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<html>
<head>
<title>
SQUARE_FELIPPA_RULE - Quadrature Rules for a Square in 2D
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SQUARE_FELIPPA_RULE <br> Quadrature Rules for a Square in 2D
</h1>
<hr>
<p>
<b>SQUARE_FELIPPA_RULE</b>
is a MATLAB library which
generates the points and weights of a Felippa quadrature rule over
the interior of a square in 2D.
</p>
<p>
Actually, the word "square" is meant to designate any quadrature region
defined by:
<pre>
A(1) <= X <= B(1)
A(2) <= Y <= B(2)
</pre>
</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>SQUARE_FELIPPA_RULE</b> is available in
<a href = "../../c_src/square_felippa_rule/square_felippa_rule.html">a C version</a> and
<a href = "../../cpp_src/square_felippa_rule/square_felippa_rule.html">a C++ version</a> and
<a href = "../../f77_src/square_felippa_rule/square_felippa_rule.html">a FORTRAN77 version</a> and
<a href = "../../f_src/square_felippa_rule/square_felippa_rule.html">a FORTRAN90 version</a> and
<a href = "../../m_src/square_felippa_rule/square_felippa_rule.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/circle_rule/circle_rule.html">
CIRCLE_RULE</a>,
a MATLAB library which
computes quadrature rules
over the circumference of a circle in 2D.
</p>
<p>
<a href = "../../m_src/cube_arbq_rule/cube_arbq_rule.html">
CUBE_ARBQ_RULE</a>,
a MATLAB library which
computes quadrature rules
with exactness up to total degree 15,
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../m_src/cube_felippa_rule/cube_felippa_rule.html">
CUBE_FELIPPA_RULE</a>,
a MATLAB library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../m_src/disk_rule/disk_rule.html">
DISK_RULE</a>,
a MATLAB library which
computes quadrature rules
over the interior of a disk in 2D.
</p>
<p>
<a href = "../../m_src/pyramid_felippa_rule/pyramid_felippa_rule.html">
PYRAMID_FELIPPA_RULE</a>,
a MATLAB library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a pyramid in 3D.
</p>
<p>
<a href = "../../m_src/pyramid_rule/pyramid_rule.html">
PYRAMID_RULE</a>,
a MATLAB program which
computes a quadrature rule
over the interior of a pyramid in 3D.
</p>
<p>
<a href = "../../m_src/simplex_gm_rule/simplex_gm_rule.html">
SIMPLEX_GM_RULE</a>,
a MATLAB library which
defines Grundmann-Moeller quadrature rules
over the interior of a simplex in M dimensions.
</p>
<p>
<a href = "../../m_src/sphere_lebedev_rule/sphere_lebedev_rule.html">
SPHERE_LEBEDEV_RULE</a>,
a MATLAB library which
computes Lebedev quadrature rules
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../m_src/square_arbq_rule/square_arbq_rule.html">
SQUARE_ARBQ_RULE</a>,
a MATLAB 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 = "../../m_src/square_exactness/square_exactness.html">
SQUARE_EXACTNESS</a>,
a MATLAB library which
investigates the polynomial exactness of quadrature rules
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../m_src/square_grid/square_grid.html">
SQUARE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../m_src/square_integrals/square_integrals.html">
SQUARE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit cube in 3D.
</p>
<p>
<a href = "../../m_src/square_monte_carlo/square_monte_carlo.html">
SQUARE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of the unit cube in 3D;
</p>
<p>
<a href = "../../m_src/square_symq_rule/square_symq_rule.html">
SQUARE_SYMQ_RULE</a>,
a MATLAB 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 = "../../m_src/tetrahedron_arbq_rule/tetrahedron_arbq_rule.html">
TETRAHEDRON_ARBQ_RULE</a>,
a MATLAB 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>
<a href = "../../m_src/tetrahedron_felippa_rule/tetrahedron_felippa_rule.html">
TETRAHEDRON_FELIPPA_RULE</a>,
a MATLAB library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/tetrahedron_keast_rule/tetrahedron_keast_rule.html">
TETRAHEDRON_KEAST_RULE</a>,
a MATLAB library which
defines ten quadrature rules, with exactness degrees 0 through 8,
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/tetrahedron_ncc_rule/tetrahedron_ncc_rule.html">
TETRAHEDRON_NCC_RULE</a>,
a MATLAB library which
defines Newton-Cotes closed quadrature rules
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/tetrahedron_nco_rule/tetrahedron_nco_rule.html">
TETRAHEDRON_NCO_RULE</a>,
a MATLAB library which
defines Newton-Cotes open quadrature rules
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/triangle_dunavant_rule/triangle_dunavant_rule.html">
TRIANGLE_DUNAVANT_RULE</a>,
a MATLAB library which
defines Dunavant rules for quadrature
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_fekete_rule/triangle_fekete_rule.html">
TRIANGLE_FEKETE_RULE</a>,
a MATLAB library which
defines Fekete rules for interpolation or quadrature
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_felippa_rule/triangle_felippa_rule.html">
TRIANGLE_FELIPPA_RULE</a>,
a MATLAB library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_lyness_rule/triangle_lyness_rule.html">
TRIANGLE_LYNESS_RULE</a>,
a MATLAB library which
returns Lyness-Jespersen quadrature rules
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_monte_carlo/triangle_monte_carlo.html">
TRIANGLE_MONTE_CARLO</a>,
a MATLAB program which
uses the Monte Carlo method to estimate integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_ncc_rule/triangle_ncc_rule.html">
TRIANGLE_NCC_RULE</a>,
a MATLAB library which
defines Newton-Cotes Closed (NCC) quadrature rules
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_nco_rule/triangle_nco_rule.html">
TRIANGLE_NCO_RULE</a>,
a MATLAB library which
defines Newton-Cotes Open (NCO) quadrature rules
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_symq_rule/triangle_symq_rule.html">
TRIANGLE_SYMQ_RULE</a>,
a MATLAB 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 = "../../m_src/triangle_wandzura_rule/triangle_wandzura_rule.html">
TRIANGLE_WANDZURA_RULE</a>,
a MATLAB library which
defines Wandzura rules for quadrature
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/wedge_felippa_rule/wedge_felippa_rule.html">
WEDGE_FELIPPA_RULE</a>,
a MATLAB 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>
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 = "comp_next.m">comp_next.m</a>,
computes the compositions of the integer N into K parts.
</li>
<li>
<a href = "line_unit_o01.m">line_unit_o01.m</a>,
returns a 1 point quadrature rule for the unit line.
</li>
<li>
<a href = "line_unit_o02.m">line_unit_o02.m</a>,
returns a 2 point quadrature rule for the unit line.
</li>
<li>
<a href = "line_unit_o03.m">line_unit_o03.m</a>,
returns a 3 point quadrature rule for the unit line.
</li>
<li>
<a href = "line_unit_o04.m">line_unit_o04.m</a>,
returns a 4 point quadrature rule for the unit line.
</li>
<li>
<a href = "line_unit_o05.m">line_unit_o05.m</a>,
returns a 5 point quadrature rule for the unit line.
</li>
<li>
<a href = "monomial_value.m">monomial_value.m</a>,
evaluates a monomial.
</li>
<li>
<a href = "square_monomial.m">square_monomial.m</a>,
returns the exact integral of a monomial in a square in 2D.
</li>
<li>
<a href = "square_monomial_test.m">square_monomial_test.m</a>,
tests SQUARE_MONOMIAL.
</li>
<li>
<a href = "square_quad_test.m">square_quad_test.m</a>,
tests the quadrature rules for a square in 2D.
</li>
<li>
<a href = "square_rule.m">square_rule.m</a>,
returns a quadrature rule for a square in 2D;
</li>
<li>
<a href = "square_volume.m">square_volume.m</a>,
returns the volume of a square in 2D;
</li>
<li>
<a href = "r8vec_direct_product.m">r8vec_direct_product.m</a>,
creates a direct product of R8VEC's.
</li>
<li>
<a href = "r8vec_direct_product2.m">r8vec_direct_product2.m</a>,
creates a direct product of R8VEC's.
</li>
<li>
<a href = "subcomp_next.m">subcomp_next.m</a>,
computes the next subcomposition of N into K parts.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the YMDHMS date as a timestamp;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "square_felippa_rule_test.m">square_felippa_rule_test.m</a>,
runs all the tests.
</li>
<li>
<a href = "square_felippa_rule_test_output.txt">
square_felippa_rule_test_output.txt</a>,
the output file.
</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 September 2014.
</i>
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