tetrahedron_arbq_rule

tetrahedron_arbq_rule, a MATLAB 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.

The original source code, from which this library was developed, is available from the Courant Mathematics and Computing Laboratory, at https://www.cims.nyu.edu/cmcl/quadratures/quadratures.html ,

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

tetrahedron_arbq_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_arbq_rule_test

matlab_rule, a MATLAB 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).

Reference:

1. Hong Xiao, Zydrunas Gimbutas,
   A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions,
   Computers and Mathematics with Applications,
   Volume 59, 2010, pages 663-676.

Source Code:

• kjacoypols3.m, evaluates modified Jacobi polynomials.
• klegeypols.m, evaluates scaled Legendre polynomials.
• ortho3eva.m, evaluates polynomials orthogonal in the reference triangle.
• ref_to_koorn.m, maps points from the reference to Koornwinder's tetrahedron.
• 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.
• tetrahedron_arbq.m, returns a quadrature rule for the tetrahedron.
• tetrahedron_arbq_gnuplot.m, GNUPLOT plot of a quadrature rule for the tetrahedron.
• tetrahedron_arbq_size.m, returns the size of a quadrature rule for the tetrahedron.
• tetrahedron_ref.m, returns the vertices of the reference tetrahedron.