tetrahedron_keast_rule


tetrahedron_keast_rule a C++ code which defines ten quadrature rules, of degree of exactness 0 through 8, over the interior of the tetrahedron in 3D.

The ten rules have the following orders and precisions:
RuleOrderPrecision
1 1 1
2 4 2
3 5 3
410 3
511 4
614 4
715 5
824 6
931 7
1045 8

Licensing:

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

Languages:

tetrahedron_keast_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

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

SIMPLEX_GM_RULE, a C++ code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

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.

STROUD, a C++ code which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

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_EXACTNESS, a C++ code which investigates the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.

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

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

tetrahedron_keast_rule_test

TETRAHEDRON_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TETRAHEDRON_NCC_RULE, a C++ code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCO_RULE, a C++ code which defines Newton-Cotes Open (NCO) quadrature rules 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.

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

Reference:

  1. Patrick Keast,
    Moderate Degree Tetrahedral Quadrature Formulas,
    Computer Methods in Applied Mechanics and Engineering,
    Volume 55, Number 3, May 1986, pages 339-348.

Source Code:


Last revised on 30 April 2020.