THE TWO-SWEEP METHOD FOR HETEROGENEOUS BODY’S PERMITTIVITY DETERMINATION IN A WAVEGUIDE 

Smirnov Yuriy Gennad'evich, Doctor of physical and mathematica sciences, professor, head of sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), mmm@pnzgu.ru
Moskaleva Marina Aleksandrovna, Researcher, the research center “Supercomputer modeling in electrodynamics”, Penza State University (40 Krasnaya street, Penza, Russia), m.a.moskaleva1@gmail.com

517.3, 517.6

10.21685/2072-3040-2017-4-10

Background. The determination of characteristics of a material sample placed in a waveguide by measuring the electromagnetic field is an actual problem in radio electronics. The objective of the work is to study a mathematical model of electromagnetic waves scattering on volumetric heterogeneous bodies in a rectangular waveguide.
Materials and methods. The direct problem of electromagnetic waves on a heterogeneous body placed in a waveguide is considered. This problem is reduced to solving the integro-differential equation. To solve the resulting equation, the projection method of Galerkin is used. The inverse problem of permittivity determination of a heterogeneous body in a waveguide is formulated. The inverse problem is reduced to solving an integral equation of the first kind and recalculating the function of permittivity through the polarization current.
Results. The two-sweep method for heterogeneous body’s permittivity determination in a waveguide is constructed. Numerical results of the solution of the inverse problem of the diffraction recovery of body’s permittivity in a rectangular waveguide are obtained.
Conclusions. The results can be applied in practice, for example, in studying of various nanocomposite materials and complex nanostructures by the nondestructive method of testing.

boundary value problem, inverse problem of diffraction, permittivity tensor, tensor Green's function, integrodifferential equation

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