Olof Runborg: Multiscale methods for wave propagation problems

Wave propagation problems with rapidly varying coefficients are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We consider numerical methods for such wave propagation in the framework of the heterogeneous multiscale method. These methods couple simulations on macro- and microscales for problems with rapidly oscillating coefficients. The complexity is significantly lower than that of traditional techniques with a computational cost that is essentially independent of the microscale. In this talk we show analysis of how the method works in the long time case, where the macroscale solution show dispersive behavior, and how the method, although designed for wave problems, can be beneficial for solving multiscale elliptic problems.