A probabilistic approach to wave propagation and scattering

Abstract

[1] The probabilistic approach to wave propagation starts in a way that is similar to ray theory, from the representation of the wave field as a product of the amplitude and of the exponent of the eikonal, which is computed by a canonical technique of analytical mechanics. However, an important difference is that the amplitude is not approximated but is represented by exact probabilistic formulas that admit efficient numerical evaluation, and that is a direct improvement of many asymptotic solutions. This approach is shown to be an effective tool for the analysis of numerous wave propagation problems, including those of wave diffraction by a screen occupying a plane angular sector and of electromagnetic diffraction by a wedge with anisotropic impedance boundary conditions. Citation: Budaev, B. V., and D. B. Bogy (2005), A probabilistic approach to wave propagation and scattering, Radio Sci., 40, RS6S07,

On random time and on the relation between wave and telegraph equations

“…1(c) that the coefficient of dN (t), viz., ν(t) is to be evaluated at t−, which confirms the rules laid out in Section II-A in relation to (7). Furthermore,…”

“…Subsequent researchers have developed random walk method for the Helmholtz and wave equations [4], [5], and [6]. Budaev and Bogy [7] The same technique was used in [8] and [9] to address the problem of wedge diffraction with impedance boundary conditions. The basic differential equations that form the subject matter of the present paper are the 3D version of the telegrapher's equation and the wave equation and certain stochastic quantities that relate the two.…”

Diffraction by a convex polygon with side-wise constant impedance

“…The probabilistic approach to wave propagation and diffraction surveyed in [4] made it possible to obtain explicit solutions of a number of difficult problems of diffraction, including the scalar problem of diffraction by a plane angular sector [2] and the vector problem of diffraction of the electromagnetic wave by a wedge with anisotropic impedance faces [3]. Although these problems are notoriously difficult for analysis by conventional methods, the obtained probabilistic solutions appear to be simple, transparent, compatible with intuitive ideas about diffraction, and easy for numerical implementation.…”

Diffraction by a wedge with a face of variable impedance

“…[37] The version of the probabilistic random walk method surveyed by Budaev and Bogy [2005a] made it possible to obtain a solution of the problem of diffraction by a wedge with a nonconstant impedance faces. The obtained solution is not considerably more complex than the similar solution of the standard problems of diffraction by a wedge with constant impedances, and it admits numerical simulation based on a simple very short algorithm.…”