tetrahedron_jaskowiec_rule


tetrahedron_jaskowiec_rule, a Python 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.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

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:

ccn_rule, a Python code which defines a Clenshaw Curtis Nested (CCN) quadrature rule.

clenshaw_curtis_rule, a Python code which returns a Clenshaw Curtis quadrature rule.

hermite_rule, a Python code which returns a Gauss-Hermite quadrature rule for estimating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).

jacobi_rule, a Python code which returns a Gauss-Jacobi quadrature rule.

laguerre_rule, a Python code which returns a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).

legendre_rule, a Python code which returns a Gauss-Legendre quadrature rule for estimating the integral of a function with density rho(x)=1 over the interval [-1,+1].

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

tetrahedron, a Python code which carries out geometric calculations involving a general tetrahedron, including solid and facial angles, face areas, point containment, distances to a point, circumsphere and insphere, measures of shape quality, centroid, barycentric coordinates, edges and edge lengths, random sampling, and volumes.

tetrahedron_arbq_rule, a Python 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_integrals, a Python 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 Python code which uses the Monte Carlo method to estimate integrals over the interior of a general tetrahedron in 3D.

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

tetrahedron01_monte_carlo, a Python code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

Reference:

  1. Jan Jaskowiec, Natarajan Sukumar,
    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.
  2. Jan Jaskowiec, Natarajan Sukumar,
    High order symmetric cubature rules for tetrahedra and pyramids,
    International Journal of Numerical Methods in Engineering,
    Volume 122, Number 1, pages 148-171, 24 August 2020.

Source Code:


Last revised on 13 April 2023.