hexahedron_witherden_rule

hexahedron_witherden_rule, a Python 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:

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clenshaw_curtis_rule, a Python code which returns a Clenshaw Curtis quadrature rule.

hermite_rule, a Python code which returns a Gauss-Hermite quadrature rule for estimating the integral of a function with density exp(-x^2) over the interval (-oo,+oo).

jacobi_rule, a Python code which returns a Gauss-Jacobi quadrature rule.

laguerre_rule, a Python code which returns a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).

legendre_rule, a Python code which returns a Gauss-Legendre quadrature rule for estimating the integral of a function with density rho(x)=1 over the interval [-1,+1].

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:

• hexahedron_witherden_rule_test.m, calls all the tests.
• hexahedron_witherden_rule_test.sh, runs all the tests.
• hexahedron_witherden_rule_test.txt, the output file.