Wave scattering by surface-breaking cracks and cavities

Here we suggest a new approach to the analysis of two-dimensional wave scattering by arbitrarily shaped irregularities of a boundary of the half-space. This approach employs the probabilistic method of a rigorously justified representation of the scattered waves by explicit formulas involving the computation of mathematical expectations which average the values of certain functionals computed along the trajectories of the random motion governed by specified stochastic differential equations. As typical for the random walk method, the obtained solutions admit numerical implementations by simple algorithms which are practically independent of the particular geometry of the scatterer, which are inexpensive in terms of computer memory requirements, and which have virtually unrestricted capability for parallel processing. Illustrative numerical examples include problems of wave scattering by a tilted straight crack and by a circular cavity. (C) 2004 Elsevier B.V. All rights reserved.