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Abstract
We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled by the socalled impedancesheet boundary conditions. By means of KontorovichLebedev integral representations for the Debye potentials and a 'partial' separation of variables, the problem is reduced to coupled functional difference (FD) equations for the relevant spectral functions. For a circular cone, the FD equations are then further reduced to integral equations, which are subsequently shown to be Fredholmtype equations via a semiinversion by use of Dixon's resolvent. We then solve the integral equations numerically using an appropriate quadrature method. Certain useful further integral representations for the solution of 'WatsonBessel' and Sommerfeld types are developed, which gives a theoretical basis for subsequent calculation of the farfield (highfrequency) asymptotics for the diffracted field. Based on this asymptotics, the radar cross section in the domain, which is free from both the reflected and the surface waves, has been computed numerically.
Original language  English 

Pages (fromto)  676719 
Number of pages  44 
Journal  IMA Journal of Applied Mathematics 
Volume  75 
Issue number  5 
DOIs  
Publication status  Published  Oct 2010 
Keywords
 numerical evaluation of the vertex diffracted wave
 the farfield asymptotics
 semitransparent cone
 functional difference equations
 diffraction
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Projects
 1 Finished

Boundary Integral Equation Methods for HF Scattering Problems
Graham, I. & Smyshlyaev, V. P.
Engineering and Physical Sciences Research Council
24/03/09 → 23/09/12
Project: Research council