# 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 ,

### 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:

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:

Last revised on 10 June 2023.