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.