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Diffraction by a convex polygon with side-wise constant impedance. (English) Zbl 1231.35050

Summary: The recently developed probabilistic approach to wave propagation and diffraction is applied to the two-dimensional problem of diffraction by an arbitrary convex polygon with side-wise constant impedance boundary conditions. Surprisingly, the new method provides a rigorous solution which is simple, transparent and complimentary to the ray approximation. It is easy to implement and it is compatible with intuitive ideas about diffraction. The numerical examples confirm the feasibility of the solution.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35P25 Scattering theory for PDEs
60H30 Applications of stochastic analysis (to PDEs, etc.)
78A45 Diffraction, scattering
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References:

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