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Title: Fast multiscale Gaussian beam methods for wave equations in bounded convex domains

Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for pure initial-value problems of wave equations, we develop fast multiscale Gaussian beam methods for initial boundary value problems of wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, we have to take into account reflecting multiscale Gaussian beams, which are accomplished by enforcing reflecting boundary conditions during beam propagation and carrying out suitable reflecting beam summation. To propagate multiscale beams efficiently, we prove that the ratio of the squared magnitude of beam amplitude and the beam width is roughly conserved, and accordingly we propose an effective indicator to identify significant beams. We also prove that the resulting multiscale Gaussian beam methods converge asymptotically. Numerical examples demonstrate the accuracy and efficiency of the method.
Authors:
 [1] ;  [2] ;  [3] ;  [3]
  1. Department of Mathematics, Zhejiang University, Hangzhou 310027 (China)
  2. (United States)
  3. Department of Mathematics, Michigan State University, East Lansing, MI 48824 (United States)
Publication Date:
OSTI Identifier:
22230878
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 261; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; AMPLITUDES; BEAMS; BOUNDARY CONDITIONS; BOUNDARY-VALUE PROBLEMS; WAVE EQUATIONS; WAVE PACKETS; WAVE PROPAGATION