TRIANGLE_FELIPPA_RULE
Felippa's Quadrature Rules for Triangles

TRIANGLE_FELIPPA_RULE, a MATLAB library 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 GNU LGPL 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 MATLAB library which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

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

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

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

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

TRIANGLE_DUNAVANT_RULE, a MATLAB library which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.

TRIANGLE_EXACTNESS, a MATLAB program which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.

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

triangle_felippa_rule_test

TRIANGLE_LYNESS_RULE, a MATLAB library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

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

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

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

TRIANGLE_SVG, a MATLAB library 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 MATLAB 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 MATLAB 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 MATLAB library 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:

• comp_next.m, computes the compositions of the integer N into K parts.
• monomial_value.m, evaluates a monomial.
• subcomp_next.m, computes the next subcomposition of N into K parts.
• timestamp.m, prints the YMDHMS date as a timestamp;
• triangle_unit_monomial.m, returns the exact integral of a monomial in a unit triangle;
• triangle_unit_o01.m, returns a 1 point quadrature rule for the unit triangle.
• triangle_unit_o03.m, returns a 3 point quadrature rule for the unit triangle.
• triangle_unit_o03b.m, returns a 3 point quadrature rule for the unit triangle.
• triangle_unit_o06.m, returns a 6 point quadrature rule for the unit triangle.
• triangle_unit_o06b.m, returns a 6 point quadrature rule for the unit triangle.
• triangle_unit_o07.m, returns a 7 point quadrature rule for the unit triangle.
• triangle_unit_o12.m, returns a 12 point quadrature rule for the unit triangle.
• triangle_unit_volume.m, returns the volume of the unit triangle;