Integration classes

This class and its sub-classes provide support for numeric integration over common element domains.

Implement most of the methods presented in http://me.rice.edu/~akin/Elsevier/Chap_10.pdf.

Usage:

Instantiate the Integration object most suitable for your element domain. Provide order as the highest polynomial order of the function you want to integrate exactly.
call points() or weights() or parameters() to obatin a list of integration point coordinates or weights or both, respectively.

Integrating a 4th-order function f(s,t) over a triangular domain

integrator = TriangleIntegration(order=4)
F = 0.0
xis, wis = integrator.parameters()
for xi, wi in zip(xis, wis):
    F += f(xi[0], xi[1]) * J(xi[0], xi[1]) * wi

print(f"Int_A f(s,t) dA = {F}")

Integrating a tri-quadratic function g(s,t,u) over a brick-shaped domain

integrator = BrickIntegration(order=2)
F = 0.0
xis, wis = integrator.parameters()
for xi, wi in zip(xis, wis):
    F += g(xi[0], xi[1], xi[2]) * J(xi[0], xi[1], xi[2]) * wi

print(f"Int_V g(s,t,u) dV = {F}")