prism_witherden_rule

prism_witherden_rule, a MATLAB 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:

• comp_next.m, returns the next composition of an integer.
• monomial_value.m, evaluates a multidimensional monomial.
• prism_unit_monomial_integral.m, returns the exact integral of a given monomial over the unit prism.
• prism_unit_volume.m, returns the volume of a unit prism.
• prism_witherden_rule.m, returns a quadrature rule of given precision for the unit prism.
• rule_order.m, returns the number of points in rules of order 0 through 10.
• rule00.m, returns the rule of degree 0.
• rule01.m, returns the rule of degree 1.
• rule02.m, returns the rule of degree 2.
• rule03.m, returns the rule of degree 3.
• rule04.m, returns the rule of degree 4.
• rule05.m, returns the rule of degree 5.
• rule06.m, returns the rule of degree 6.
• rule07.m, returns the rule of degree 7.
• rule08.m, returns the rule of degree 8.
• rule09.m, returns the rule of degree 9.
• rule10.m, returns the rule of degree 10.