square_arbq_rule, a C code which returns quadrature rules, with exactness up to total degree 30, over the interior of the symmetric square in 2D, 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 MIT license
square_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_ARBQ_RULE, a C code which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.
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.
gnuplot_test, C codes which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.
PYRAMID_FELIPPA_RULE, a C code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
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_GRID, a C code which computes a grid of points over the interior of a square in 2D.
SQUARE_INTEGRALS, a C code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.
SQUARE_MINIMAL_RULE, a C code which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric square in 2D, by Mattia Festa and Alvise Sommariva.
SQUARE_MONTE_CARLO, a C code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.
SQUARE_SYMQ_RULE, a C code which returns efficient symmetric quadrature rules, with exactness up to total degree 15, over the interior of a 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.
TOMS886, a C code which defines the Padua points for interpolation in a 2D region, including the rectangle, triangle, and ellipse, by Marco Caliari, Stefano de Marchi, Marco Vianello. This is a version of ACM TOMS algorithm 886.
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.