wedge_felippa_rule


wedge_felippa_rule, a FORTRAN90 code 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:

CUBE_FELIPPA_RULE, a FORTRAN90 code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

DISK_RULE, a FORTRAN90 code which computes quadrature rules over the interior of the unit disk in 2D.

PYRAMID_FELIPPA_RULE, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

PYRAMID_RULE, a FORTRAN90 code which computes a quadrature rule over the interior of the unit pyramid in 3D.

SIMPLEX_GM_RULE, a FORTRAN90 code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.

SQUARE_FELIPPA_RULE, a FORTRAN90 code which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.

STROUD, a FORTRAN90 code which defines quadrature rules for a variety of unusual areas, surfaces and volumes in 2D, 3D and N-dimensions.

TETRAHEDRON_FELIPPA_RULE, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.

TETRAHEDRON_KEAST_RULE, a FORTRAN90 code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCC_RULE, a FORTRAN90 code which defines Newton-Cotes closed quadrature rules over the interior of a tetrahedron in 3D.

TETRAHEDRON_NCO_RULE, a FORTRAN90 code which defines Newton-Cotes open quadrature rules over the interior of a tetrahedron in 3D.

TRIANGLE_DUNAVANT_RULE, a FORTRAN90 code which defines Dunavant rules for quadrature over the interior of a triangle in 2D.

TRIANGLE_FEKETE, a FORTRAN90 code which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE, a FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.

TRIANGLE_LYNESS_RULE, a FORTRAN90 code which returns Lyness-Jespersen quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCC_RULE, a FORTRAN90 code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_NCO_RULE, a FORTRAN90 code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.

TRIANGLE_WANDZURA_RULE, a FORTRAN90 code which defines Wandzura rules for quadrature over the interior of a triangle in 2D.

WEDGE_EXACTNESS, a FORTRAN90 code which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

wedge_felippa_rule_test

WEDGE_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

WEDGE_MONTE_CARLO, a FORTRAN90 code 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:


Last revised on 11 September 2020.