# CUBE_FELIPPA_RULE Quadrature Rules for a Cube in 3D

CUBE_FELIPPA_RULE is a MATLAB library which generates the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

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

```        A(1) <= X <= B(1)
A(2) <= Y <= B(2)
A(3) <= Z <= B(3)
```

### Languages:

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

### Related Data and Programs:

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

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

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

CUBE_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;

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_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

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.

### Examples and Tests:

You can go up one level to the MATLAB source codes.

Last revised on 05 September 2014