triangle_felippa_rule


triangle_felippa_rule, a C++ code which generates the points and weights of Felippa's quadrature rules over the interior of a triangle in 2D.

Licensing:

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

Languages:

triangle_felippa_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

CUBE_FELIPPA_RULE, a C++ code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

PYRAMID_FELIPPA_RULE, a C++ code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

SQUARE_FELIPPA_RULE, a C++ code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

TETRAHEDRON_FELIPPA_RULE, a C++ code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

TRIANGLE_ANALYZE, a C++ code 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_FEKETE_RULE, a C++ code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_DUNAVANT_RULE, a C++ code which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.

TRIANGLE_EXACTNESS, a C++ code which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.

TRIANGLE_FEKETE_RULE, a C++ code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

triangle_felippa_rule_test

TRIANGLE_LYNESS_RULE, a C++ code which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a C++ code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a C++ code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_SVG, a C++ code which uses Scalable Vector Graphics (SVG) to plot a triangle and any number of points, to illustrate quadrature rules and sampling techniques.

TRIANGLE_SYMQ_RULE, a C++ code 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++ code 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++ code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

Reference:

  1. Carlos Felippa,
    A compendium of FEM integration formulas for symbolic work,
    Engineering Computation,
    Volume 21, Number 8, 2004, pages 867-890.

Source Code:


Last revised on 03 May 2020.