TETRAHEDRON_FELIPPA_RULE
Quadrature Rules for a Tetrahedron

TETRAHEDRON_FELIPPA_RULE, a MATLAB library which generates Felippa quadrature rules over the interior of a tetrahedron in 3D.

Licensing:

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

Languages:

TETRAHEDRON_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.

DISK_RULE, a MATLAB library which computes quadrature rules over the interior of a disk in 2D.

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

PYRAMID_RULE, a MATLAB program which computes a quadrature rule over the interior of the unit pyramid in 3D.

SIMPLEX_GM_RULE, a MATLAB library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

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.

STROUD, a MATLAB library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

tetrahedron_felippa_rule_test

TETRAHEDRON_KEAST_RULE, a MATLAB library 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 the interior of a tetrahedron in 3D.

TETRAHEDRON_NCC_RULE, a MATLAB library which defines Newton-Cotes closed quadrature rules over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCO_RULE, a MATLAB library which defines Newton-Cotes open quadrature rules over the interior of a tetrahedron in 3D.

TRIANGLE_DUNAVANT_RULE, a MATLAB library which defines Dunavant rules for quadrature over the interior of a triangle in 2D.

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

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

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.
• tetrahedron_unit_monomial.m, returns the exact integral of a monomial in a unit tetrahedron;
• tetrahedron_unit_o01.m, returns a 1 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o04.m, returns a 4 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o08.m, returns an 8 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o08b.m, returns an 8 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o14.m, returns a 14 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o14b.m, returns a 14 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o15.m, returns a 15 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o15.m, returns a 15 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_o24.m, returns a 24 point quadrature rule for the unit tetrahedron.
• tetrahedron_unit_volume.m, computes the volume of the unit tetrahedron;
• timestamp.m, prints the YMDHMS date as a timestamp;