Mathematics

Determination of the structure of objects and their visualization in the problem of restoring the permittivity by the results of measurements of the near electromagnetic field

B. A. Zaytsev, M. Yu. Medvedik

Penza State University, Penza

Abstract: Background. The main purpose of this study is to develop an effective method for determining the structure of the spherical object. To do this, the inverse diffraction problem is solved using modified combined or generalized computational grids. Materials and methods. The paper presents a description of the direct and inverse problems, as well as a method for constructing a computational grid. Results and conclusions. The result of solving the direct problem is obtained as a solution to the corresponding volume integral equation. To solve the inverse problem, a two-step method is used. A detailed description of the numerical method is presented. The numerical results of solving the problem with noisy data are compared with non-noisy data.

Keywords: diffraction problem, integral equation, collocation method, visualization, numerical method, mathematical model

UDC: 517.3

DOI: 10.21685/2072-3040-2025-2-2