PYRAMID_FELIPPA_RULE
Quadrature Rules for the Pyramid

PYRAMID_FELIPPA_RULE, a MATLAB library which returns Felippa quadrature rules over the interior of the unit pyramid 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:

PYRAMID_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 the unit disk in 2D.

pyramid_felippa_rule_test

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

SIMPLEX_GM_RULE, a MATLAB library which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the 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 M-dimensions.

TETRAHEDRON_EXACTNESS, a MATLAB program which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.

TETRAHEDRON_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.

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 library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

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

TETRAHEDRON_NCO_RULE, a MATLAB library which defines Newton-Cotes Open (NCO) quadrature rules 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_FEKETE_RULE, a MATLAB library which defines Fekete rules for quadrature or interpolation 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.
• pyra_unit_monomial.m, returns the exact integral of a monomial in a unit pyramid;
• pyra_unit_o01.m, returns a 1 point quadrature rule for the unit pyramid.
• pyra_unit_o05.m, returns a 5 point quadrature rule for the unit pyramid.
• pyra_unit_o06.m, returns a 6 point quadrature rule for the unit pyramid.
• pyra_unit_o08.m, returns an 8 point quadrature rule for the unit pyramid.
• pyra_unit_o08b.m, returns an 8 point quadrature rule for the unit pyramid.
• pyra_unit_o09.m, returns a 9 point quadrature rule for the unit pyramid.
• pyra_unit_o13.m, returns a 13 point quadrature rule for the unit pyramid.
• pyra_unit_o18.m, returns an 18 point quadrature rule for the unit pyramid.
• pyra_unit_o27.m, returns a 27 point quadrature rule for the unit pyramid.
• pyra_unit_o48.m, returns a 48 point quadrature rule for the unit pyramid.
• pyra_unit_volume.m, returns the volume of a unit pyramid;
• r8_choose.m, computes the binomial coefficient C(N,K) as an R8.
• r8_mop.m, returns the I-th power of -1 as an R8.
• subcomp_next.m, computes the next subcomposition of N into K parts.
• timestamp.m, prints the YMDHMS date as a timestamp;