How should we improve the ray-tracing method?
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B. V. Budaev
Translated by: S. Kislyakov - St. Petersburg Math. J. 22 (2011), 877-881
- DOI: https://doi.org/10.1090/S1061-0022-2011-01173-2
- Published electronically: August 18, 2011
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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.References
- V. M. Babich and V. S. Buldyrev, Asimptoticheskie metody v zadachakh difraktsii korotkikh voln. Tom l, Izdat. “Nauka”, Moscow, 1972 (Russian). Metod ètalonnykh zadach. [The method of canonical problems]; With the collaboration of M. M. Popov and I. A. Molotkov. MR 0426630
- Mark Freidlin, Functional integration and partial differential equations, Annals of Mathematics Studies, vol. 109, Princeton University Press, Princeton, NJ, 1985. MR 833742, DOI 10.1515/9781400881598
- 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, DOI 10.1016/j.wavemoti.2006.05.007
Bibliographic Information
- B. V. Budaev
- Affiliation: Department of Mechanical Engineering, University of California at Berkeley, Berkeley, California 94720-1740
- Email: budaev@berkeley.edu
- Received by editor(s): September 7, 2010
- Published electronically: August 18, 2011
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 877-881
- MSC (2010): Primary 81Q30
- DOI: https://doi.org/10.1090/S1061-0022-2011-01173-2
- MathSciNet review: 2798765
Dedicated: Dedicated to V. M. Babich