triangle_dunavant_rule

triangle_dunavant_rule, a MATLAB code which returns a Dunavant quadrature rules over the interior of a triangle in 2D.

These rules are almost optimal, in the sense that, for each polynomial degree, the number of points used in the rule is close to, or equal to, the theoretical minimum possible value.

A few of the rules include one or two points which are "slightly" outside the triangle; a few of the rules include weights which are negative. Both of these occurrences are generally undesirable.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

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

Related Data and Programs:

triangle_dunavant_rule_test

matlab_rule, a MATLAB code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Reference:

1. David Dunavant,
   High Degree Efficient Symmetrical Gaussian Quadrature Rules for the Triangle,
   International Journal for Numerical Methods in Engineering,
   Volume 21, 1985, pages 1129-1148.
2. 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.

Source Code:

• dunavant_degree.m returns the degree of a Dunavant rule for the triangle.
• dunavant_order_num.m returns the order of a given Dunavant rule for the triangle.
• dunavant_rule.m returns the points and weights of a Dunavant rule.
• dunavant_rule_num.m returns the number of available Dunavant rules.
• dunavant_suborder.m returns the suborders for a Dunavant rule.
• dunavant_suborder_num.m returns the number of suborders for a Dunavant rule.
• dunavant_subrule.m returns a compressed Dunavant rule.
• 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.