prism_witherden_rule
prism_witherden_rule,
a Fortran90 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:

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:

prism_unit_volume.m,
returns the volume of a 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.
Last revised on 27 April 2023.