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 information on this web page is 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 and an Octave version and a Python version.

Related Data and Programs:

wedge_exactness_test

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

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

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

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

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

triangle_exactness, a C code which computes the exactness of a quadrature rule over the interior of a triangle in 2D.

wedge_felippa_rule, a C code which returns a Felippa quadrature rule 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.