pyramid_felippa_rule

pyramid_felippa_rule, an Octave code which returns a Felippa quadrature rule 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 MIT license

Languages:

pyramid_felippa_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:

pyramid_felippa_rule_test

alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

annulus_rule, an Octave code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2d.

cube_felippa_rule, an Octave code which returns a Felippa quadrature rule over the interior of a cube in 3d.

disk_rule, an Octave code which computes quadrature rules over the interior of the unit disk in 2d.

hexagon_stroud_rule, an Octave code which computes one of four Stroud quadrature rules over the interior of the unit hexagon.

pyramid_exactness, an Octave code which investigates the monomial exactness of a quadrature rule over the interior of the unit pyramid in 3d.

pyramid_grid, an Octave code which computes a grid of points over the interior of the unit pyramid in 3d;

pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

pyramid_jaskowiec_rule, an Octave code which returns quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.

pyramid_monte_carlo, an Octave code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;

pyramid_rule, an Octave code which computes a conical product quadrature rule over the interior of a unit pyramid in 3d.

pyramid_witherden_rule, an Octave code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid in 3D.

simplex_gm_rule, an Octave code 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, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.

stroud, an Octave code which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2d, 3d and m-dimensions.

tetrahedron_exactness, an Octave code which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3d.

tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

tetrahedron_keast_rule, an Octave code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3d.

tetrahedron_monte_carlo, an Octave code which uses the monte carlo method to estimate integrals over the interior of the unit tetrahedron in 3d.

tetrahedron_ncc_rule, an Octave code which defines newton-cotes closed (ncc) quadrature rules over the interior of a tetrahedron in 3d.

tetrahedron_nco_rule, an Octave code which defines newton-cotes open (nco) quadrature rules over the interior of a tetrahedron in 3d.

triangle_dunavant_rule, an Octave code which sets up a dunavant quadrature rule over the interior of a triangle in 2d.

triangle_fekete_rule, an Octave code which defines fekete rules for quadrature or interpolation over the interior of a triangle in 2d.

triangle_lyness_rule, an Octave code which returns lyness-jespersen quadrature rules over the interior of a triangle in 2d.

triangle_ncc_rule, an Octave code which defines newton-cotes closed (ncc) quadrature rules over the interior of a triangle in 2d.

triangle_nco_rule, an Octave code which defines newton-cotes open (nco) quadrature rules over the interior of a triangle in 2d.

triangle_wandzura_rule, an Octave code 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_mop.m, returns the I-th power of -1 as an R8.
• subcomp_next.m, computes the next subcomposition of N into K parts.