triangle_symq_rule


triangle_symq_rule, a C code which returns symmetric quadrature rules, with exactness up to total degree 50, over the interior of a triangle, 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 and a Python version.

Related Data and Programs:

triangle_symq_rule_test

simplex_gm_rule, a C code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

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triangle_exactness, a C code which investigates the monomial exactness quadrature rule over the interior of a triangle in 2D.

triangle_fekete_rule, a C code which defines a Fekete rule for interpolation or quadrature over the interior of a triangle in 2D.

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

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

triangle_monte_carlo, a C 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 C code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

triangle_nco_rule, a C code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

triangle_witherden_rule, a C 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 22 August 2019.