hexagon_rule

hexagon_rule, a MATLAB library which computes a quadrature rule over the interior of the unit hexagon.

Licensing:

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

Languages:

hexagon_rule is available in a MATLAB version.

Related Data and Programs:

ANNULUS_RULE, a MATLAB library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

CIRCLE_RULE, a MATLAB library which computes quadrature rules over the circumference of the unit circle in 2D.

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.

DISK_RULE, a MATLAB program which computes a quadrature rule over the interior of the unit disk in 2D, with radius 1 and center (0,0).

DISK01_QUARTER_RULE, a MATLAB program which computes a quadrature rule over the interior of the unit quarter disk in 2D, with radius 1 and center (0,0).

DISK01_RULE, a MATLAB library which computes quadrature rules over the interior of the unit disk in 2D.

hexagon_rule_test

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

PYRAMID_RULE, a MATLAB program which computes a quadrature rule over the interior of a pyramid in 3D.

SPHERE_LEBEDEV_RULE, a MATLAB library which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.

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 defines quadrature rules for a variety of M-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the M-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.

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

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.

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, Giovanni Monegato,
   Quadrature rules for regions having regular hexagonal symmetry,
   SIAM Journal on Numerical Analysis.
   Volume 14 Number 2, April 1977, pages 283-295.
2. Arthur Stroud,
   Approximate Calculation of Multiple Integrals,
   Prentice Hall, 1971.

Source Code:

• hexagon01_area.m, returns the area of the unit hexagon.
• hexagon_rule_lyness01.m, Lyness rule 01.
• hexagon_rule_lyness02.m, Lyness rule 02.
• hexagon_rule_lyness03.m, Lyness rule 03.
• hexagon_rule_lyness04.m, Lyness rule 04.
• hexagon_rule_lyness05.m, Lyness rule 05.
• hexagon_rule_lyness06.m, Lyness rule 06.
• hexagon_rule_lyness07.m, Lyness rule 07.
• hexagon_rule_lyness08.m, Lyness rule 08.
• hexagon_rule_lyness09.m, Lyness rule 09.
• hexagon_rule_lyness10.m, Lyness rule 10.
• hexagon_rule_lyness11.m, Lyness rule 11.
• hexagon_rule_lyness12.m, Lyness rule 12.
• hexagon_rule_lyness13.m, Lyness rule 13.
• hexagon_rule_stroud1.m, Stroud rule 1.
• hexagon_rule_stroud2.m, Stroud rule 2.
• hexagon_rule_stroud3.m, Stroud rule 3.
• hexagon_rule_stroud4.m, Stroud rule 4.
• monomial_value_2d.m, returns the value of a monomial x^ex y^ey.
• timestamp.m, prints the current YMDHMS date as a time stamp.