tetrahedron_jaskowiec_rule


tetrahedron_jaskowiec_rule, a MATLAB 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:

tetrahedron_jaskowiec_rule_test

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

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

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 23 May 2023.