simplex_gm_rule, a FORTRAN90 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 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 FORTRAN90 code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
pyramid_felippa_rule, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
simplex_grid, a FORTRAN90 code which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
SQUARE_FELIPPA_RULE, a FORTRAN90 code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
STROUD, a FORTRAN90 code which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and M-dimensions.
TETRAHEDRON_FELIPPA_RULE, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TETRAHEDRON_KEAST_RULE, a FORTRAN90 code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.
TETRAHEDRON_MONTE_CARLO, a MATLAB program which uses the Monte Carlo method to estimate integrals over a tetrahedron.
TETRAHEDRON_NCC_RULE, a FORTRAN90 code which defines Newton-Cotes closed quadrature rules over the interior of a tetrahedron in 3D.
TETRAHEDRON_NCO_RULE, a FORTRAN90 code which defines Newton-Cotes open quadrature rules over the interior of a tetrahedron in 3D.
TRIANGLE_DUNAVANT_RULE, a FORTRAN90 code which defines Dunavant rules for quadrature over the interior of a triangle in 2D.
TRIANGLE_FEKETE_RULE, a FORTRAN90 code which defines Fekete rules for interpolation or quadrature on a triangle.
TRIANGLE_FELIPPA_RULE, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
TRIANGLE_LYNESS_RULE, a FORTRAN90 code which returns Lyness-Jespersen quadrature rules for the triangle.
TRIANGLE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over a triangle.
TRIANGLE_NCC_RULE, a FORTRAN90 code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_NCO_RULE, a FORTRAN90 code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_WANDZURA_RULE, a FORTRAN90 code which definine Wandzura rules for quadrature over the interior of a triangle in 2D.
WEDGE_FELIPPA_RULE, a FORTRAN90 code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.