tetrahedron_jaskowiec_rule, a Fortran90 code which returns quadrature rules, with exactness up to total degree 20, over the interior of a tetrahedron in 3D, by Jan Jaskowiec, Natarajan Sukumar.

The quadrature rules are described in terms of barycentric coordinates (a,b,c,d), with weights w that sum to 1.

Languages:

tetrahedron_jaskowiec_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

simplex_gm_rule, a Fortran90 code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2d, a tetrahedron in 3d, or over the interior of the simplex in m dimensions.

tetrahedron_arbq_rule, a Fortran90 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, a Fortran90 code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3d.

tetrahedron_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

tetrahedron_keast_rule, a Fortran90 code which returns a Keast quadrature rule, with exactness between 0 and 8, over the interior of a tetrahedron in 3D.

tetrahedron_monte_carlo, a Fortran90 code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit tetrahedron in 3d.

tetrahedron_ncc_rule, a Fortran90 code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.

tetrahedron_nco_rule, a Fortran90 code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a tetrahedron in 3D.

tetrahedron_witherden_rule, a Fortran90 code which returns a symmetric Witherden quadrature rule for the tetrahedron, with exactness up to total degree 10.

Reference:

High order cubature rules for tetrahedra and pyramids,
International Journal of Numerical Methods in Engineering,
Volume 121, Number 11, pages 2418-2436, 15 June 2020.