WEDGE_FELIPPA_RULE
Quadrature Rules for the Wedge

WEDGE_FELIPPA_RULE is a C++ 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 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 the unit 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 the 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_FELIPPA_RULE, a C++ library which returns Felippa's quadratures rules for approximating integrals over the interior of a 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_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.

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

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

WEDGE_INTEGRALS, a C++ 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 C++ 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.cpp, the source code.
• wedge_felippa_rule.hpp, the include file.

Examples and Tests:

• wedge_felippa_rule_test.cpp, a sample calling program.
• wedge_felippa_rule_test.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 C++ source codes.