TRIANGLE_WANDZURA_RULE
Quadrature Rules for Triangles

TRIANGLE_WANDZURA_RULE, a MATLAB library 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 GNU LGPL license.

Languages:

TRIANGLE_WANDZURA_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version

Related Data and Programs:

ANNULUS_RULE, a MATLAB library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

CUBE_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

PYRAMID_FELIPPA_RULE, a MATLAB library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

SIMPLEX_GM_RULE, a MATLAB library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

SQUARE_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

STROUD, a MATLAB library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TETRAHEDRON_FELIPPA_RULE, a MATLAB library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

TRIANGLE_DUNAVANT_RULE, a MATLAB library which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.

TRIANGLE_FEKETE_RULE, a MATLAB library which defines Fekete rules for quadrature or interpolation over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a MATLAB library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_LYNESS_RULE, a MATLAB library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_MONTE_CARLO, a MATLAB program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a MATLAB library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a MATLAB library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

triangle_wandzura_rule_test

WEDGE_FELIPPA_RULE, a MATLAB library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

Reference:

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.
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:

file_name_inc.m increments a partially numeric filename.
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.
timestamp.m prints the current YMDHMS date as a time stamp.
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.