Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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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 Citation - WoS: 10Citation - Scopus: 12Applications of the Pseudo Residual-Free Bubbles To the Stabilization of the Convection-Diffusion Problems in 2d(Elsevier Ltd., 2014) Şendur, Ali; Neslitürk, Ali İhsan; Kaya, AdemA stabilized finite element method is studied herein for two-dimensional convection-diffusion-reaction problems. The method is based on the residual-free bubbles (RFB) method. However we replace the RFB functions by their cheap, yet efficient approximations computed on a specially chosen subgrid, which retain the same qualitative behavior. Since the correct spot of subgrid points plays a crucial role in the approximation, it is important to determine their optimal locations, which we do it through a minimization process with respect to the L1-norm. The resulting numerical method has similar stability features with the well-known stabilized methods in the literature for the whole range of problem parameters and this fact is also confirmed by numerical experiments.Conference Object Citation - WoS: 2Citation - Scopus: 4Computational Cost Analysis of Elliptic Curve Arithmetic(Institute of Electrical and Electronics Engineers Inc., 2006) Atay, Serap; Koltuksuz, Ahmet; Hışıl, Hüseyin; Eren, ŞabanElliptic curves are proposed for the asymmetrical cryptography by Neal Koblitz and Victor Miller in 1986 separately. Elliptic curve cryptography (ECC) is utilized by hardware embedded solutions on mobile equipments and smart cards after 2000. Currently, software implementation of ECC faces the computational speed problem. One of the proposed solutions is to do the arithmetic operations on different Euclidean coordinate systems. This paper concentrates on the research of this technique and delineates the performance results of the implementation of the aforementioned technique on the different cryptographic libraries such as CRYMPIX, GMP and MIRACL.