DUNAVANT
Quadrature Rules for the Triangle


DUNAVANT is a FORTRAN90 library which defines the weights and abscisass for a sequence of 20 quadrature rules on a triangle, which are exact for polynomials up to degree 20.

These rules are almost optimal, in the sense that, for each polynomial degree, the number of points used in the rule is close to, or equal to, the theoretical minimum possible value.

A few of the rules include one or two points which are "slightly" outside the triangle; a few of the rules include weights which are negative. Both of these occurrences are generally undesirable.

Licensing:

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

Languages:

DUNAVANT is available in a C++ version and a FORTRAN90 version and a MATLAB version

Related Data and Programs:

FELIPPA, a FORTRAN90 library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.

GM_RULE, a FORTRAN90 library which defines a Grundmann-Moeller rule for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.

LYNESS_RULE, a FORTRAN90 library which returns Lyness-Jespersen quadrature rules for the triangle.

NCC_TRIANGLE, a FORTRAN90 library which defines Newton-Cotes closed quadrature rules on a triangle.

NCO_TRIANGLE, a FORTRAN90 library which defines Newton-Cotes open quadrature rules on a triangle.

NINTLIB, a FORTRAN90 library which contains a variety of routines for numerical estimation of integrals in multiple dimensions.

QUADRATURE_RULES_TRI, a dataset directory which contains triples of files which defines various quadrature rules on triangles.

QUADRULE, a FORTRAN90 library which defines quadrature rules on a variety of intervals with different weight functions.

STROUD, a FORTRAN90 library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and M-dimensions.

TRIANGLE_EXACTNESS, a FORTRAN90 program which investigates the polynomial exactness of a quadrature rule for the triangle.

TRIANGLE_FEKETE, a FORTRAN90 library which defines Fekete rules for interpolation or quadrature on a triangle.

TRIANGLE_MONTE_CARLO, a FORTRAN90 program which uses the Monte Carlo method to estimate integrals over a triangle.

WANDZURA, a FORTRAN90 library which defines Wandzura rules for quadrature on a triangle.

Reference:

  1. David Dunavant,
    High Degree Efficient Symmetrical Gaussian Quadrature Rules for the Triangle,
    International Journal for Numerical Methods in Engineering,
    Volume 21, 1985, pages 1129-1148.
  2. James Lyness, Dennis Jespersen,
    Moderate Degree Symmetric Quadrature Rules for the Triangle,
    Journal of the Institute of Mathematics and its Applications,
    Volume 15, Number 1, February 1975, pages 19-32.

Source Code:

Examples and Tests:

One of the tests in the sample calling program creates EPS files of the Dunavant points in the unit triangle. These have been converted to PNG files for display here.

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 27 December 2010.