# wedge_felippa_rule

wedge_felippa_rule, an Octave code which generates quadrature rules to estimate integrals over the interior of the unit wedge in 3D.

The interior of the unit wedge in 3D is defined by the constraints:

```        0 <= X
0 <= Y
X + Y <= 1
-1 <= Z <= +1
```

### Languages:

wedge_felippa_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB versionand 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.

cube_felippa_rule, an Octave code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

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

pyramid_felippa_rule, an Octave code which returns Felippa's quadratures 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 the pyramid in 3D.

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

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.

stroud, an Octave code which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and M-dimensions.

tetrahedron_felippa_rule, an Octave code which returns Felippa's quadratures 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 sets up a Dunavant quadrature rule over the interior of a triangle in 2D.

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

triangle_felippa_rule, an Octave code which returns Felippa's quadratures 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_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_wandzura_rule, an Octave code which defines Wandzura rules for quadrature over the interior of a triangle in 2D.

wedge_exactness, an Octave code which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

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

wedge_monte_carlo, an Octave code which uses the Monte Carlo method to estimate the value of an integral over the interior of a 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_o01.m, returns a 1 point quadrature rule for the unit line.
• line_o02.m, returns a 2 point quadrature rule for the unit line.
• line_o03.m, returns a 3 point quadrature rule for the unit line.
• line_o04.m, returns a 4 point quadrature rule for the unit line.
• line_o05.m, returns a 5 point quadrature rule for the unit line.
• monomial_value.m, evaluates a monomial.
• subcomp_next.m, computes the next subcomposition of N into K parts.
• triangle_o01.m, returns a 1 point quadrature rule for the unit triangle.
• triangle_o03.m, returns a 3 point quadrature rule for the unit triangle.
• triangle_o03b.m, returns a 3 point quadrature rule for the unit triangle.
• triangle_o06.m, returns a 6 point quadrature rule for the unit triangle.
• triangle_o06b.m, returns a 6 point quadrature rule for the unit triangle.
• triangle_o07.m, returns a 7 point quadrature rule for the unit triangle.
• triangle_o12.m, returns a 12 point quadrature rule for the unit triangle.
• wedge_integral.m, returns the exact integral of a monomial in a unit wedge;
• wedge_rule.m, returns a quadrature rule for the unit wedge;
• wedge_volume.m, returns the volume of a unit wedge;

Last revised on 06 October 2022.