hexagon_lyness_rule

hexagon_lyness_rule, an Octave code which returns one of 13 Lyness quadrature rules over the interior of the unit hexagon.

The Lyness rules assume the hexagon has a "peaked top and bottom:

             *
          *     *
          *     *
             * 
    

Licensing:

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

Languages:

hexagon_lyness_rule is available in a MATLAB version and an Octave version..

Related Data and Programs:

hexagon_lyness_rule_test

alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

annulus_rule, an Octave code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

circle_rule, an Octave code which computes quadrature rules over the circumference of the unit circle in 2D.

cube_felippa_rule, an Octave code which returns a Felippa quadrature rule over the interior of a cube in 3D.

disk_rule, an Octave code which computes a quadrature rule over the interior of the unit disk in 2D, with radius 1 and center (0,0).

disk01_quarter_rule, an Octave code which computes a quadrature rule over the interior of the unit quarter disk in 2D, with radius 1 and center (0,0).

disk01_rule, an Octave code which computes quadrature rules over the interior of the unit disk in 2D.

hexagon_stroud_rule, an Octave code which computes one of four Stroud quadrature rules over the interior of the unit hexagon.

pyramid_felippa_rule, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.

pyramid_rule, an Octave code which computes a quadrature rule over the interior of a pyramid in 3D.

sphere_lebedev_rule, an Octave code which computes Lebedev quadrature rules on the surface of the unit sphere in 3D.

square_felippa_rule, an Octave code which returns a Felippa quadrature rule over the interior of a square in 2D.

stroud, an Octave code 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, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3D.

triangle_fekete_rule, an Octave code which defines a Fekete rule for quadrature or interpolation over the interior of a triangle in 2D.

triangle_felippa_rule, an Octave code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.

wedge_felippa_rule, an Octave code which returns a Felippa quadrature rule 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.

Source Code:

• hexagon01_area.m, returns the area of the unit hexagon.
• hexagon_lyness_rule01.m, Lyness rule 01.
• hexagon_lyness_rule02.m, Lyness rule 02.
• hexagon_lyness_rule03.m, Lyness rule 03.
• hexagon_lyness_rule04.m, Lyness rule 04.
• hexagon_lyness_rule05.m, Lyness rule 05.
• hexagon_lyness_rule06.m, Lyness rule 06.
• hexagon_lyness_rule07.m, Lyness rule 07.
• hexagon_lyness_rule08.m, Lyness rule 08.
• hexagon_lyness_rule09.m, Lyness rule 09.
• hexagon_lyness_rule10.m, Lyness rule 10.
• hexagon_lyness_rule11.m, Lyness rule 11.
• hexagon_lyness_rule12.m, Lyness rule 12.
• hexagon_lyness_rule13.m, Lyness rule 13.
• monomial_value_2d.m, returns the value of a monomial x^ex y^ey.