Ivanyshyn Yaman, Olha
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Yaman, Olha Ivanyshyn
Ivanyshyn, Olha
Ivanyshyn Yaman, O.
Ivanyshyn, Olha
Ivanyshyn Yaman, O.
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olhaivanyshyn@iyte.edu.tr
Main Affiliation
04.02. Department of Mathematics
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Current Staff
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Documents
21
Citations
431
h-index
10
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Scholarly Output
14
Articles
11
Views / Downloads
50650/5435
Supervised MSc Theses
2
Supervised PhD Theses
1
WoS Citation Count
42
Scopus Citation Count
46
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0
Projects
1
WoS Citations per Publication
3.00
Scopus Citations per Publication
3.29
Open Access Source
9
Supervised Theses
3
| Journal | Count |
|---|---|
| Journal of Numerical and Applied Mathematics | 2 |
| Applied Ocean Research | 1 |
| Computers and Mathematics with Applications | 1 |
| Inverse Problems | 1 |
| Journal of Computational Physics | 1 |
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14 results
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Now showing 1 - 10 of 14
Article Citation - WoS: 3On the Non-Linear Integral Equation Approaches for the Boundary Reconstruction in Double-Connected Planar Domains(Ivan Franko National University of Lviv,, 2016) Chapko, R. S.; Yaman, Olha Ivanyshyn; Kanafotskyi, T. S.We consider the reconstruction of an interior curve from the given Cauchy data of a harmonic function on the exterior boundary of the planar domain. With the help of Green's function and potential theory the non-linear boundary reconstruction problem is reduced to the system of non-linear boundary integral equations. The three iterative algorithms are developed for its numerical solution. We find the Frechet derivatives for the corresponding operators and show unique solviability of the linearized systems. Full discretization of the systems is realized by a trigonometric quadrature method. Due to the inherited ill-possedness in the obtained system of linear equations we apply the Tikhonov regularization. The numerical results show that the proposed methods give a good accuracy of reconstructions with an economical computational cost.Article Citation - WoS: 2Citation - Scopus: 2An 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, FrederiqueWe 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: 7Citation - Scopus: 7Nonlinear Integral Equations for Bernoulli's Free Boundary Value Problem in Three Dimensions(Elsevier Ltd., 2017) Ivanyshyn Yaman, Olha; Kress, RainerIn this paper we present a numerical solution method for the Bernoulli free boundary value problem for the Laplace equation in three dimensions. We extend a nonlinear integral equation approach for the free boundary reconstruction (Kress, 2016) from the two-dimensional to the three-dimensional case. The idea of the method consists in reformulating Bernoulli's problem as a system of boundary integral equations which are nonlinear with respect to the unknown shape of the free boundary and linear with respect to the boundary values. The system is linearized simultaneously with respect to both unknowns, i.e., it is solved by Newton iterations. In each iteration step the linearized system is solved numerically by a spectrally accurate method. After expressing the Fréchet derivatives as a linear combination of single- and double-layer potentials we obtain a local convergence result on the Newton iterations and illustrate the feasibility of the method by numerical examples.Master Thesis Fredholm Integral Equations of First Kind(01. Izmir Institute of Technology, 2023) Oruklu, Yıldız; Tanoğlu, Gamze; Ivanyshyn Yaman, OlhaA unique variation of the inverse problem is the first type of Fredholm integral equation. To address the computing issue, inverse mathematical physics problems have been converted into the first type of Fredholm integral equation. We also use the Landweber iteration as an alternative to the well-known Tikhonov regularization technique , which has been shown to be most effective in solving ill-posed inverse problems. The Landweber iteration is a straight-forward and effective technique that exhibits convergence towards the accurate solution given specific conditions. Consequently, it serves as a valuable instru-ment for resolving inverse problems across diverse domains, including signal processing and geophysics. Following the examination of the properties of uniqueness and existence pertaining to solutions of integral equations of the first kind, the aforementioned equations are resolved through the utilization of the collocation method. The trapezoidal rule is widely utilized in numerical integration due to its straight-forward implementation and computational efficiency. However, it may not be appropriate for integrals with significant oscillatory behavior. In instances of this nature, it may be imperative to employ more sophisticated numerical integration methods, such as Gaussian quadrature or adaptive quadrature, in order to attain precise outcomes. For weakly singular integrals that appear in formulations of integral equations of potential problems in domains with corners and edges, we provide n-points Gaussian quadrature procedures which are particularly useful in numerical integration problems where the integral is difficult to evaluate. The accuracy of the method depends on the number of points used in the procedure, with higher order rules providing more accurate results.Article Citation - WoS: 2Citation - Scopus: 2Boundary Integral Equations for the Exterior Robin Problem in Two Dimensions(Elsevier, 2018) Ivanyshyn Yaman, Olha; Özdemir, GaziWe propose two methods based on boundary integral equations for the numerical solution of the planar exterior Robin boundary value problem for the Laplacian in a multiply connected domain. The methods do not require any a-priori information on the logarithmic capacity. Investigating the properties of the integral operators and employing the Riesz theory we prove that the obtained boundary integral equations for both methods are uniquely solvable. The feasibility of the numerical methods is illustrated by examples obtained via solving the integral equations by the Nyström method based on weighted trigonometric quadratures on an equidistant mesh.Article An Interior Inverse Generalized Impedance Problem for the Modified Helmholtz Equation in Two Dimensions(Wiley-v C H verlag Gmbh, 2025) Yaman, Olha Ivanyshyn; Ozdemir, GaziWe consider the inverse interior problem of recovering the surface impedances of the cavity from sources and measurements placed on a curve inside of it. The uniqueness issue is investigated, and a hybrid method is proposed for the numerical solution. The approach takes advantages of both direct and iterative schemes, such as it does not require an initial guess and has an accuracy of a Newton-type method. Presented numerical experiments demonstrate the feasibility and effectiveness of the approach.Doctoral Thesis Direct and Interior Inverse Generalized Impedance Problems for the Modified Helmholtz Equation(01. Izmir Institute of Technology, 2022) Özdemir, Gazi; Ivanyshyn Yaman, Olha; Yılmaz, OğuzOur research is motivated by the classical inverse scattering problem to reconstruct impedance functions. This problem is ill-posed and nonlinear. This problem can be solved by Newton-type iterative and regularization methods. In the first part, we suggest numerical methods for resolving the generalized impedance boundary value problem for the modified Helmholtz equation. We follow some strategies to solve it. The strategies of the first method are founded on the idea that the problem can be reduced to the boundary integral equation with a hyper-singular kernel. While the strategy of the second approach makes use of the concept of numerical differentiation, the first approach treats the hyper singular integral operator by splitting off the singularity. We also show the convergence of the first method in the Sobolev sense and the solvability of the boundary integral equation. We give numerical examples which show exponential convergence for analytical data. In the second part of this work, we take into account the inverse scattering problem of reconstructing the cavity’s surface impedance from sources and measurements positioned on a curve within it. For the approximate solution of an ill-posed and nonlinear problem, we propose a direct and hybrid method which is a Newton-type method based on a boundary integral equation approach for the boundary value problem for the modified Helmholtz equation. As a consequence of this, the numerical algorithm combines the benefits of direct and iterative schemes and has the same level of accuracy as a Newton-type method while not requiring an initial guess. The results are confirmed by numerical examples which show that the numerical method is feasible and effective.Article Citation - WoS: 7Citation - Scopus: 10A Boundary Integral Equation for the Transmission Eigenvalue Problem for Maxwell Equation(John Wiley and Sons Inc., 2018) Cakoni, Fioralba; Ivanyshyn Yaman, Olha; Kress, Rainer; Le Louër, FrédériqueWe propose a new integral equation formulation to characterize and compute transmission eigenvalues in electromagnetic scattering. As opposed to the approach that was recently developed by Cakoni, Haddar and Meng (2015) which relies on a two-by-two system of boundary integral equations, our analysis is based on only one integral equation in terms of the electric-to-magnetic boundary trace operator that results in a simplification of the theory and in a considerable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further, we use the numerical algorithm for analytic nonlinear eigenvalue problems that was recently proposed by Beyn (2012) for the numerical computation of the transmission eigenvalues via this new integral equation.Article Citation - WoS: 4Citation - Scopus: 4Numerical Solution of a Generalized Boundary Value Problem for the Modified Helmholtz Equation in Two Dimensions(Elsevier, 2021) Ivanyshyn Yaman, Olha; Özdemir, GaziWe 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.Article Citation - WoS: 12Citation - Scopus: 17Material Derivatives of Boundary Integral Operators in Electromagnetism and Application To Inverse Scattering Problems(IOP Publishing Ltd., 2016) Ivanyshyn Yaman, Olha; Louër, Frederique LeThis 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.