simplex_gm_rule, a Fortran77 code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or 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 MIT license
simplex_gm_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
cube_felippa_rule, a Fortran77 library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
pyramid_felippa_rule, a Fortran77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
PYRAMID_RULE, a Fortran77 program which computes a quadrature rule over the interior of the unit pyramid in 3D;
QUADRATURE_RULES_TET, a dataset directory which contains triples of files defining various quadrature rules over the interior of a triangle in 2D.
QUADRATURE_RULES_TRI, a dataset directory which contains triples of files defining various quadrature rules on triangles.
SIMPACK, a Fortran77 library which approximate the integral of a function or vector of functions over a M-dimensional simplex, or a region which is the sum of M-dimensional simplexes.
SIMPLEX_COORDINATES, a Fortran77 library which computes the Cartesian coordinates of the vertices of a regular simplex in M dimensions.
SIMPLEX_GRID, a Fortran77 library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
SQUARE_FELIPPA_RULE, a Fortran77 library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
STROUD, a Fortran77 library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and M-dimensions.
TETRAHEDRON_FELIPPA_RULE, a Fortran77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TETRAHEDRON_MONTE_CARLO, a Fortran77 program which uses the Monte Carlo method to estimate integrals over the interior of a tetrahedron in 3D.
TRIANGLE_FELIPPA_RULE, a Fortran77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
TRIANGLE_MONTE_CARLO, a Fortran77 program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.
WEDGE_FELIPPA_RULE, a Fortran77 library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.