Optimal fixed‐point method for solving 3D nonlinear periodic eddy current problems

Abstract

Purpose

The purpose of the paper is to present a method for efficiently obtaining the steady‐state solution of the quasi‐static Maxwell's equations in case of nonlinear material properties and periodic excitations.

Design/methodology/approach

The fixed‐point method is used to take account of the nonlinearity of the material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all nonlinear iterations. Owing to the application of the fixed‐point technique the harmonics are decoupled. The optimal parameter of the fixed‐point method is determined to accelerate its convergence speed. It is shown how this algorithm works with iterative linear equation solvers.

Findings

The optimal parameter of the fixed‐point method is determined and it is also shown how this method works if the equation systems are solved iteratively.

Originality/value

The convergence criterion of the iterative linear equation solver is determined. The method is used to solve three‐dimensional problems.

Citation

Koczka, G., Außerhofer, S., Bíró, O. and Preis, K. (2009), "Optimal fixed‐point method for solving 3D nonlinear periodic eddy current problems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 4, pp. 1059-1067. https://doi.org/10.1108/03321640910959107