Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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

Browse

Filters

2017 - 20182

Settings

Author: search.filters.author.Ivanyshyn Yaman, OlhaSubject: search.filters.subject.Laplace equation

Search Results

Now showing 1 - 2 of 2
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Boundary Integral Equations for the Exterior Robin Problem in Two Dimensions
    (Elsevier, 2018) Ivanyshyn Yaman, Olha; Özdemir, Gazi; Ivanyshyn Yaman, Olha; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We 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
    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; Ivanyshyn Yaman, Olha; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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.