# triangle_lyness_rule

triangle_lyness_rule, a FORTRAN90 code which produces the Lyness-Jespersen family of quadrature rules over the interior of the triangle in 2D.

The rules have the following orders (number of points) and precisions (maximum degree of polynomials whose integrals they can compute exactly):
RuleOrderPrecision
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 2711
21 2811

### Languages:

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

### Related Data and Programs:

TRIANGLE_DUNAVANT_RULE, a FORTRAN90 code which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.

TRIANGLE_EXACTNESS, a FORTRAN90 code which investigates the polynomial exactness of a quadrature rule over the interior of the triangle in 2D.

TRIANGLE_FEKETE_RULE, a FORTRAN90 code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a FORTRAN90 code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a FORTRAN90 code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_WANDZURA_RULE, a FORTRAN90 code which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of a triangle in 2D.

### 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:

Last revised on 10 September 2020.