cube_arbq_rule, a C code which returns quadrature rules, with exactness up to total degree 15, over the interior of a cube in 3D, by Hong Xiao and Zydrunas Gimbutas.
The original source code, from which this library was developed, is available from the Courant Mathematics and Computing Laboratory, at https://www.cims.nyu.edu/cmcl/quadratures/quadratures.html ,
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
cube_arbq_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
ANNULUS_RULE, a C code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.
CUBE_EXACTNESS, a C code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.
CUBE_FELIPPA_RULE, a C code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
CUBE_GRID, a C code which computes a grid of points over the interior of a cube in 3D.
CUBE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
CUBE_MONTE_CARLO, a C code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;
gnuplot_test, examples which illustrate the use of the gnuplot graphics program.
PYRAMID_FELIPPA_RULE, a C code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
SQUARE_ARBQ_RULE, a C code which returns quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.
SQUARE_FELIPPA_RULE, a C code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
SQUARE_SYMQ_RULE, a C code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.
STROUD, a C 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_ARBQ_RULE, a C code which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3D, by Hong Xiao and Zydrunas Gimbutas.
TETRAHEDRON_FELIPPA_RULE, a C code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TRIANGLE_FEKETE_RULE, a C code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
TRIANGLE_FELIPPA_RULE, a C code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
TRIANGLE_SYMQ_RULE, a C code which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
WEDGE_FELIPPA_RULE, a C code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.