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Advanced Numerical Methods in the Mathematical Sciences

Imbo Sim, National Institute for Mathematical Sciences (South Korea)
PML for Time-Dependent Wave Equation with Highly Oscillating Coefficients

Authors

  • Oh Sung Kwon, National Institute for Mathematical Sciences (South Korea)
  • Imbo Sim, National Institute for Mathematical Sciences (South Korea)

Abstract

We consider a perfectly matched layers (PML) method for the wave equation with highly oscillating coefficients in unbounded domain. The PML approach has proved a flexible and accurate method for the simulation of waves in unbounded media. We propose a finite element heterogeneous multiscale method (HMM), which can be efficiently combined with PML formulation. HMM 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. The computational work is independent of the highly heterogeneous nature of the medium at the smallest scale. Various numerical examples illustrate the accuracy and robustness of our method.