Fixed‐point method for solving non linear periodic eddy current problems with T, Φ‐Φ formulation

Abstract

Purpose

The purpose of the paper is to show the application of the fixed‐point method with the T, Φ‐Φ formulation to get the steady‐state solution of the quasi‐static Maxwell's equations with non‐linear material properties and periodic excitations.

Design/methodology/approach

The fixed‐point method is used to solve the problem arising from the non‐linear material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all non‐linear iterations. The optimal parameter of the fixed‐point method is investigated to accelerate its convergence speed.

Findings

The Galerkin equations of the DC part are found to be different from those of the higher harmonics. The optimal parameter of the fixed‐point method is determined.

Originality/value

The establishment of the Galerkin equations of the DC part is a new result. The method is first used to solve three‐dimensional problems with the T, Φ‐Φ formulation.

Citation

Koczka, G. and Bíró, O. (2010), "Fixed‐point method for solving non linear periodic eddy current problems with T, Φ‐Φ formulation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 29 No. 6, pp. 1444-1452. https://doi.org/10.1108/03321641011078517