TRIANGLE_LYNESS_RULE
Quadrature Rules for the Triangle

TRIANGLE_LYNESS_RULE is a FORTRAN90 library 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):

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 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 FORTRAN90 library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

PYRAMID_FELIPPA_RULE, a FORTRAN90 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

SIMPLEX_GM_RULE, a FORTRAN90 library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

SQUARE_FELIPPA_RULE, a FORTRAN90 library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

STROUD, a FORTRAN90 library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and M-dimensions.

TETRAHEDRON_FELIPPA_RULE, a FORTRAN90 library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

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

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

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

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

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

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

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

TRIANGLE_WANDZURA_RULE, a FORTRAN90 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 FORTRAN90 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:

• triangle_lyness_rule.f90, the source code.

Examples and Tests:

• triangle_lyness_rule_test.f90, a sample calling program.
• triangle_lyness_rule_test.txt, the output file.

List of Routines:

• I4_MODP returns the nonnegative remainder of I4 division.
• I4_WRAP forces an I4 to lie between given limits by wrapping.
• LYNESS_ORDER returns the order of a Lyness quadrature rule.
• LYNESS_PRECISION returns the precision of a Lyness quadrature rule.
• LYNESS_RULE returns the points and weights of a Lyness quadrature rule.
• LYNESS_RULE_NUM returns the number of Lyness quadrature rules.
• LYNESS_SUBORDER returns the suborders for a Lyness rule.
• LYNESS_SUBORDER_NUM returns the number of suborders for a Lyness rule.
• LYNESS_SUBRULE returns a compressed Lyness rule.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.