Finite Element Heterogeneous Multiscale Method for the Wave Equation

Marcus J. Grote
Department of Mathematics
University of Basel
Basel, Switzerland


Following previous work of Abdulle, E, and Engquist (2003, 2005), we propose a finite element heterogeneous multiscale method (HMM) for the simulation of time dependent waves propagating through a medium with rapidly varying sound speed. Here the fine scales for the problem are accounted for in the stiffness matrix at the coarse scale by solving inside each macro-element a few micro-problems each of fixed size independent of the finest scale. A priori error estimates of the fully discrete method, which include the discretization errors from the macro- and the micro-problems, are derived. Numerical examples illustrate the theoretical convergence rates and the usefulness of this approach.