SQUARE_FELIPPA_RULE
Quadrature Rules for a Square in 2D

SQUARE_FELIPPA_RULE is a C++ library which generates the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

Actually, the word "square" is meant to designate any quadrature region defined by:

        A(1) <= X <= B(1)
        A(2) <= Y <= B(2)
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

SQUARE_FELIPPA_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CIRCLE_RULE, a C++ library which computes quadrature rules over the circumference of a circle in 2D.

CUBE_ARBQ_RULE, a C++ library which computes quadrature rules with exactness up to total degree 15, over the interior of a cube in 3D.

CUBE_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a cube in 3D.

DISK_RULE, a C++ library which computes quadrature rules over the interior of a disk in 2D.

PYRAMID_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

PYRAMID_RULE, a C++ program which computes a quadrature rule over the interior of a pyramid in 3D.

SIMPLEX_GM_RULE, a C++ library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

SPHERE_LEBEDEV_RULE, a C++ library which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.

SQUARE_ARBQ_RULE, 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.

SQUARE_EXACTNESS, a C++ library which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

SQUARE_GRID, a C++ library which computes a grid of points over the interior of a cube in 3D.

SQUARE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

SQUARE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;

SQUARE_SYMQ_RULE, 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.

TETRAHEDRON_ARBQ_RULE, 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.

TETRAHEDRON_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

TETRAHEDRON_KEAST_RULE, a C++ library which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCC_RULE, a C++ library which defines Newton-Cotes closed quadrature rules over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCO_RULE, a C++ library which defines Newton-Cotes open quadrature rules over the interior of a tetrahedron in 3D.

TRIANGLE_DUNAVANT_RULE, a C++ library which defines Dunavant rules for quadrature over the interior of a triangle in 2D.

TRIANGLE_FEKETE_RULE, a C++ library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_LYNESS_RULE, a C++ library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_MONTE_CARLO, a C++ program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a C++ library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a C++ library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_SYMQ_RULE, 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.

TRIANGLE_WANDZURA_RULE, a C++ library which defines Wandzura rules for quadrature over the interior of a triangle in 2D.

WEDGE_FELIPPA_RULE, a C++ library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

Reference:

1. Carlos Felippa,
   A compendium of FEM integration formulas for symbolic work,
   Engineering Computation,
   Volume 21, Number 8, 2004, pages 867-890.

Source Code:

• square_felippa_rule.cpp, the source code.
• square_felippa_rule.hpp, the include file.
• square_felippa_rule.sh, BASH commands to compile the source code.

Examples and Tests:

• square_felippa_rule_prb.cpp, a sample calling program.
• square_felippa_rule_prb.sh, BASH commands to compile and run the sample program.
• square_felippa_rule_prb_output.txt, the output file.

List of Routines:

• COMP_NEXT computes the compositions of the integer N into K parts.
• LINE_UNIT_O01 returns a 1 point quadrature rule for the unit line.
• LINE_UNIT_O02 returns a 2 point quadrature rule for the unit line.
• LINE_UNIT_O03 returns a 3 point quadrature rule for the unit line.
• LINE_UNIT_O04 returns a 4 point quadrature rule for the unit line.
• LINE_UNIT_O05 returns a 5 point quadrature rule for the unit line.
• MONOMIAL_VALUE evaluates a monomial.
• SQUARE_MONOMIAL integrates a monomial over a square in 2D.
• SQUARE_MONOMIAL_TEST tests SQUARE_MONOMIAL.
• SQUARE_QUAD_TEST tests the rules for a square in 2D.
• SQUARE_RULE returns a quadrature rule for a square in 2D.
• SQUARE_VOLUME: volume of a unit quadrilateral.
• R8VEC_DIRECT_PRODUCT creates a direct product of R8VEC's.
• R8VEC_DIRECT_PRODUCT2 creates a direct product of R8VEC's.
• SUBCOMP_NEXT computes the next subcomposition of N into K parts.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.