TETRAHEDRON_FELIPPA_RULE
Quadrature Rules for a Tetrahedron

TETRAHEDRON_FELIPPA_RULE is a FORTRAN77 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 FORTRAN77 version and a MATLAB version.

Related Data and Programs:

CUBE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

DISK_RULE, a FORTRAN77 library which computes quadrature rules over the interior of a disk in 2D.

PYRAMID_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

PYRAMID_RULE, a FORTRAN77 program which computes a quadrature rule over the interior of the unit pyramid in 3D.

SIMPLEX_GM_RULE, a FORTRAN77 library which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

SQUARE_FELIPPA_RULE, a FORTRAN77 library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

STROUD, a FORTRAN77 library which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TETRAHEDRON_EXACTNESS, a FORTRAN77 program which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.

TETRAHEDRON_KEAST_RULE, a FORTRAN77 library which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.

TETRAHEDRON_MONTE_CARLO, a FORTRAN77 program which uses the Monte Carlo method to estimate integrals over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCC_RULE, a FORTRAN77 library which defines Newton-Cotes closed quadrature rules over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCO_RULE, a FORTRAN77 library which defines Newton-Cotes open quadrature rules over the interior of a tetrahedron in 3D.

TRIANGLE_DUNAVANT_RULE, a FORTRAN77 library which defines Dunavant rules for quadrature over the interior of a triangle in 2D.

TRIANGLE_FEKETE_RULE, a FORTRAN77 library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_LYNESS_RULE, a FORTRAN77 library which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a FORTRAN77 library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a FORTRAN77 library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_WANDZURA_RULE, a FORTRAN77 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_rule.f, the source code.
• tetrahedron_felippa_rule.sh, commands to compile the source code.

Examples and Tests:

• tetrahedron_felippa_rule_prb.f, a sample calling program.
• tetrahedron_felippa_rule_prb.sh, commands to compile and run the sample program.
• tetrahedron_felippa_rule_prb_output.txt, the output file.

List of Routines:

• COMP_NEXT computes the compositions of the integer N into K parts.
• MONOMIAL_VALUE evaluates a monomial.
• SUBCOMP_NEXT computes the next subcomposition of N into K parts.
• TETRAHEDRON_UNIT_MONOMIAL integrates a monomial over the unit tetrahedron.
• TETRAHEDRON_UNIT_O01: 1 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O04: 4 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O08: 8 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O08B: 8 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O14: 14 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O14B: 14 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O15: 15 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O15B: 15 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_UNIT_O24: 24 point quadrature rule for the unit tetrahedron.
• TETRAHEDRON_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 FORTRAN77 source codes.