Multiscale numerical algorithms for elastic wave equations with rapidly oscillating coefficients

This paper reports a multiscale analysis and numerical algorithms for the elastic wave equations with rapidly oscillating coefficients. We mainly focus on the first-order and the second-order multiscale asymptotic expansions for the wave equations, which is proved to enjoy an explicit convergence rate. In our method, the homogenized equations are discretized by the finite element method in space and a symplectic geometric scheme in time. The multiscale solutions are then obtained efficiently by the standard multisclae asymptotic expansion framework. Several numerical simulations are carried out to validate the predicted convergence results.