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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 10, Pages 1746–1758 (Mi zvmmf12067)

Mathematical physics

a numerical method for solving the microwave tomography problem of restoring inhomogenettes in a cylindrical body

Yu. G. Smirnov, M. Yu. Medvedik, V. Yu. Martynova

Penza State University, Penza, Russia

Abstract: In this paper, a vector three-dimensional inverse diffraction problem on a cylindrical body is solved based on a two-step method. The diffuser is filled with an inhomogeneous nonmagnetic dielectric material. The initial boundary value problem for the Maxwell system of equations is reduced to a system of integro-differential equations. A numerical method for solving a first-order equation in special classes of functions is described. A distinctive feature of the proposed numerical method is its non-iteration, in addition, a two-step method for solving the inverse problem does not require a good initial approximation. The calculation results are presented. It is shown that the two-step method is an effective approach to solving vector problems of microwave tomography.

Key words: three-dimensional vector inverse diffraction problem, restoration of dielectric constant, integro-differential equation, two-step method, numerical method.

UDC: 519.635

Received: 17.06.2025
Revised: 09.07.2025
Accepted: 21.07.2025

DOI: 10.31857/S0044466925100108


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:10, 2497–2509

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© Steklov Math. Inst. of RAS, 2026