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A modification of the hybrid projection method for analysis of electromagnetic scattering by radially inhomogeneous dielectric sphere


A.R. Gabdullina – Student, Moscow Institute of Physics and Technology (State University) E-mail: O.N. Smolnikova – Ph. D. (Eng.), Associate Professor, Moscow Aviation Institute (National Research University); Head of Department, PJSC «Radiofizika» (Moscow) E-mail: S.P. Skobelev – Dr. Sc. (Phys.-Math.), Leading Research Scientist, PJSC «Radiofizika» (Moscow); Associate Professor, Moscow Institute of Physics and Technology (State University) E-mail:

A modification of the hybrid projection method is proposed in the paper for analysis of electromagnetic scattering by a radially inho-mogeneous dielectric sphere. The modification is based on projection matching of the fields on the boundaries of spherical regions, projection of the Maxwell equations on transverse spherical vector functions, and application of the one-dimensional method of finite elements in the projection form to the ordinary differential equations obtained as a result of projection of the Maxwell equations for reducing the differential equations to algebraic systems with three-diagonal matrices. Some advantages of the proposed modification over other numerical methods are shown and discussed. High effectiveness of the modification is shown by numerical results charac-terizing convergence of the method and by comparison of the results with the data available in the literature for some partial cases. Characteristics of plane wave scattering by a Lunegurg-like lens with simultaneously negative permittivity and permeability (a negative Luneberg lens) are obtained and compared to the appropriate characteristics corresponding a conventional Luneburg lens.


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