Mathematics

Using combined computational grids in the problem of reconstructing body inhomogeneities based on near-field measurement results

B. A. Zaytsev, M. Yu. Medvedik

Penza State University, Penza

Abstract: Background. The purpose of this study is to develop an effective non-invasive method for determining the properties of the object under consideration. Material and methods. For these purposes, the inverse diffraction problem is solved using combined or generalized computational grids. The paper presents a description of the direct and inverse problems. 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. Numerical results are obtained and solutions to the problem with noisy and non-noisy input data are compared.

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

UDC: 517.3

DOI: 10.21685/2072-3040-2024-3-6