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We consider the wave equationon an unbounded domainfor highly oscillatory coefficientswith the scaling. We consider settings in which the homogenization process for this equation is well understood, which means thatholds for the solutionof the homogenized problem. In this context, domain truncation methods are studied. The goal is to calculate an approximate solutionon a subdomain, say. We are ready to solve the  ε -problem on, but we want to solve only homogenized problems on the unbounded domainsor. The main task is to define transmission conditions at the interface to have small differences. We present different methods and correspondingerror estimates.

Domain truncation methods for the wave equation in a homogenization limit