triangle_lyness_rule

triangle_lyness_rule, an Octave code which produces the Lyness-Jespersen family of quadrature rules over the interior of a triangle in 2D.

The rules have the following orders (number of points) and precisions (maximum degree of polynomials whose integrals they can compute exactly):

Rule	Order	Precision
0	1	1
1	3	2
2	4	2
3	4	3
4	7	3
5	6	4
6	10	4
7	9	4
8	7	5
9	10	5
10	12	6
11	16	6
12	13	6
13	13	7
14	16	7
15	16	8
16	21	8
17	16	8
18	19	9
19	22	9
20	27	11
21	28	11

Licensing:

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

Languages:

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

Related Data and Programs:

triangle_lyness_rule_test

octave_rule, an Octave 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. 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:

• i4_modp.m returns the nonnegative remainder of I4 division.
• i4_wrap.m forces an I4 to lie between given limits by wrapping.
• lyness_order.m returns the order of a Lyness quadrature rule.
• lyness_precision.m returns the precision of a Lyness quadrature rule.
• lyness_rule.m returns the points and weights of a Lyness quadrature rule.
• lyness_rule_num.m returns the number of Lyness quadrature rules.
• lyness_suborder.m returns the suborders for a Lyness rule.
• lyness_suborder_num.m returns the number of suborders for a Lyness rule.
• lyness_subrule.m returns a compressed Lyness rule.