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How should we improve the ray-tracing method?

Author: B. V. Budaev
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 22 (2010), nomer 6.
Journal: St. Petersburg Math. J. 22 (2011), 877-881
MSC (2010): Primary 81Q30
Published electronically: August 18, 2011
MathSciNet review: 2798765
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Abstract | References | Similar Articles | Additional Information

Abstract: The possibility is discussed to improve the ray approximation up to an exact representation of a wave field by the Feynman-Kac probabilistic formula (this formula gives an exact solution of the Helmholtz equation in the form of the expectation of a certain functional on the space of Brownian random walks). Some examples illustrate an application of the solutions obtained to diffraction problems.

References [Enhancements On Off] (What's this?)

  • 1. V. M. \cyr{B}abich and V. S. \cyr{B}uldyrev, Asimptoticheskie metody v zadachakh difraktsii korotkikh voln. Tom l, Izdat. “Nauka”, Moscow, 1972 (Russian). Metod etalonnykh zadach. [The method of canonical problems]; With the collaboration of M. M. Popov and I. A. Molotkov. MR 0426630
    V. M. Babič and V. S. Buldyrev, Short-wavelength diffraction theory, Springer Series on Wave Phenomena, vol. 4, Springer-Verlag, Berlin, 1991. Asymptotic methods; Translated from the 1972 Russian original by E. F. Kuester. MR 1245488
  • 2. Mark Freidlin, Functional integration and partial differential equations, Annals of Mathematics Studies, vol. 109, Princeton University Press, Princeton, NJ, 1985. MR 833742
  • 3. Bair V. Budaev and David B. Bogy, Diffraction by a convex polygon with side-wise constant impedance, Wave Motion 43 (2006), no. 8, 631–645. MR 2267276, 10.1016/j.wavemoti.2006.05.007

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Additional Information

B. V. Budaev
Affiliation: Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740

Keywords: Diffraction, ray tracing method, stochastic equation, Feynman–Kac formula
Received by editor(s): September 7, 2010
Published electronically: August 18, 2011
Dedicated: Dedicated to V. M. Babich
Article copyright: © Copyright 2011 American Mathematical Society