hexahedron_jaskowiec_rule

hexahedron_jaskowiec_rule, an Octave 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.
       

Licensing:

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

Languages:

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_jaskowiec_rule_test

octave_rule, an Octave 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. 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:

• comp_next.m, returns the next composition of an integer.
• hexahedron_jaskowiec_rule.m, returns a quadrature rule of given precision for the unit hexahedron.
• hexahedron_unit_monomial_integral.m, returns the exact integral of a given monomial over the unit hexahedron.
• hexahedron_unit_volume.m, computes the volume of a unit hexahedron.
• monomial_value.m, evaluates a multidimensional monomial.
• rule_order.m, returns the number of quadrature points used in a rule of given degree.
• rule01.m, returns the rule of degree 1.
• rule03.m, returns the rule of degree 3.
• rule05.m, returns the rule of degree 5.
• rule07.m, returns the rule of degree 7.
• rule09.m, returns the rule of degree 9.
• rule11.m, returns the rule of degree 11.
• rule13.m, returns the rule of degree 13.
• rule15.m, returns the rule of degree 15.
• rule17.m, returns the rule of degree 17.
• rule19.m, returns the rule of degree 19.
• rule21.m, returns the rule of degree 21.

• hexahedron_jaskowiec_rule_to_matlab.m, reads a data file describing one of the rules and writes a function to return points and weights.