triangle_symq_rule

triangle_symq_rule, a MATLAB code which returns symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle 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:

triangle_symq_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:

triangle_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.
• monomial_value.m, evaluates a multidimensional monomial.
• rule_order.m, returns the number of points in rules of order 0 through 20.
• 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.
• 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 29.
• rule28.m, returns the rule of degree 28.
• rule29.m, returns the rule of degree 29.
• rule30.m, returns the rule of degree 30.
• rule31.m, returns the rule of degree 31.
• rule32.m, returns the rule of degree 32.
• rule33.m, returns the rule of degree 33.
• rule34.m, returns the rule of degree 34.
• rule35.m, returns the rule of degree 35.
• rule36.m, returns the rule of degree 36.
• rule37.m, returns the rule of degree 37.
• rule38.m, returns the rule of degree 38.
• rule39.m, returns the rule of degree 39.
• rule40.m, returns the rule of degree 40.
• rule41.m, returns the rule of degree 41.
• rule42.m, returns the rule of degree 42.
• rule43.m, returns the rule of degree 43.
• rule44.m, returns the rule of degree 44.
• rule45.m, returns the rule of degree 45.
• rule46.m, returns the rule of degree 46.
• rule47.m, returns the rule of degree 47.
• rule48.m, returns the rule of degree 48.
• rule49.m, returns the rule of degree 49.
• rule50.m, the rule of degree 50.
• triangle_symq_rule.m, returns a triangle quadrature rule of given precision.
• triangle_unit_area.m, returns the area of a unit triangle.
• triangle_unit_monomial_integral.m, integrates a monomial over the unit triangle.