Research Papers

How should we improve the ray-tracing method?

B. V. Budaev

University of California at Berkeley, Department of Mechanical Engineering, Berkeley, CA

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, 22:6, 877–881

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