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  • 1.
    Samokhin, Alexander
    et al.
    Moscow State Tech Univ Radio Engn & Automat, Moscow 117648, Russia..
    Shestopalov, Youri
    Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
    Kobayashi, Kazuya
    Chuo Univ, Bunkyo Ku, Tokyo 1128551, Japan.
    Stationary iteration methods for solving 3D electromagnetic scattering problems2013In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 222, p. 107-122Article in journal (Refereed)
    Abstract [en]

    Generalized Chebyshev iteration (GCI) applied for solving linear equations with nonselfadjoint operators is considered. Sufficient conditions providing the convergence of iterations imposed on the domain of localization of the spectrum on the complex plane are obtained. A minimax problem for the determination of optimal complex iteration parameters is formulated. An algorithm of finding an optimal iteration parameter in the case of arbitrary location of the operator spectrum on the complex plane is constructed for the generalized simple iteration method. The results are applied to numerical solution of volume singular integral equations (VSIEs) associated with the problems of the mathematical theory of wave diffraction by 3D dielectric bodies. In particular, the domain of the spectrum location is described explicitly for low-frequency scattering problems and in the general case. The obtained results are discussed and recommendations concerning their applications are given. (C) 2013 Elsevier Inc. All rights reserved.

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