pyramid_exactness


pyramid_exactness, a Fortran90 code which measures the precision of a quadrature rule over the interior of the unit pyramid in 3D.

The integration region is:

       - ( 1 - Z ) <= X <= 1 - Z
       - ( 1 - Z ) <= Y <= 1 - Z
                 0 <= Z <= 1.
      
When Z is zero, the integration region is a square lying in the (X,Y) plane, centered at (0,0,0) with "radius" 1. As Z increases to 1, the radius of the square diminishes, and when Z reaches 1, the square has contracted to the single point (0,0,1).

Usage:

pyramid_exactness filename degree_max
where

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

pyramid_exactness is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave versionand a Python version.

Related Data and Programs:

pyramid_exactness_test

cube_exactness, a Fortran90 code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

hypercube_exactness, a Fortran90 code which measures the monomial exactness of an M-dimensional quadrature rule over the interior of the unit hypercube in M dimensions.

pyramid_felippa_rule, a Fortran90 code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.

pyramid_grid, a Fortran90 code which computes a grid of points over the interior of the unit pyramid in 3D;

pyramid_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

pyramid_jaskowiec_rule, a Fortran90 code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.

pyramid_monte_carlo, a Fortran90 code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

pyramid_rule, a Fortran90 code which computes a conical product quadrature rule over the interior of the unit pyramid in 3D.

pyramid_witherden_rule, a Fortran90 code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid.

sphere_exactness, a Fortran90 code which tests the polynomial exactness of a quadrature rule over the surface of the unit sphere in 3D.

square_exactness, a Fortran90 code which investigates the polynomial exactness of quadrature rules for f(x,y) over the interior of a rectangle in 2D.

tetrahedron_exactness, a Fortran90 code which investigates the polynomial exactness of a quadrature rule over the interior of the tetrahedron in 3D.

TRIANGLE_EXACTNESS, a Fortran90 code which investigates the polynomial exactness of a quadrature rule 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.

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 20 August 2020.