triangle_twb_rule

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

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

triangle_twb_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_twb_rule_test

alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

triangle_fekete_rule, an Octave code which defines fekete rules for interpolation or quadrature over the interior of a triangle in 2d.

triangle_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a triangle in 2d.

triangle_ncc_rule, an Octave code which defines newton-cotes closed (ncc) quadrature rules over the interior of a triangle in 2d.

triangle_nco_rule, an Octave code which defines newton-cotes open (nco) quadrature rules over the interior of a triangle in 2d.

triangle_symq_rule, an Octave code which returns efficient 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.

Reference:

1. Rouben Rostamian,
   Programming Projects in C for Students of Engineering, Science, and Mathematics,
   SIAM, 2014,
   ISBN:978-1-611973-49-5,
   LC: Q183.9R67.
2. Mark Taylor, Beth Wingate, Len Bos,
   Several new quadrature formulas for polynomial integration in the triangle,
   https://arxiv.org/abs/math/0501496v2,
   08 February 2007.

Source Code:

• monomial_value_2d.m, evaluates a monomial in 2D.
• triangle_unit_monomial.m, returns the integral of a monomial over the unit triangle.
• triangle_unit_volume.m, returns the area of the unit triangle.
• twb_rule_n.m, returns orders of a TWB rule.
• twb_rule_w.m, returns weights of a TWB rule.
• twb_rule_x.m, returns x abscissas of a TWB rule.
• twb_rule_y.m, returns y abscissas of a TWB rule.