do numerical integration

Question

Hi all,

I am very new to FEniCS, I have a quick question. How to do numerical integration of a function in FEniCS？

Thanks.

Answer 1

It depends what is your function. For example

from dolfin import *
mesh = UnitSquareMesh(42, 42)

c = Constant(42.0)
print assemble(c*ds, mesh=mesh)

f = Expression("1.0 + x[0]*x[1]", degree=2)
print assemble(f*dx, mesh=mesh)

V = FunctionSpace(mesh, "Lagrange", 2)
u = project(f, V)
print assemble(u*dx)

Necessary quadrature degree is automatically estimated by algorithms in UFL (altough they are not flawless) and corresponding Gauss rule is used. Note explicit setting of polynomial degree of compiled expression f - it is not recognized in any way.

Comments

This doesn't work anymore due to some changes in ufl.

UFLException: An Integral without a Domain is now illegal.

what is the domain here?

---

from dolfin import *
mesh = UnitSquareMesh(42, 42)

c = Constant(42.0)
print assemble(c*ds(mesh))

f = Expression("1.0 + x[0]*x[1]", degree=2)
print assemble(f*dx(mesh))

V = FunctionSpace(mesh, "Lagrange", 2)
u = project(f, V)
print assemble(u*dx)