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Vector electromagnetic potentials for сontinuous media electromagnetics


M.V. Davidovich – Dr.Sc. (Phys.-Math.), Professor, Department «Radioengineering and Electrodynamics», Saratov State Technical University named after Gagarin Yu.A. E-mail:

The possible methods of introduction of the vector of potentials for inhomogeneous anisotropic and bianisotropic media and structures are considered and the differential and integrodifferential equations are formulated for them. The formulations are based on the tensor Green’s functions of the Maxwell equations. For the constructive realization of the algorithms, the tensor Green’s functions of sources in free space are used. Several equations for several possible forms of introduction vector potentials and considered the most convenient of them for specific boundary problems have been received. The advantages of formulations of boundary value problems regarding potentials in comparison with the field are shown and the proposed algorithms for them, based on finite elements and iterative procedures, are presented. The benefits are associated with less singularity of the kernels of the corresponding equations and with the possibility to use a less smooth and basic functions. The algorithms of solutions of the equations use the volume integral and integrodifferential equations and the volume finite elements for them. The potentials and the corresponding equations for heterogeneous structures are introduced. The algorithm for analysis of open dielectric resonators eigen modes, based on the simultaneous iteration solution of the integral equation, is described and stationary values of the corresponding functional are obtained. The oscillations of cylindrical dielectric resonators with homogenous permittivity and inhomogeneous permittivity given by the formula, as well as rectangular dielectric resonator modes are investigated. The calculated frequency and quality factor of these modes are presented, which are in a good agreement with known results. The proposed method is applicable both to open and shielded structures, provided that the Green’s function without studied inclusions is known. It can also be applied to formulation of the dispersion equations of homogeneous structures (for example, waveguides) filled with complicated (for example, bianisotropic) media.

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