Article 10417

Title of the article

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

Authors

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

Index UDK

517.3, 517.6

DOI

10.21685/2072-3040-2017-4-10

Abstract

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.

Key words

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

Download PDF
References

1. Medvedik M. Yu., Smirnov Yu. G. Obratnye zadachi vosstanovleniya dielektricheskoy pronitsaemosti neodnorodnogo tela v volnovode [Inverse problems of heterogeneous body’s dielectric permittivity recovery in a waveguide]. Penza: Izd-vo PGU, 2014, 76p.
2. Medvedik M. Yu., Smirnov Yu. G. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2008, no. 2, pp. 2–14.
3. Medvedik M. Yu., Smirnov Yu. G. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2009, no. 4, pp. 55–71.
4. Medvedik M. Yu., Smirnov Yu. G. Radiotekhnika i elektronika [Radio engineering and electronics]. 2011, vol. 56, no. 8, pp. 940–945.
5. Smirnov Yu. G., Tsupak A. A. Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki [Journal of calculus mathematics and mathematical physics]. 2004, vol. 44, no. 12, pp. 2252–2267.
6. Smirnov Yu. G. Matematicheskie metody issledovaniya zadach elektrodinamiki [Mathematical methods of researching problems of electrodynamics]. Penza: Inf.-izd. tsentr PGU, 2009, 268 p. 
7. Il'inskiy A. S., Smirnov Yu. G. Difraktsiya elektromagnitnykh voln na provodyashchikh tonkikh ekranakh [Diffraction of electromagnetic waves on conducting thin screens]. Moscow: IPRZhR, 1996, 176 p.
8. Smirnov Yu. G., Medvedik M. Yu., Vasyunin D. I. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki [University proceedings. Volga region. Physical and mathematical sciences]. 2009, no. 3, pp. 71–87.

 

Дата создания: 06.02.2018 11:00
Дата обновления: 23.04.2018 09:30