triangle_wandzura_rule

triangle_wandzura_rule, an Octave code which can return any of six Wandzura rules for quadrature over the interior of a triangle in 2D.

There are six rules, which have polynomial degree of exactness of 5, 10, 15, 20, 25, and 30.

Licensing:

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

Languages:

triangle_wandzura_rule is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

triangle_wandzura_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.

annulus_rule, an Octave code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2d.

cube_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a cube in 3d.

pyramid_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3d.

simplex_gm_rule, an Octave code which defines grundmann-moeller quadrature rules over the interior of a simplex in m dimensions.

square_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.

stroud, an Octave code which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2d, 3d and n-dimensions.

tetrahedron_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3d.

triangle_dunavant_rule, an Octave code which sets up a dunavant quadrature rule over the interior of a triangle in 2d.

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

triangle_monte_carlo, an Octave code which uses the monte carlo method to estimate 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.

wedge_felippa_rule, an Octave code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3d.

Reference:

1. James Lyness, Dennis Jespersen,
   Moderate Degree Symmetric Quadrature Rules for the Triangle,
   Journal of the Institute of Mathematics and its Applications,
   Volume 15, Number 1, February 1975, pages 19-32.
2. Stephen Wandzura, Hong Xiao,
   Symmetric Quadrature Rules on a Triangle,
   Computers and Mathematics with Applications,
   Volume 45, Number 12, June 2003, pages 1829-1840.

Source Code:

• i4_modp.m returns the nonnegative remainder of integer division.
• i4_wrap.m forces an integer to lie between given limits by wrapping.
• reference_to_physical_t3.m maps T3 reference points to physical points.
• triangle_area.m computes the area of a triangle.
• triangle_points_plot.m plots a triangle and some points.
• wandzura_degree.m returns the degree of a given Wandzura rule for the triangle.
• wandzura_order_num.m returns the order of a given Wandzura rule for the triangle.
• wandzura_rule.m returns the points and weights of a Wandzura rule.
• wandzura_rule_num.m returns the number of Wandzura rules available.
• wandzura_suborder.m returns the suborders for a Wandzura rule.
• wandzura_suborder_num.m returns the number of suborders for a Wandzura rule.
• wandzura_subrule.m returns a compressed Wandzura rule.
• wandzura_subrule2.m returns a compressed Wandzura rule, using the nonstandard reference triangle.