# SQUARE_FELIPPA_RULE Quadrature Rules for a Square in 2D

SQUARE_FELIPPA_RULE is a FORTRAN90 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)
```

### 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:

CIRCLE_RULE, a FORTRAN90 library which computes quadrature rules over the circumference of a circle in 2D.

CUBE_ARBQ_RULE, a FORTRAN90 library which computes quadrature rules with exactness up to total degree 15, over the interior of a cube in 3D.

CUBE_FELIPPA_RULE, a FORTRAN90 library which returns Felippa's quadratures rules for approximating integrals over the interior of a cube in 3D.

DISK_RULE, a FORTRAN90 library which computes quadrature rules over the interior of a disk in 2D.

PYRAMID_FELIPPA_RULE, a FORTRAN90 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

PYRAMID_RULE, a FORTRAN90 program which computes a quadrature rule over the interior of a pyramid in 3D.

SIMPLEX_GM_RULE, a FORTRAN90 library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

SPHERE_LEBEDEV_RULE, a FORTRAN90 library which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.

SQUARE_ARBQ_RULE, a FORTRAN90 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 FORTRAN90 library which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

SQUARE_GRID, a FORTRAN90 library which computes a grid of points over the interior of a cube in 3D.

SQUARE_INTEGRALS, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

TETRAHEDRON_KEAST_RULE, a FORTRAN90 library which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCC_RULE, a FORTRAN90 library which defines Newton-Cotes closed quadrature rules over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCO_RULE, a FORTRAN90 library which defines Newton-Cotes open quadrature rules over the interior of a tetrahedron in 3D.

TRIANGLE_DUNAVANT_RULE, a FORTRAN90 library which defines Dunavant rules for quadrature over the interior of a triangle in 2D.

TRIANGLE_FEKETE_RULE, a FORTRAN90 library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a FORTRAN90 library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_LYNESS_RULE, a FORTRAN90 library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_MONTE_CARLO, a FORTRAN90 program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a FORTRAN90 library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a FORTRAN90 library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_SYMQ_RULE, a FORTRAN90 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 FORTRAN90 library which defines Wandzura rules for quadrature over the interior of a triangle in 2D.

WEDGE_FELIPPA_RULE, a FORTRAN90 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.

### 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 FORTRAN90 source codes.

Last revised on 05 September 2014.