hexahedron_witherden_rule
hexahedron_witherden_rule,
a MATLAB 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
hexahedron_jaskowiec_rule,
a MATLAB code which
returns a symmetric Jaskowiec quadrature rule for the hexahedron,
with exactness up to total degree 21.
Reference:

Freddie Witherden, Peter Vincent,
On the identification of symmetric quadrature rules for finite element methods,
Computers and Mathematics with Applications,
Volume 69, pages 12321241, 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_witherden_rule.m,
returns a Witherden quadrature rule of given precision for 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.
Last revised on 20 May 2023.