Grundmann-Moeller Quadrature Rules for the Simplex in M dimensions

SIMPLEX_GM_RULE is a Python library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

The user can choose the spatial dimension M, thus defining the region to be a triangle (M = 2), tetrahedron (M = 3) or a general M-dimensional simplex.

The user chooses the index S of the rule. Rules are available with index S = 0 on up. A rule of index S will exactly integrate any polynomial of total degree 2*S+1 or less.

The rules are defined on the unit M-dimensional simplex. A simple linear transformation can be used to map the vertices and weights to an arbitrary simplex, while preserving the accuracy of the rule.


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


SIMPLEX_GM_RULE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ANNULUS_RULE, a Python library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

SIMPLEX_GRID, a Python library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.


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Source Code:

Examples and Tests:

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

Last revised on 03 March 2017.