Radiation boundary conditions for time-dependent waves based on complete plane wave expansions

  • Authors:

  • Thomas Hagstrom;Timothy Warburton;Dan Givoli

  • Affiliations:

  • Department of Mathematics and Statistics, The University of New Mexico, Albuquerque, NM 87131, USA;Department of Computational and Applied Mathematics, Rice University, 6100 Main Street - MS 134, Houston, TX 77005, USA;Department of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

We develop complete plane wave expansions for time-dependent waves in a half-space and use them to construct arbitrary order local radiation boundary conditions for the scalar wave equation and equivalent first order systems. We demonstrate that, unlike other local methods, boundary conditions based on complete plane wave expansions provide nearly uniform accuracy over long time intervals. This is due to their explicit treatment of evanescent modes. Exploiting the close connection between the boundary condition formulations and discretized absorbing layers, corner compatibility conditions are constructed which allow the use of polygonal artificial boundaries. Theoretical arguments and simple numerical experiments are given to establish the accuracy and efficiency of the proposed methods.