wedge_exactness

wedge_exactness, a C code which measures the precision of a quadrature rule 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

Usage:

wedge_exactness filename degree_max
where

Licensing:

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

Languages:

wedge_exactness is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CUBE_EXACTNESS, a C code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

PYRAMID_EXACTNESS, a C code which investigates the polynomial exactness of a quadrature rule over the interior of the unit pyramid in 3D.

SPHERE_EXACTNESS, a C code which tests the polynomial exactness of a quadrature rule over the surface of the unit sphere in 3D.

SQUARE_EXACTNESS, a C code which investigates the polynomial exactness of quadrature rules for f(x,y) over the interior of a rectangle in 2D.

TETRAHEDRON_EXACTNESS, a C code which investigates the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.

TRIANGLE_EXACTNESS, a C code which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.

wedge_exactness_test

WEDGE_FELIPPA_RULE, a C code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

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 integrals over the interior of the unit 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.
  2. Arthur Stroud,
    Approximate Calculation of Multiple Integrals,
    Prentice Hall, 1971,
    ISBN: 0130438936,
    LC: QA311.S85.

Source Code:

Last revised on 13 August 2019.