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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.

The purpose of this paper is to access performance of existing computational techniques to model strongly non‐linear coupled thermo‐electric problems.

A thermistor is studied as an example of a strongly non‐linear diffusion problem. The temperature field and the current flow in the device are mutually coupled via ohmic heating and very rapid variations of electric conductivity with temperature and applied electric field, which makes the problem an ideal test case for the computational techniques. The finite volume fully coupled and fractional steps (splitting) approaches on a fixed computational grid are compared with a fully coupled front‐fixing method. The algorithms' input parameters are verified by comparison with published experiments.

It was found that fully coupled methods are more effective for non‐linear diffusion problems. The front fixing provides additional improvements in terms of accuracy and computational cost.

This paper for the first time compares in detail advantages and implementation complications of each method being applied to the coupled thermo‐electric problems. Particular attention is paid to conservation properties of the algorithms and accurate solutions in the transition region with rapid changes in material properties.

Benchmark problem 13 of the TEAM Workshop consists of steel plates around a coil (a nonlinear magnetostatic problem). Seventeen computer codes developed by twelve groups are applied, and twenty‐five solutions are compared with each other and with experimental results. In addition to the numerical calculations, two theoretical presentations are given in order to explain discrepancies between the calculations and the experiment.

Although edge elements satisfactorily solve the eddy current problem, formulations allowing the use of standard, node‐based elements, are still looked for. But “well‐posed” formulations have been elusive up to now. We propose one, based on a particular gauge, div(σ α)=−σ ²μ v, close to the “Lorenz gauge” of several recent publications, but not identical if one does not assume a piecewise uniform conductivity.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

An algorithm for simultaneous solution of equations describing transient 3D magnetic field coupled to the Kirchhoff’s equations and the equation of motion has been presented. The nonlinearity and anisotropy of the magnetic core have been taken into account. Numerical implementation of the algorithm is based on the finite element method. In order to solve the 3D problem a special iterative procedure, in which the 3D task is substituted with a sequence of 2D problems, has been proposed. The time‐stepping backward difference algorithm for the time‐discretization of the electric circuit equations has been applied. To determine the moving armature position, an implicit procedure, which is unconditionally stable has been proposed. For the sake of example, the calculations of dynamic operation of the E‐type electromagnetic actuator equipped with the shading coil have been performed.

The paper presents an efficient modeling technique for the fluxset magnetic field sensor. Using separate numerical solutions for the electric and magnetic fields, an equivalent SPICE circuit is extracted in the postprocessing phase. The main contribution of the paper is the technique used to model the distributed capacitive effects in insulation between coils, by concentrating them in an “Extended II scheme”, an infinite circuit which is optimally reduced to a finite one. The results are in qualitative agreement with the experimental ones.

Benchmark problem 5 of the TEAM workshops consists of four aluminium blocks placed in the space between the jaws of an electromagnet. Three dimensional eddy currents are induced by 50 Hz time‐varying flux. Eleven sets of results from nine groups of contributors are compared with experimental measurements. The results from most of the computer codes tend to converge to common limits. These limits are in some places slightly different from some of the measured results. The reason for this discrepancy is thought to be due to the idealised boundary conditions, ignoring any losses in laminated iron, which are assumed in all the computer models.

We discuss a model that is capable of describing the process of induction hardening of steel: induction heating – heat transfer – solid‐solid phase transitions in steel. It consists of a reduced system of Maxwell’s equations, the heat transfer eqaution and a system of ordinary differential equations for the volume fractions of the occuring phases. The model is applied to simulate surface heat treatments, which play an important role in the manufacturing of steel. The numerical methods are implemented with tools from pdelib, a collection of modular algorithms. We present numerical simulations of surface hardening applied to the steel 42 CrMo 4.

The convergence of the transfinite‐element (TFE) method for high frequency methods is analyzed in this paper. Two different potential formulations will be compared in the frequency and time domain.

The A*‐and A,v‐formulation for time domain and frequency domain transfinite elements are described. The convergence properties of the methods are investigated and demonstrated on a simple test problem.

It is shown that the convergence of the frequency domain method depends also on the discretization of areas where the field values do not change very much. A numerical example shows that for the calculation of the whole frequency range, the time domain approach is much more faster than the frequency domain method.

Further, work should also cover additional formulations like, e.g. the T,Φ‐formulation.

Pros and cons of different formulations and methods for solving high frequency problems for printed circuit boards or microwave structures are investigated.

The originality of the paper is the comparison, the discussion and the explanations of the convergence of the TFE method for wave propagation.