square_arbq_rule

square_arbq_rule, a MATLAB code which returns quadrature rules, with exactness up to total degree 30, over the interior of the symmetric square in 2D, 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:

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

Related Data and Programs:

square_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:

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• lege2eva.m, evaluates orthogonal polynomials on the symmetric square.
• llegepols1.m, evaluates orthogonal polynomials on the symmetric interval.
• 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.
• rule21.m, returns the rule of degree 21.
• rule22.m, returns the rule of degree 22.
• rule23.m, returns the rule of degree 23.
• rule24.m, returns the rule of degree 24.
• rule25.m, returns the rule of degree 25.
• rule26.m, returns the rule of degree 26.
• rule27.m, returns the rule of degree 27.
• rule28.m, returns the rule of degree 28.
• rule29.m, returns the rule of degree 29.
• rule30.m, returns the rule of degree 30.
• square_arbq.m, returns a quadrature rule for the symmetric square.
• square_arbq_gnuplot.m, GNUPLOT plot of a quadrature rule for the symmetric square.
• square_arbq_size.m, returns the size of a quadrature rule for the symmetric square.