Integral over a certain area

Question

I've already had the solution u over a unitsquare domain. Now I want to compute the integral over a certain subdomain, say x[0] and x[1] in range(0,0.25), how do I define the subdomain and then compute the integrals over it?

Answer 1

By constructing a custom integration element, you can then integrate over that subdomain. Hopefully this helps.

from dolfin import *

mesh = UnitSquareMesh(256, 256)
V = FunctionSpace(mesh, 'CG', 2)
u = interpolate(Expression('x[0]*x[0] + x[1]*x[1]'), V)

cf = CellFunction('size_t', mesh, 0)
region = AutoSubDomain(lambda x, on: x[0] <= 0.25 and x[1] <= 0.25)
region.mark(cf, 1)
dx_sub = Measure('dx', subdomain_data=cf)

print assemble(u*dx_sub(1))