triangle_lyness_rule

triangle_lyness_rule, a MATLAB 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 computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

triangle_lyness_rule is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

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

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

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

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

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

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

triangle_exactness, a MATLAB code which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2d.

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

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

triangle_lyness_rule_test

triangle_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of a triangle in 2d.

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

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

triangle_wandzura_rule, a MATLAB code which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of a triangle in 2d.

wedge_felippa_rule, a MATLAB 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.

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.