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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.

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.

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.

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

Grain‐oriented steel has a distinctly anisotropic and nonlinear behaviour. Only in rare cases is the magnetisation curve known for directions other than the principal ones. The paper aims at providing a model to obtain these curves for any direction if those in the easy and hard directions are only given.

The well‐known elliptic model is modified in order to correctly mimic the typical behaviour of grain‐oriented steel which is not described correctly by the original elliptic model. An additional condition is introduced to fix the angle between the flux density and magnetic field intensity.

The model is found to yield good agreement with measurements in case of a special material for which measured curves for intermediate angles are available.

Further research is necessary to establish whether the model is applicable to other materials.

The new model can be used in numerical analyses of devices comprising saturated grain‐oriented steel material if the magnetisation curves are given in the principal directions.

The purpose of this paper is to describe a method for solving eddy current problems. Discontinuous basis functions are applied to conducting regions in eddy‐current problems. This results in a block‐diagonal mass matrix allowing explicit time stepping without having to solve large algebraic systems.

The effect of the basis functions in the conducting region is limited to the respective finite element. This yields to a block‐diagonal mass matrix, whereas each block in this matrix belongs to one finite element. In the nonconducting region, traditional finite elements are used which leads to well‐conditioned system matrices. For the two regions, different time steps are used.

To avoid instability, a term which penalizes the tangential jump of the magnetic vector potential A has to be added. A value for weighting this term is suggested and tested on a simple two dimensional example.

The proposed method leads to a potentially fast method for solving eddy‐current problems.