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J Acoust Soc Am. 2003 Oct;114(4 Pt 1):1733-41.

Random walk approach to wave propagation in wedges and cones.

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  • 1Department of Mechanical Engineering, University of California, Berkeley, California 94720, USA.


Two- and three-dimensional Helmholtz equations in wedge-shaped and conical domains are addressed by the random walk method. The solutions of the Dirichlet problems in such domains are represented as mathematical expectations of specified functionals on trajectories of multidimensional random motions whose radial components run in a complex space while the angular components remain real valued. This technique is applied to the Sommerfeld problem of diffraction by a semi-infinite screen which is explicitly solved here in the probabilistic form. The numerical results confirm the efficiency of the random walk approach to the analysis of wave propagation.

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