tetrahedron_keast_rule, an Octave code which defines ten quadrature rules, of degree of exactness 0 through 8, over the interior of the tetrahedron in 3D.
The ten rules have the following orders and precisions:
| Rule | Order | Precision |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 2 |
| 3 | 5 | 3 |
| 4 | 10 | 3 |
| 5 | 11 | 4 |
| 6 | 14 | 4 |
| 7 | 15 | 5 |
| 8 | 24 | 6 |
| 9 | 31 | 7 |
| 10 | 45 | 8 |
The computer code and data files described and made available on this web page are distributed under the MIT license
tetrahedron_keast_rule is available in a C version and 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 defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2d, 3d and n-dimensions.
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_exactness, an Octave code which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3d.
tetrahedron_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3d.
tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
tetrahedron_monte_carlo, an Octave code which uses the monte carlo method to estimate integrals 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_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.
wedge_felippa_rule, an Octave code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3d.