TETRAHEDRON_FELIPPA_RULE
Quadrature Rules for a Tetrahedron

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

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

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

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

TETRAHEDRON_NCO_RULE, a C++ library which defines Newton-Cotes open 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_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals 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_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 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:

• tetrahedron_felippa.cpp, the source code.
• tetrahedron_felippa.hpp, the include file.

Examples and Tests:

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

List of Routines:

• COMP_NEXT computes the compositions of the integer N into K parts.
• MONOMIAL_VALUE evaluates a monomial.
• 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.
• TETR_UNIT_MONOMIAL integrates a monomial over the unit tetrahedron.
• TETR_UNIT_MONOMIAL_TEST tests TETR_UNIT_MONOMIAL.
• TETR_UNIT_O01 returns a 1 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O04 returns a 4 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O08 returns an 8 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O08B returns an 8 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O14 returns a 14 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O14B returns a 14 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O15 returns a 15 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O15B returns a 15 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_O24 returns a 24 point quadrature rule for the unit tetrahedron.
• TETR_UNIT_QUAD_TEST tests the rules for the unit tetrahedron.
• TETR_UNIT_VOLUME returns the volume of the unit tetrahedron.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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