Explicit short-wave asymptotics for diffraction by finite-length discontinuities in waveguides: Closed structures

Abstract

The paper is concerned with a high-frequency diffraction by finite-length plane discontinuities located in infinite waveguides. The problem is reduced to a convolution integral equation of the first kind holding over a finite interval. It is shown that the specific physical nature of the wave process in the closed structures complicates considerably the high-frequency analysis, due to a high density of the resonance frequencies. A self-consistent asymptotic method is developed that permits explicit analytical representation for the solution. The method is tested in comparison with a direct numerical solution constructed by using a co-location technique.Mathematics Subject Classification (2000). 74G; 45E; 78B.