Stationary iteration methods for solving 3D electromagnetic scattering problems
2013 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 222, 107-122 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2013. Vol. 222, 107-122 p.
3-D electromagnetic scattering; Chebyshev iteration; Localization of the spectrum; Low-frequency scattering; Mathematical theory; Numerical solution; Optimal iterations; Singular integral equations, Integral equations; Optimization, Iterative methods
IdentifiersURN: urn:nbn:se:hig:diva-22867DOI: 10.1016/j.amc.2013.07.019ISI: 000326877300011ScopusID: 2-s2.0-84882280420OAI: oai:DiVA.org:hig-22867DiVA: diva2:1050224