KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation
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- King Abdullah University of Science and Technology (KAUST)
- Thuwal, Saudi Arabia
- Assyr Abdulle, Swiss Federal Institute of Technology in Lausanne (Switzerland)
- Finite Element Heterogeneous Multiscale Method for the Wave Equation
Authors
- A. Abdulle
- M. Grote
- C. Stohrer
Abstract
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 \(L^{2}\) 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.