tetrahedron_jaskowiec_rule

tetrahedron_jaskowiec_rule, an Octave 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

simplex_gm_rule, an Octave 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, an Octave 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, 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_felippa_rule, an Octave code which returns a Felippa quadrature rule 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_keast_rule, an Octave code which returns a Keast quadrature rule for approximating integrals over the interior of a tetrahedron in 3d.

tetrahedron_monte_carlo, an Octave 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, 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.

tetrahedron_witherden_rule, an Octave 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:

• comp_next.m, returns the next composition of an integer.
• monomial_value.m, evaluates a multidimensional monomial.
• rule_order.m, returns the number of quadrature points used in a rule of given degree.
• rule00.m, returns the rule of degree 0.
• rule01.m, returns the rule of degree 1.
• rule02.m, returns the rule of degree 2.
• rule03.m, returns the rule of degree 3.
• rule04.m, returns the rule of degree 4.
• rule05.m, returns the rule of degree 5.
• rule06.m, returns the rule of degree 6.
• rule07.m, returns the rule of degree 7.
• rule08.m, returns the rule of degree 8.
• rule09.m, returns the rule of degree 9.
• rule10.m, returns the rule of degree 10.
• rule11.m, returns the rule of degree 11.
• rule12.m, returns the rule of degree 12.
• rule13.m, returns the rule of degree 13.
• rule14.m, returns the rule of degree 14.
• rule15.m, returns the rule of degree 15.
• rule16.m, returns the rule of degree 16.
• rule17.m, returns the rule of degree 17.
• rule18.m, returns the rule of degree 18.
• rule19.m, returns the rule of degree 19.
• rule20.m, returns the rule of degree 20.
• tetrahedron_jaskowiec_rule.m, returns a tetrahedron rule of given precision.
• tetrahedron_unit_monomial_integral.m, integrates a monomial over the unit tetrahedron.
• tetrahedron_unit_volume.m, computes the volume of a unit tetrahedron.
• tetrahedron_volume.m, computes the volume of a tetrahedron.

• tetrahedron_jaskowiec_rule_to_matlab.m, a MATLAB code which reads a data file describing one of the rules (with 128 digits) and writes a function to return points and weights.