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The impedance boundary condition is widely used in order to reduce a multiple region electromagnetic field problem to a magnetic field problem analyzed in a nonconducting region only. It is obvious that the solution to the latter problem is much easier to obtain than those for conducting regions. There are several versions of the impedance boundary condition formulation which depend mainly on the choice of a field state variable and the solution technique applied.

Eddy current imaging is a relatively new technique of electromagnetic nondestructive testing that makes possible an accurate geometrical characterization of flaws. On contrary to the traditional approach to eddy current testing, spatially correlated information, that can be extracted from two‐dimensional eddy current images, is used to infer about flaw shape and dimensions. In general the problem of flaw reconstruction from the eddy current images belongs to the class of three‐dimensional nonlinear inverse problems. These problems can not be solved without properly chosen simplifications. In recent literature most of the authors tried to take advantage from the problem linearization. They used the eddy current image of a small diameter hole as a point spread function (two‐dimensional impulse response) and applied the classical linear filtering to deblur the image. Although this approach results in the restoration of the top view of the flaw it seems to be inadequate for full flaw reconstruction.

Development in microcomputer systems has led to their use for a three‐dimensional magnetic field calculation. It caused a great progress in numerical methods used for a magnetic field analysis in electric machines and devices. Determination of the calculations quality may be achieved by comparing with the measurements. For this purpose real objects or simplified models can be used.

This paper presents the practical configuration for detecting cracks in material, by applying an electromagnetic field along the largest dimension of the crack. An electromagnetic field formulation is proposed using Helmholtz's equation and Biot‐ Savart's law. The system equation is solved by using the finite element method (FEM). The exemplary results of calculation ‐ eddy currents lines in material and relative resistance versus probe position are presented.

The paper presents a numerical version of a method which makes it possible to calculate any quasi‐stationary two‐dimensional field in non‐ferromagnetic conductors of limited cross‐sections for unknown boundary conditions on the conductor surfaces. The principle of the method depends on the application of a finite‐element network within the current region and the method of variable division within the no‐current region. The conditions of the continuity of the vector potential and the continuity of the tangential component of the magnetic induction vector are considered in the form of functions defined by the Bubnov‐Galerkin method. Since the separation of the variables is used in the region without current, it is easy to satisfy the conditions at infinity for different types of input. The shapes of the conductors in the current region are, on the other hand, illustrated by discretization by means of the finite element method. An example of the application of the method for two‐dimensional analysis of power losses in two thick solid circular conductors placed in a sinusoidally varying transverse field is presented. Plots of power losses were drawn based on numerical computation.

Investigations which have been carried out up to the present have shown that trajectories of the arc spot over the extinguishing plate drift always towards the plate axis. Results of calculations presented in this paper are different from the results which have been obtained till now. The calculations have been made with the use of computer programs based on the boundary element method. The results of the calculations show that for some areas of plates of specific shapes potential gradient of a field of forces acting against the arc spot may approach zero. When the arc reaches any point of such an area it is stopped and the arc spot trajectory does not end at the plate axis.

The paper presents a historical review, the state of the art and recent advances in the field of computational electromagnetics at leading universities and research institutes in Poland. Contributions made by Polish scientists to the development of fundamental electromagnetism, as well as to computational methods, are emphasized, and some conclusions are drawn regarding expected future developments.