surfaces
and volumes in 2D, 3D and N-dimensions.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_exactness/tetrahedron_exactness.html">
TETRAHEDRON_EXACTNESS</a>,
a C++ program which
investigates the monomial exactness of a quadrature rule
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_keast_rule/tetrahedron_keast_rule.html">
TETRAHEDRON_KEAST_RULE</a>,
a C++ library which
defines ten quadrature rules, with exactness degrees 0 through 8,
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_monte_carlo/tetrahedron_monte_carlo.html">
TETRAHEDRON_MONTE_CARLO</a>,
a C++ program which
uses the Monte Carlo method to estimate integrals over a tetrahedron.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_ncc_rule/tetrahedron_ncc_rule.html">
TETRAHEDRON_NCC_RULE</a>,
a C++ library which
defines Newton-Cotes Closed (NCC) quadrature rules
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_nco_rule/tetrahedron_nco_rule.html">
TETRAHEDRON_NCO_RULE</a>,
a C++ library which
defines Newton-Cotes Open (NCO) quadrature rules
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/triangle_dunavant_rule/triangle_dunavant_rule.html">
TRIANGLE_DUNAVANT_RULE</a>,
a C++ library which
defines Dunavant rules for quadrature
over the interior of a triangle in 2D.
</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_lyness_rule/triangle_lyness_rule.html">
TRIANGLE_LYNESS_RULE</a>,
a C++ library which
returns Lyness-Jespersen quadrature rules
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a C++ program which
uses the Monte Carlo method to estimate integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/triangle_ncc_rule/triangle_ncc_rule.html">
TRIANGLE_NCC_RULE</a>,
a C++ library which
defines Newton-Cotes Closed (NCC) quadrature rules
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/triangle_nco_rule/triangle_nco_rule.html">
TRIANGLE_NCO_RULE</a>,
a C++ library which
defines Newton-Cotes Open (NCO) quadrature rules
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/triangle_wandzura_rule/triangle_wandzura_rule.html">
TRIANGLE_WANDZURA_RULE</a>,
a C++ library which
defines Wandzura rules for quadrature rules
over the interior of a triangle in 2D.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Carlos Felippa,<br>
A compendium of FEM integration formulas for symbolic work,<br>
Engineering Computation,<br>
Volume 21, Number 8, 2004, pages 867-890.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "pyramid_felippa_rule.cpp">pyramid_felippa_rule.cpp</a>, the source code.
</li>
<li>
<a href = "pyramid_felippa_rule.hpp">pyramid_felippa_rule.hpp</a>, the include file.
</li>
<li>
<a href = "pyramid_felippa_rule.sh">pyramid_felippa_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 = "pyramid_felippa_rule_prb.cpp">pyramid_felippa_rule_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "pyramid_felippa_rule_prb.sh">pyramid_felippa_rule_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "pyramid_felippa_rule_prb_output.txt">pyramid_felippa_rule_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>COMP_NEXT</b> computes the compositions of the integer N into K parts.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>MONOMIAL_VALUE</b> evaluates a monomial.
</li>
<li>
<b>PYRAMID__UNIT_MONOMIAL:</b> monomial integral in a unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O01</b> returns a 1 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O05</b> returns a 5 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O06</b> returns a 6 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O08</b> returns an 8 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O08B</b> returns an 8 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O09</b> returns a 9 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O13</b> returns a 13 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O18</b> returns an 18 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O27</b> returns a 27 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_O48</b> returns a 48 point quadrature rule for the unit pyramid.
</li>
<li>
<b>PYRAMID__UNIT_VOLUME:</b> volume of a unit pyramid with square base.
</li>
<li>
<b>R8_CHOOSE</b> computes the binomial coefficient C(N,K) as an R8.
</li>
<li>
<b>R8_MOP</b> returns the I-th power of -1 as an R8.
</li>
<li>
<b>R8VEC_COPY</b> copies an R8VEC.
</li>
<li>
<b>R8VEC_DOT_PRODUCT</b> computes the dot product of a pair of R8VEC's.
</li>
<li>
<b>SUBCOMP_NEXT</b> computes the next subcomposition of N into K parts.
</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 28 August 2014.
</i>
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