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 computer code and data files made available on this web page are 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.

Related Data and Programs:

triangle_symq_rule_test

simplex_gm_rule, a MATLAB code which defines a Grundmann-Moeller quadrature rule over the interior of a simplex in m dimensions.

triangle_dunavant_rule, a MATLAB code which returns a Dunavant quadrature rule over the interior of a triangle in 2d.

triangle_fekete_rule, a MATLAB code which returns a Fekete rule for quadrature or interpolation over the interior of a triangle in 2d.

triangle_felippa_rule, a MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2d.

triangle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.

triangle_lyness_rule, a MATLAB code which returns a Lyness-Jespersen quadrature rule over the interior of a triangle in 2d.

triangle_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit triangle in 2d.

triangle_ncc_rule, a MATLAB code which defines Newton-Cotes closed quadrature rules on a triangle.

triangle_nco_rule, a MATLAB code which defines Newton-Cotes open quadrature rules over the interior of a triangle in 2d.

triangle_symq_to_ref, a MATLAB code which creates quadrature rules defined on the half-unit square from symmetric quadrature rules defined on an equilateral triangle, defined by triangle_symq_rule(), by Hong Xiao and Zydrunas Gimbutas.

triangle_twb_rule, a MATLAB code which generates the points and weights of quadrature rules over the interior of a triangle in 2D, determined by Taylor, Wingate, and Bos.

triangle_wandzura_rule, a MATLAB code which returns a Wandzura quadrature rule of exactness 5, 10, 15, 20, 25 and 30 over the interior of the triangle in 2D.

triangle_witherden_rule, a MATLAB code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.

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.