Solution of the inhomogeneity localization problem in objects with the given index refraction index 

Nikita I. Terekhin, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: ghj.ghh.13@mail.ru
Aleksey A. Tsupak, Candidate of physical and mathematical sciences, associate professor, associate professor of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: altsupak@yandex.ru 

Background. The purpose of the work is the development and software implementation of the brute force method for solving inverse diffraction problem. Material and methods. For solving the problem integral equations approach is used; for the numerical solution of the Lippmann – Schwinger equation, the collocation method is applied; for the effective solution of systems of linear algebraic equations, a special method of matrix inversion is used. Results. An efficient method for solving the problem of localization of a region of inhomogeneity with a given refractive index has been developed. Conclusions. The proposed method can be used for solving problems of microwave tomography with a small number of field measurements. 

inverse diffraction problem, microwave tomography, Lippmann – Schwinger equation, collocation method, peer perturbation of reversible matrices, localization of heterogeneity of complex shape 

Terekhin N.I., Tsupak A.A. Solution of the inhomogeneity localization problem in objects with the given index refraction index. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki = University proceedings. Volga region. Physical and mathematical sciences. 2024;(3):31–42. (In Russ.). doi: 10.21685/2072-3040-2024-3-3