# cube_felippa_rule

cube_felippa_rule, an Octave code 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 MATLAB version and an Octave version.

### Related Data and Programs:

alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

annulus_rule, an Octave code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

circle_rule, an Octave code which computes quadrature rules over the circumference of a circle in 2D.

cube_arbq_rule, an Octave code which computes quadrature rules with exactness up to total degree 15, over the interior of a cube in 3D.

cube_exactness, an Octave code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

cube_grid, an Octave code which computes a grid of points over the interior of a cube in 3D.

cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

cube_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;

disk_rule, an Octave code which computes quadrature rules over the interior of a disk in 2D.

pyramid_felippa_rule, an Octave code which returns Felippa's quadrature rules for approximating integrals over the interior of a pyramid in 3D.

pyramid_rule, an Octave code which computes a quadrature rule over the interior of a pyramid in 3D.

simplex_gm_rule, an Octave code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

sphere_lebedev_rule, an Octave code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.

square_arbq_rule, an Octave code 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, an Octave code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

square_symq_rule, an Octave code 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, an Octave code 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, an Octave code which returns Felippa's quadrature rules for approximating integrals over the interior of a tetrahedron in 3D.

tetrahedron_keast_rule, an Octave code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.

tetrahedron_ncc_rule, an Octave code which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.

tetrahedron_nco_rule, an Octave code which defines Newton-Cotes open )NCO) quadrature rules over the interior of a tetrahedron in 3D.

triangle_dunavant_rule, an Octave code which defines Dunavant rules for quadrature over the interior of a triangle in 2D.

triangle_fekete_rule, an Octave code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

triangle_felippa_rule, an Octave code which returns Felippa's quadrature rules for approximating integrals over the interior of a triangle in 2D.

triangle_lyness_rule, an Octave code which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

triangle_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

triangle_ncc_rule, an Octave code which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a triangle in 2D.

triangle_nco_rule, an Octave code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a triangle in 2D.

triangle_symq_rule, an Octave code 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, an Octave code which defines Wandzura rules for quadrature over the interior of a triangle in 2D.

wedge_felippa_rule, an Octave code which returns quadrature 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:

Last revised on 22 December 2018.