Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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Access Right: Closed AccessAuthor: search.filters.author.Ivanyshyn Yaman, Olha

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  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    An Inverse Parameter Problem With Generalized Impedance Boundary Condition for Two-Dimensional Linear Viscoelasticity
    (Society for Industrial and Applied Mathematics Publications, 2021) Ivanyshyn Yaman, Olha; Le Louer, Frederique
    We analyze an inverse boundary value problem in two-dimensional viscoelastic media with a generalized impedance boundary condition on the inclusion via boundary integral equation methods. The model problem is derived from a recent asymptotic analysis of a thin elastic coating as the thickness tends to zero [F. Caubet, D. Kateb, and F. Le Louer, J. Elasticity, 136 (2019), pp. 17-53]. The boundary condition involves a new second order surface symmetric operator with mixed regularity properties on tangential and normal components. The well-posedness of the direct problem is established for a wide range of constant viscoelastic parameters and impedance functions. Extending previous research in the Helmholtz case, the unique identification of the impedance parameters from measured data produced by the scattering of three independent incident plane waves is established. The theoretical results are illustrated by numerical experiments generated by an inverse algorithm that simultaneously recovers the impedance parameters and the density solution to the equivalent boundary integral equation reformulation of the direct problem.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Numerical Solution of a Generalized Boundary Value Problem for the Modified Helmholtz Equation in Two Dimensions
    (Elsevier, 2021) Ivanyshyn Yaman, Olha; Özdemir, Gazi
    We propose numerical schemes for solving the boundary value problem for the modified Helmholtz equation and generalized impedance boundary condition. The approaches are based on the reduction of the problem to the boundary integral equation with a hyper-singular kernel. In the first scheme the hyper-singular integral operator is treated by splitting off the singularity technique whereas in the second scheme the idea of numerical differentiation is employed. The solvability of the boundary integral equation and convergence of the first method are established. Exponential convergence for analytic data is exhibited by numerical examples. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.Y. All rights reserved.