  In this paper we explore how non trivial boundary conditions could influence
the entanglement entropy in a topological order in 2+1 dimensions. Specifically
we consider the special class of topological orders describable by the quantum
double. We will find very interesting dependence of the entanglement entropy on
the boundary conditions particularly when the system is non-Abelian. Along the
way, we demonstrate a streamlined procedure to compute the entanglement
entropy, which is particularly efficient when dealing with systems with
boundaries. We also show how this method efficiently reproduces all the known
results in the presence of anyonic excitations.
