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Convergence acceleration in the polarization method for nonlinear periodic fields

Ioan R. Ciric (Department of Electrical and Computer Engineering, The University of Manitoba, Winnipeg, Canada)
Florea I. Hantila (Department of Electrical Engineering, Politehnica University of Bucharest, Bucharest, Romania)
Mihai Maricaru (Department of Electrical Engineering, Politehnica University of Bucharest, Bucharest, Romania)

Abstract

Purpose

The purpose of this paper is to present three novel techniques aimed at increasing the efficiency of the polarization fixed point method for the solution of nonlinear periodic field problems.

Design/methodology/approach

Firstly, the characteristic BM resulting from the constitutive relation BH is replaced by a relation between the components of the harmonics of the vectors B and M. Secondly, a dynamic overrelaxation method is implemented for the convergence acceleration of the iterative process involved. Thirdly, a modified dynamic overrelaxation method is proposed, where only the relation BM between the magnitudes of the field vectors is used.

Findings

By approximating the actual characteristic BM by the relation between the components of the harmonics of the vectors B and M, the amount of computation required for the field analysis is substantially reduced. The rate of convergence of the iterative process is increased by implementing the proposed dynamic overrelaxation technique, with the convergence being further accelerated by applying the modified dynamic overrelaxation presented. The memory space is also well reduced with respect to existent methods and accurate results for nonlinear fields in a real world structure are obtained utilizing a normal size processor notebook in a time of about one‐half of one minute when no induced currents are considered and of about one minute when eddy currents induced in solid ferromagnetic parts are also fully analyzed.

Originality/value

The originality of the novel techniques presented in the paper consists in the drastic approximations proposed for the material characteristics of the nonlinear ferromagnetic media in the analysis of periodic electromagnetic fields. These techniques are highly efficient and yield accurate numerical results.

Keywords

Citation

Ciric, I.R., Hantila, F.I. and Maricaru, M. (2011), "Convergence acceleration in the polarization method for nonlinear periodic fields", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 6, pp. 1688-1700. https://doi.org/10.1108/03321641111168020

Publisher

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Emerald Group Publishing Limited

Copyright © 2011, Emerald Group Publishing Limited