Assyr Abdulle, École Polytechnique Fédérale de Lausanne (EPFL)

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

May 7-8, 2011

King Abdullah University of Science and Technology (KAUST)

Thuwal, Kingdom of Saudi Arabia

Finite Element Heterogeneous Multiscale Method for the Wave Equation

Based on joint work with M. Grote and C. Stohrer.

Following the framework of the heterogeneous multiscale method, we present a finite element method for wave propagation in heterogeneous media (modeled by the wave equation with highly oscillatory coefficients). The numerical method is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coefficients are computed on sampling domains at the micro scale within each macro finite element. Optimal fully discrete error estimates in the energy norm and the L² norm and convergence to the homogenized problem are given.

Numerical examples confirm the theoretical convergence rates and illustrate the performance and versatility of our approach.