Adding Noise to a Neumann boundary.

Question

How can I add noise to a Neumann boundary? Usually we take care of the Neumann boundary by adding another term in the linear form. (See attached link to FEniCS demo with Poisson equation and Neuman boundaries.) In the attached demo the normal derivative is set equal to g = Expression("-sin(5*x[0])"). How can I add noise to this boundary condition?

Poisson with Neumann.
http://fenicsproject.org/documentation/dolfin/1.6.0/python/demo/documented/neumann-poisson/python/documentation.html

Comments

It depends on the kind of noise you want to add. Is it white noise? Or it is spatially correlated?
Do you need to be consistent with an infinite dimensional stochastic PDE?
Or any random forcing term is ok with you?

Answer 1

See the InitialCondition class in http://fenicsproject.org/documentation/dolfin/1.6.0/python/demo/documented/cahn-hilliard/python/documentation.html#implementation.

Comments

I don't see how this corresponds to the weak form. The InitialCondition class is used to initialize u0. How do I alter the weak form to introduce noise? I'd like to modify the gvds term in the demo I referenced.

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It's an Expression which can be used for initial condition, boundary condition, or as a coefficient in a form, etc.

class G(Expression):
    # implementation, see e.g. use of random in InitialCondition

g = G()
L = f*v*dx \
  + g*v*ds # Neumann term