This article is cited in 2 papers

Mathematics

The microwave tomography method for solving the inverse problem on cylindrical bodies

A. O. Lapich, M. Yu. Medvedik

Penza State University, Penza

Abstract: Background. The main purpose of this study is finding of solution the inverse problem of diffraction. The application of this problem may be relevant in the diagnosis of breast cancer. Materials and methods. The initial boundary value problem for the Helmholtz equation is reduced to integral equation. This equation is solved numerically. A two-step algorithm is used to solve the inverse problem. Results. The graphic images which illustrate the value of the dielectric constant inside the body for the initial problem and for reconstructed one are presented. Conclusions. A numerical method for finding the wave function is proposed and implemented, which makes it possible to identify the structure of an object without damaging or destroying them.

Keywords: Lippmann-Schwinger integral equation, boundary value problem for the Helmholtz equation, numerical method, inverse problem, two-step method, combined computational grids, Galerkin method

UDC: 517.9

DOI: 10.21685/2072-3040-2024-1-9