tetrahedron_keast_rule

tetrahedron_keast_rule, an Octave 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

Languages:

tetrahedron_keast_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

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.

cube_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a cube in 3d.

pyramid_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3d.

simplex_gm_rule, an Octave code which defines grundmann-moeller quadrature rules over the interior of a simplex in m dimensions.

square_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.

stroud, an Octave code which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2d, 3d and n-dimensions.

tetrahedron_arbq_rule, an Octave 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, an Octave code which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3d.

tetrahedron_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3d.

tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

tetrahedron_monte_carlo, an Octave code which uses the monte carlo method to estimate integrals over the interior of a tetrahedron in 3d.

tetrahedron_ncc_rule, an Octave code which defines newton-cotes closed (ncc) quadrature rules over the interior of a tetrahedron in 3d.

tetrahedron_nco_rule, an Octave code which defines newton-cotes open (nco) quadrature rules over the interior of a tetrahedron in 3d.

triangle_fekete_rule, an Octave code which defines fekete rules for quadrature or interpolation over the interior of a triangle in 2d.

triangle_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a triangle in 2d.

wedge_felippa_rule, an Octave code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3d.

Reference:

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

Source Code:

Last revised on 03 April 2019.