TRIANGLE_LYNESS_RULE
Quadrature Rules for the Triangle


TRIANGLE_LYNESS_RULE is a MATLAB library 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):
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

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

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

Related Data and Programs:

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 M-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_EXACTNESS, a MATLAB program which investigates the polynomial exactness of a 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_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, a MATLAB library 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 library 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:

Examples and Tests:

You can go up one level to the MATLAB source codes.


Last revised on 28 June 2014.