WEDGE_FELIPPA_RULE
Quadrature Rules for the Wedge

WEDGE_FELIPPA_RULE is a FORTRAN77 library which generates quadrature rules to estimate integrals over the interior of the unit wedge in 3D.

The interior of the unit wedge in 3D is defined by the constraints:

        0 <= X
        0 <= Y
             X + Y <= 1
       -1 <= Z <= +1
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

WEDGE_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 the unit 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_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals 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_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.

WEDGE_EXACTNESS, a FORTRAN77 program which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

WEDGE_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit wedge in 3D.

WEDGE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

WEDGE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate the value of an integral over the interior of a wedge in 3D.

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:

• wedge_felippa_rule.f, the source code.
• wedge_felippa_rule.sh, commands to compile the source code.

Examples and Tests:

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

List of Routines:

• COMP_NEXT computes the compositions of the integer N into K parts.
• GET_UNIT returns a free FORTRAN unit number.
• LINE_O01 returns a 1 point quadrature rule for the unit line.
• LINE_O02 returns a 2 point quadrature rule for the unit line.
• LINE_O03 returns a 3 point quadrature rule for the unit line.
• LINE_O04 returns a 4 point quadrature rule for the unit line.
• LINE_O05 returns a 5 point quadrature rule for the unit line.
• MONOMIAL_VALUE evaluates a monomial.
• R8MAT_WRITE writes an R8MAT file.
• SUBCOMP_NEXT computes the next subcomposition of N into K parts.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_O01 returns a 1 point quadrature rule for the unit triangle.
• TRIANGLE_O03 returns a 3 point quadrature rule for the unit triangle.
• TRIANGLE_O03B returns a 3 point quadrature rule for the unit triangle.
• TRIANGLE_O06 returns a 6 point quadrature rule for the unit triangle.
• TRIANGLE_O06B returns a 6 point quadrature rule for the unit triangle.
• TRIANGLE_O07 returns a 7 point quadrature rule for the unit triangle.
• TRIANGLE_O12 returns a 12 point quadrature rule for the unit triangle.
• WEDGE_INTEGRAL: monomial integral in a unit wedge.
• WEDGE_RULE returns a quadrature rule for the unit wedge.
• WEDGE_VOLUME: volume of a unit wedge.

You can go up one level to the FORTRAN77 source codes.