wedge_felippa_rule


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

WEDGE_EXACTNESS, a C 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 C 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 C 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 13 August 2019.