Integral Equation Methods for Scattering by Periodic Lipschitz Surfaces
Bo Zhang, Guozheng Yan · Birkhäuser Boston eBooks · 2004
In this paper we consider the two-dimensional Dirichlet and impedance boundary value problems for the Helmholtz equation, Δ u + k 2 u = 0, in a non-locally perturbed half-plane with a periodic Lipschitz boundary. The Dirichlet problem arises in a study of time-harmonic acoustic scattering of an incident field by a sound-soft, non-smooth (Lipschitz) periodic surface where the total field u t (the sum of the incident field u i and the scattered field u ) vanishes. The impedance problem, with the boundary condition ∂ u /∂ v + i λ u = 0, where λ ∈ ℂ is a constant, models acoustic or electromagnetic scattering (in both polarization cases) by a one-dimensional Lipschitz periodic boundary of finite surface impedance. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.