TRIANGLE_LYNESS_RULE\ Quadrature Rules for the Triangle {#triangle_lyness_rule-quadrature-rules-for-the-triangle align=”center”} =================================
TRIANGLE_LYNESS_RULE is a C++ library which produces the Lyness-Jespersen family of quadrature rules over the interior of a triangle in 2D.
The rules have the following orders (number of points) and precisions (maximum degree of polynomials whose integrals they can compute exactly):
Rule Order Precision —— ——- ———– 0 1 1 1 3 2 2 4 2 3 4 3 4 7 3 5 6 4 6 10 4 7 9 4 8 7 5 9 10 5 10 12 6 11 16 6 12 13 6 13 13 7 14 16 7 15 16 8 16 21 8 17 16 8 18 19 9 19 22 9 20 27 11 21 28 11
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
TRIANGLE_LYNESS_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
CUBE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
PYRAMID_FELIPPA_RULE, a C++ library which returns Felippa’s quadratures rules for approximating integrals over the interior of a pyramid in 3D.
SIMPLEX_GM_RULE, a C++ library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.
SQUARE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
STROUD, a C++ library which contains quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and M-dimensions.
TETRAHEDRON_FELIPPA_RULE, a C++ library which returns Felippa’s quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TRIANGLE_ANALYZE, a C++ program which reads a triangle defined in a file, and uses the triangle_properties() library to compute angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.
TRIANGLE_DUNAVANT_RULE, a C++ library which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.
TRIANGLE_EXACTNESS, a C++ program which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.
TRIANGLE_FEKETE_RULE, a C++ library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
TRIANGLE_FELIPPA_RULE, a C++ library which returns Felippa’s quadratures rules for approximating integrals over the interior of a triangle in 2D.
TRIANGLE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
TRIANGLE_MONTE_CARLO, a C++ program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.
TRIANGLE_NCC_RULE, a C++ library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_NCO_RULE, a C++ library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_SYMQ_RULE, a C++ library which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2D, by Hong Xiao and Zydrunas Gimbutas.
TRIANGLE_WANDZURA_RULE, a C++ library which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of a triangle in 2D.
WEDGE_FELIPPA_RULE, a C++ library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.
You can go up one level to the FORTRAN90 source codes.
Last revised on 30 September 2010.