High order marching schemes for the wave equation in complex geometry

  • Authors:

  • Jing-Rebecca Li;Leslie Greengard

  • Affiliations:

  • Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY;Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

We present a new class of explicit marching schemes for the wave equation in complex geometry. They rely on a simple embedding of the domain in a uniform Cartesian grid, which allows for efficient and automatic implementation but creates irregular cells near the boundary. While existing explicit finite difference schemes are generally restricted in the size of the time step that can be taken by the dimensions of the smallest cell, the schemes described here are capable of taking time steps dictated by the uniform grid spacing. This should be of significant benefit in a wide variety of simulation efforts.