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Algebra i Analiz, 2010, Volume 22, Issue 6, Pages 43–49 (Mi aa1212)  
Research Papers

How should we improve the ray-tracing method?

B. V. Budaev

University of California at Berkeley, Department of Mechanical Engineering, Berkeley, CA
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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.
Keywords: diffraction, ray tracing method, stochastic equation, Feynman–Kac formula.
Received: 07.09.2010
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 6, Pages 877–881
DOI: https://doi.org/10.1090/S1061-0022-2011-01173-2
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. V. Budaev, “How should we improve the ray-tracing method?”, Algebra i Analiz, 22:6 (2010), 43–49; St. Petersburg Math. J., 22:6 (2011), 877–881
Citation in format AMSBIB
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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