hexahedron_witherden_rule

hexahedron_witherden_rule, an Octave code which returns a Witherden quadrature rule, with exactness up to total degree 11, over the interior of a hexahedron.

The unit hexahedron has vertices (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1).

Licensing:

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

Languages:

hexahedron_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:

hexahedron_witherden_rule_test

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:

• comp_next.m, returns the next composition of an integer.
• 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.
• hexahedron_witherden_rule.m, returns a quadrature rule of given precision for the 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.

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