Domain truncation methods for the wave equation in a homogenization limit

We consider the wave equation partial derivative(2)(t)v(epsilon)-del center dot(a(epsilon del))v(epsilon) = f on an unbounded domain Omega(infinity) for highly oscillatory coefficients a(epsilon) with the scaling a(epsilon)(x) = a(x/epsilon). We consider settings in which the homogenization process for this equation is well understood, which means that v(epsilon)->(v) over bar holds for the solution (v) over bar of the homogenized problem partial derivative(2)(t)(v) over bar-del center dot(a(*)del)(v) over bar = f. In this context, domain truncation methods are studied. The goal is to calculate an approximate solution u(epsilon) on a subdomain, say Omega(-)subset of Omega(infinity). We are ready to solve the epsilon-problem on Omega(-), but we want to solve only homogenized problems on the unbounded domains Omega(infinity) or Omega(infinity)\(Omega) over bar (-). The main task is to define transmission conditions at the interface to have small differences u(epsilon )- v(epsilon). We present different methods and corresponding O(epsilon) error estimates.