SQUARE_FELIPPA_RULE
Quadrature Rules for a Square in 2D

SQUARE_FELIPPA_RULE, a MATLAB 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 FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ANNULUS_RULE, a MATLAB library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

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

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

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

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

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

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

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

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

SQUARE_ARBQ_RULE, 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.

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

square_felippa_rule_test

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

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

SQUARE_MINIMAL_RULE, a MATLAB library which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2D, by Mattia Festa and Alvise Sommariva.

SQUARE_MONTE_CARLO, 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;

SQUARE_SYMQ_RULE, 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.

TETRAHEDRON_ARBQ_RULE, 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.

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

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

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

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

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

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

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

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

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

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

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

TRIANGLE_SYMQ_RULE, 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.

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

WEDGE_FELIPPA_RULE, a MATLAB 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:

• comp_next.m, computes the compositions of the integer N into K parts.
• line_unit_o01.m, returns a 1 point quadrature rule for the unit line.
• line_unit_o02.m, returns a 2 point quadrature rule for the unit line.
• line_unit_o03.m, returns a 3 point quadrature rule for the unit line.
• line_unit_o04.m, returns a 4 point quadrature rule for the unit line.
• line_unit_o05.m, returns a 5 point quadrature rule for the unit line.
• monomial_value.m, evaluates a monomial.
• square_monomial.m, returns the exact integral of a monomial in a square in 2D.
• square_monomial_test.m, tests SQUARE_MONOMIAL.
• square_quad_test.m, tests the quadrature rules for a square in 2D.
• square_rule.m, returns a quadrature rule for a square in 2D;
• square_volume.m, returns the volume of a square in 2D;
• r8vec_direct_product.m, creates a direct product of R8VEC's.
• r8vec_direct_product2.m, creates a direct product of R8VEC's.
• subcomp_next.m, computes the next subcomposition of N into K parts.
• timestamp.m, prints the YMDHMS date as a timestamp;