Multiscale asymptotic expansions methods and numerical algorithms for the wave equations in perforated domains

In this paper, we are concerned with the wave equations in perforated domains with a homogeneous Neumann condition on the boundary of the holes. The multiscale asymptotic expansion of the solution for the problem are constructed and associated explicit convergence rates are obtained. A multiscale numerical method is introduced. Finally, we present some numerical results which support strongly the convergence theorem.