PYRAMID_FELIPPA_RULE
Quadrature Rules for the Pyramid

PYRAMID_FELIPPA_RULE is a C++ 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 FORTRAN77 version and a MATLAB version.

Related Data and Programs:

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

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

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

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

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

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

TETRAHEDRON_INTEGRALS, a C++ 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 C++ library which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.

TETRAHEDRON_MONTE_CARLO, a C++ program which uses the Monte Carlo method to estimate integrals over a tetrahedron.

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

TETRAHEDRON_NCO_RULE, a C++ library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a tetrahedron in 3D.

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

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

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

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

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

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

TRIANGLE_WANDZURA_RULE, a C++ library which defines Wandzura rules for quadrature rules 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:

• pyramid_felippa_rule.cpp, the source code.
• pyramid_felippa_rule.hpp, the include file.
• pyramid_felippa_rule.sh, BASH commands to compile the source code.

Examples and Tests:

• pyramid_felippa_rule_prb.cpp, a sample calling program.
• pyramid_felippa_rule_prb.sh, BASH commands to compile and run the sample program.
• pyramid_felippa_rule_prb_output.txt, the output file.

List of Routines:

• COMP_NEXT computes the compositions of the integer N into K parts.
• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the minimum of two I4's.
• MONOMIAL_VALUE evaluates a monomial.
• PYRAMID__UNIT_MONOMIAL: monomial integral in a unit pyramid.
• PYRAMID__UNIT_O01 returns a 1 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O05 returns a 5 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O06 returns a 6 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O08 returns an 8 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O08B returns an 8 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O09 returns a 9 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O13 returns a 13 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O18 returns an 18 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O27 returns a 27 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_O48 returns a 48 point quadrature rule for the unit pyramid.
• PYRAMID__UNIT_VOLUME: volume of a unit pyramid with square base.
• R8_CHOOSE computes the binomial coefficient C(N,K) as an R8.
• R8_MOP returns the I-th power of -1 as an R8.
• R8VEC_COPY copies an R8VEC.
• R8VEC_DOT_PRODUCT computes the dot product of a pair of R8VEC's.
• SUBCOMP_NEXT computes the next subcomposition of N into K parts.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.