prism_witherden_rule

prism_witherden_rule, a C code which returns a symmetric Witherden quadrature rule for a prism with triangular base, with exactness up to total degree 10.

The data is given for the unit prism: with vertices (1,0,0), (0,1,0), (0,0,0), (1,0,1), (0,1,1), (0,0,1).

Suppose we are given a triangular prism P with vertices (1,0,0), (0,1,0), (0,0,0), (1,0,1), (0,1,1), (0,0,1). We call a rule with n points, returning coordinates x, y, z, and weights w. Then the integral I of f(x,y,z) over P is approximated by Q as follows:

        Q = volume(P) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i))

Licensing:

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

Languages:

prism_witherden_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave versionand a Python version.

Related Data and Programs:

prism_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:

• prism_witherden_rule.c, the source code.
• prism_witherden_rule.h, the include file.
• prism_witherden_rule.sh, compiles the source code.