hexahedron_jaskowiec_rule, a Fortran90 code which returns quadrature rules, with exactness up to total degree 21, over the interior of a hexahedron in 3D, by Jan Jaskowiec, Natarajan Sukumar.

The integration region is:

       0 <= X <= 1
       0 <= Y <= 1
       0 <= Z <= 1.


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


hexahedron_jaskowiec_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:


hexahedron_witherden_rule, a Fortran90 code which returns a symmetric Witherden quadrature rule for the hexahedron, with exactness up to total degree 11.


  1. Jan Jaskowiec, Natarajan Sukumar,
    High order cubature rules for tetrahedra and hexahedrons,
    International Journal of Numerical Methods in Engineering,
    Volume 121, Number 11, pages 2418-2436, 15 June 2020.

Source Code:

Last revised on 06 May 2023.