Two-dimensional problems of diffraction by finite collinear structures

Abstract

Two closely related problems of diffraction are solved by use of the probabilistic random walk method. The first concerns diffraction by a boundary of a half-space with a piecewise constant boundary impedance, and the second solves the problem of diffraction by a finite segment with different impedances on its sides. The solutions are represented as superpositions of predefined geometric fields with several diffracted fields, which are explicitly represented as mathematical expectations of certain functionals along the trajectories of specified random motions running across multisheet analytic manifolds associated with the boundary conditions. Numerical examples confirm the feasibility of the solutions.