tetrahedron_keast_rule, a C 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 information on this web page is 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.
c_rule, a C code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).
tetrahedron_exactness, a C code which investigates the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
tetrahedron_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
tetrahedron_monte_carlo, a C code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.