TETRAHEDRON_ARBQ_RULE
Quadrature Rules for Tetrahedrons.


TETRAHEDRON_ARBQ_RULE is a C library 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.

The original source code, from which this library was developed, is available from the Courant Mathematics and Computing Laboratory, at http://www.cims.nyu.edu/cmcl/quadratures/quadratures.html ,

Licensing:

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

Languages:

TETRAHEDRON_ARBQ_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

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

SIMPLEX_GM_RULE, a C library which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.

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

SQUARE_SYMQ_RULE, a C library 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 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_EXACTNESS, a C program which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.

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

TETRAHEDRON_INTEGRALS, a C library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

TETRAHEDRON_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit tetrahedron in 3D.

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

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

TRIANGLE_SYMQ_RULE, a C library 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 library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

Reference:

  1. Hong Xiao, Zydrunas Gimbutas,
    A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions,
    Computers and Mathematics with Applications,
    Volume 59, 2010, pages 663-676.

Source Code:

Examples and Tests:

TETRAHEDRON08 is a degree 8 rule in the reference tetrahedron.

List of Routines:

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


Last revised on 10 July 2014.