stroud


stroud, a MATLAB 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.

A few other rules have been collected as well, particularly for quadrature over the interior of a triangle, which is useful in finite element calculations.

Arthur Stroud published his vast collection of quadrature formulas for multidimensional regions in 1971. In a few cases, he printed sample FORTRAN77 programs to compute these integrals. Integration regions included:

We have added a few new terms for regions:

Licensing:

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

Languages:

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

Related Data and Programs:

stroud_test

disk_rule, a MATLAB code which computes quadrature rules for the unit disk in 2d, that is, the interior of the circle of radius 1 and center (0,0).

pyramid_rule, a MATLAB code which computes a quadrature rule for a pyramid.

simplex_gm_rule, a MATLAB code 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.

sphere_lebedev_rule, a MATLAB code which computes lebedev quadrature rules on the surface of the unit sphere in 3d.

tetrahedron_arbq_rule, a MATLAB 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_keast_rule, a MATLAB code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3d.

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

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

triangle_dunavant_rule, a MATLAB code which defines dunavant rules for quadrature over the interior of a triangle in 2d.

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

triangle_lyness_rule, a MATLAB library which returns lyness-jespersen quadrature rules over the interior of a triangle in 2d.

triangle_ncc_rule, a MATLAB code which defines newton-cotes closed (ncc) quadrature rules over the interior of a triangle in 2d.

triangle_nco_rule, a MATLAB code which defines newton-cotes open (nco) quadrature rules over the interior of a triangle in 2d.

triangle_wandzura_rule, a MATLAB code which returns quadrature rules of exactness 5, 10, 15, 20, 25 and 30 over the interior of the triangle in 2d.

Reference:

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    Handbook of Mathematical Functions,
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    LC: QA47.A34.
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    Volume 18, Number 3, September 1992, pages 329-342.
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    LC: QA47.M315.

Source Code:


Last revised on 11 January 2021.