Browsing by Subject "Acceleration techniques"

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    Comparative study of acceleration techniques for integrals and series in electromagnetic problems
    (IEEE, 1995-06) Kinayman, Noyan; Aksun, M. I.
    Most of the electromagnetic problems can be reduced down to either integrating oscillatory integrals or summing up complex series. However, limits of the integrals and the series usually extend to infinity. In addition, they may be slowly convergent. Therefore, numerically efficient techniques for evaluating the integrals or for calculating the sum of infinite series have to be used to make the numerical solution feasible and attractive. In the literature, there are a wide range of applications of such methods to various EM problems. In this paper, our main aim is to critically examine the popular series transformation (acceleration) methods which are used in electromagnetic problems and compare them by numerical examples.
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    A novel approach for the efficient computation of 1-D and 2-D summations
    (Institute of Electrical and Electronics Engineers Inc., 2016) Karabulut, E. P.; Ertürk, V. B.; Alatan, L.; Karan, S.; Alisan, B.; Aksun, M. I.
    A novel computational method is proposed to evaluate 1-D and 2-D summations and integrals which are relatively difficult to compute numerically. The method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials. For a convergent summation, the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation. Since the procedure requires the evaluation of relatively small number of terms, the computation time for the evaluation of the summation is reduced significantly. In addition, by using the proposed method, very accurate and convergent results are obtained for the summations which are not even absolutely convergent. The efficiency and accuracy of the method are verified by evaluating some challenging 1-D and 2-D summations and integrals. © 2016 IEEE.