Search

We consider the wave equation ∂ t 2 v ϵ − ∇ ⋅ (a ϵ ∇) v ϵ = f on an unbounded domain Ω ∞ for highly oscillatory coefficients a ϵ with the scaling a ϵ (x) = a (x / ϵ). We consider settings in which the homogenization process for this equation is well understood, which means that v ϵ → v ¯ holds for the solution v ¯ of the homogenized problem ∂ t 2 v ¯ − ∇ ⋅ (a ∗ ∇) v ¯ = f. In this context, domain truncation methods are studied. The goal is to calculate an approximate solution u ϵ on a subdomain, say Ω − ⊂ Ω ∞ . We are ready to solve the ε-problem on Ω − , but we want to solve only homogenized problems on the unbounded domains Ω ∞ or Ω ∞ ∖ Ω ¯ − . The main task is to define transmission conditions at the interface to have small differences u ϵ − v ϵ . We present different methods and corresponding O (ϵ) error estimates. [ABSTRACT FROM AUTHOR]