Evstigneev Roman Olegovich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), Roman_cezar@mail.ru
Background. Direct and inverse electromagnetic and acoustic problems play a crucial role in applied science. The paper focuses on the scalar inverse problem in which the scattered field is measured at the point located closely outside the body. In many contemporary devices the detectors are located in a circle. Such a disposition of the detectors prevents using rectangular grids for numerical study of the problem. In this case, it is much more convenient to use cylindrical coordinates together with bodies of cylindrical shapes.
Materials and methods. The problem under consideration is described by the Lippman-Schwinger equation. With this equation one calculates the field inside the body. Then, the function heterogeneity, which characterizes the body, is reconstructed using the measured field outside the body and the calculated field distribution inside the body.
Results. The main result of the paper is an algorithm that allows solving the inverse problem. This algorithm is applicable to real as well as complex-valued fields. The article analyzes the algorithm’s resistance to measurement errors.
Conclusions. The developed algorithm allows one to reconstruct some parameters of a cylindrical body. The algorithm is stable against measurement errors.
volume singular integral equation, integral equation, boundary value problem, numerical methods, inverse problem
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