WEDGE_EXACTNESS
Precision Test for Wedge Quadrature Rules


WEDGE_EXACTNESS is a FORTRAN90 program 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 GNU LGPL license.

Languages:

WEDGE_EXACTNESS is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CUBE_EXACTNESS, a FORTRAN90 library which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

HYPERCUBE_EXACTNESS, a FORTRAN90 program which measures the monomial exactness of an M-dimensional quadrature rule over the interior of the unit hypercube in M dimensions.

PYRAMID_EXACTNESS, a FORTRAN90 program which investigates the polynomial exactness of a quadrature rule over the interior of the unit pyramid in 3D.

SPHERE_EXACTNESS, a FORTRAN90 program which tests the polynomial exactness of a quadrature rule over the surface of the unit sphere in 3D.

SQUARE_EXACTNESS, a FORTRAN90 library which investigates the polynomial exactness of quadrature rules for f(x,y) over the interior of a rectangle in 2D.

TETRAHEDRON_EXACTNESS, a FORTRAN90 program which investigates the polynomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.

TRIANGLE_EXACTNESS, a FORTRAN90 program which investigates the polynomial exactness of a quadrature rule over the interior of a triangle in 2D.

WEDGE_FELIPPA_RULE, a FORTRAN90 library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

WEDGE_GRID, a FORTRAN90 library which computes a grid of points over the interior of the unit wedge in 3D.

WEDGE_INTEGRALS, a FORTRAN90 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 FORTRAN90 library 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:

Examples and Tests:

WEDGE_FELIPPA_3x2 is a quadrature rule based on a 3 point triangle rule and a 2 point Legendre rule for the line.

List of Routines:

You can go up one level to the FORTRAN90 source codes.


Last revised on 24 August 2014.