triangle_lyness_rule, an Octave code which produces the Lyness-Jespersen family of quadrature rules over the interior of a triangle in 2D.
The rules have the following orders (number of points) and precisions (maximum degree of polynomials whose integrals they can compute exactly):
Rule | Order | Precision |
---|---|---|
0 | 1 | 1 |
1 | 3 | 2 |
2 | 4 | 2 |
3 | 4 | 3 |
4 | 7 | 3 |
5 | 6 | 4 |
6 | 10 | 4 |
7 | 9 | 4 |
8 | 7 | 5 |
9 | 10 | 5 |
10 | 12 | 6 |
11 | 16 | 6 |
12 | 13 | 6 |
13 | 13 | 7 |
14 | 16 | 7 |
15 | 16 | 8 |
16 | 21 | 8 |
17 | 16 | 8 |
18 | 19 | 9 |
19 | 22 | 9 |
20 | 27 | 11 |
21 | 28 | 11 |
The computer code and data files described and made available on this web page are distributed under the MIT license
triangle_lyness_rule is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
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.
pyramid_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals 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.
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 contains 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.
triangle_dunavant_rule, an Octave code which sets up a dunavant quadrature rule over the interior of a triangle in 2d.
triangle_exactness, an Octave code which investigates the polynomial exactness of a 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_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_wandzura_rule, an Octave code which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of a triangle in 2d.
wedge_felippa_rule, an Octave code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3d.