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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

   

 

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.


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Additional Information

B. V. Budaev
Affiliation: Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740
Email: budaev@berkeley.edu

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01173-2
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



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