pyramid_witherden_rule

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 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).

Licensing:

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

Languages:

pyramid_witherden_rule 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:

pyramid_witherden_rule_test

f90_rule, a Fortran90 code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Reference:

  1. Freddie Witherden, Peter Vincent,
    On the identification of symmetric quadrature rules for finite element methods,
    Computers and Mathematics with Applications,
    Volume 69, pages 1232-1241, 2015.

Source Code:

Last revised on 26 April 2023.