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This paper aims to discuss the relationship between the continued fraction form of the analytical solution in the frequency domain, the orthogonal function expansion and their circuit realization to derive an efficient representation of the eddy-current field in the conducting sheet and wire/cylinder. Effective frequency ranges of representations are analytically derived.

The Cauer circuit representation is derived from the continued fraction form of analytical solution and from the orthogonal polynomial expansion. Simple circuit calculations give the upper frequency bounds where the truncated circuit and orthogonal expansion are applicable.

The Cauer circuit representation and the orthogonal polynomial expansions for the magnetic sheet in the E-mode and for the wire in the axial H-mode are derived. The upper frequency bound for the Cauer circuit is roughly proportional to N⁴ with N inductive elements, whereas the frequency bound for the finite element eddy-current analysis with uniform N elements is roughly proportional to N².

The Cauer circuit representation is expected to provide an efficient homogenization method because it requires only several elements to describe the eddy-current field over a wide frequency range.

The applicable frequency ranges are analytically derived depending on the conductor geometry and on the truncation types.

The benchmark problem 4 (the FELIX brick) defined in the International Workshops for Eddy Current Code Comparison is solved by 11 different computer codes. This problem is time‐dependent and three dimensional eddy current problem with a hole. 13 sets of results in total are presented. The results are in fairly good agreement although the formulations and methods in the codes are different from each other. The problem of the hole (multi‐connectivity) is successfully solved in the results.

The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA).

Nonlinear magnetic field analysis is achieved by using Newton-Raphson method implemented by relaxed convergence criterion of Krylov subspace method.

This paper mathematically analyzes the reason why nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed.

The proposed method is essential to reduce the elapsed time in nonlinear magnetic field analysis of quasi-stationary field.

The proposed method is able to be extended to not only static field but also time domain FEA strongly coupled with circuit equation.

Because the speedup of performance evaluation of electrical machines would be achieved using proposed method, the work efficiency in manufacturing would be accelerated.

It can be seen that the nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed. The verification of proposed method is demonstrated using practical nonlinear magnetic field problem.

A series of six workshops was held to compare eddy current codes, using the six benchmark problems described in the following six papers. The problems include transient and steady‐state ac magnetic fields, close and far boundary conditions, magnetic and non‐magnetic materials. All the problems are based either on experiments or on geometries that can be solved analytically. The workshops and solutions to the problems are described. Results show that many different methods and formulations give satisfactory solutions, and that in many cases reduced dimensionality or coarse discretization can give acceptable results while reducing the computer time required.