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.Kress, Rainer

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  • Article
    Citation - WoS: 7
    Citation - Scopus: 10
    A 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, Frédérique
    We 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: 7
    Citation - Scopus: 7
    Nonlinear Integral Equations for Bernoulli's Free Boundary Value Problem in Three Dimensions
    (Elsevier Ltd., 2017) Ivanyshyn Yaman, Olha; Kress, Rainer
    In 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.