High-frequency wave propagation by the segment projection method

  • Authors:

  • Björn Engquist;Olof Runborg;Anna-Karin Tornberg

  • Affiliations:

  • Department of Mathematics, Princeton University, Princeton, New Jersey;Department of Numerical Analysis and Computer Science, KTH, stockholm, Sweden;Courant Institute of Mathematical Sciences, New York University, New York, New York

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

Geometrical optics is a standard technique used for the approximation of high-frequency wave propagation. Computational methods based on partial differential equations instead of the traditional ray tracing have recently been applied to geometrical optics. These new methods have a number of advantages but typically exhibit difficulties with linear superposition of waves. In this paper we introduce a new partial differential technique based on the segment projection method in phase space. The superposition problem is perfectly resolved and so is the problem of computing amplitudes in the neighborhood of caustics. The computational complexity is of the same order as that of ray tracing. The new algorithm is described and a number of computational examples are given, including a simulation of waveguides.