square_symq_rule

square_symq_rule, a MATLAB code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the unit square, 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_symq_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and a Octave version and a Python version.

Related Data and Programs:

square_symq_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:

• comp_next.m, returns the next composition of an integer.
• lege2eva.m, evaluates orthogonal polynomials on the symmetric square.
• llegepols1.m, evaluates orthogonal polynomials on the symmetric interval.
• monomial_value.m, evaluates a multidimensional monomial.
• quadrilateral_unit_area.m, computes the area of a unit quadrilateral.
• quadrilateral_unit_monomial_integral.m, returns the exact integral of a given monomial over the unit quadrilateral.
• rule_order.m, returns the order of the requested quadrature rule.
• 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.
• square_symq.m, returns a symmetric quadrature rule for the square.
• square_symq_plot.m, plots the symmetric square quadrature rule.