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On the reconstruction of material properties of a radially inhomogeneous cylindrical waveguide
Author(s) -
Vatulyan Alexandr Ovanesovich,
Yurov Victor Olegovich
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7067
Subject(s) - tikhonov regularization , mathematics , waveguide , fredholm integral equation , regularization (linguistics) , inverse problem , mathematical analysis , integral equation , displacement (psychology) , range (aeronautics) , iterative method , mathematical optimization , optics , physics , computer science , psychology , materials science , artificial intelligence , composite material , psychotherapist
The scheme of solving the inverse problem (IP) for reconstructing three functions characterizing the radial change in the Lamé parameters and in the density in a cylindrical waveguide is presented. The displacement fields corresponding to three types of loading are used as an additional information for solving the IP. An iterative process is constructed, at each step of which a direct problem is solved for the radially inhomogeneous waveguide, and the corrections to the restored functions are determined. The corrections are identified by solving the system of three Fredholm integral equations of the first kind with smooth kernels. The solution is constructed by the A. N. Tikhonov regularization method. A series of computational experiments was carried out. The role of the initial approximation and the frequency range is discussed.