Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Ivanyshyn Yaman, OlhaSubject: search.filters.subject.Inverse problems

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  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Reconstruction of Generalized Impedance Functions for 3d Acoustic Scattering
    (Academic Press Inc., 2019) Ivanyshyn Yaman, Olha
    We consider the inverse obstacle scattering problem of determining both of the surface impedance functions from far field measurements for a few incident plane waves at a fixed frequency. The reconstruction algorithm we propose is based on an iteratively regularized Newton-type method and nonlinear integral equations. The mathematical foundation of the method is presented and the feasibility is illustrated by numerical examples. (C) 2019 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 17
    Material Derivatives of Boundary Integral Operators in Electromagnetism and Application To Inverse Scattering Problems
    (IOP Publishing Ltd., 2016) Ivanyshyn Yaman, Olha; Louër, Frederique Le
    This paper deals with the material derivative analysis of the boundary integral operators arising from the scattering theory of time-harmonic electromagnetic waves and its application to inverse problems. We present new results using the Piola transform of the boundary parametrisation to transport the integral operators on a fixed reference boundary. The transported integral operators are infinitely differentiable with respect to the parametrisations and simplified expressions of the material derivatives are obtained. Using these results, we extend a nonlinear integral equations approach developed for solving acoustic inverse obstacle scattering problems to electromagnetism. The inverse problem is formulated as a pair of nonlinear and ill-posed integral equations for the unknown boundary representing the boundary condition and the measurements, for which the iteratively regularized Gauss-Newton method can be applied. The algorithm has the interesting feature that it avoids the numerous numerical solution of boundary value problems at each iteration step. Numerical experiments are presented in the special case of star-shaped obstacles.