On the role of symmetry and antisymmetry in BIE formulations of eddy current problems of multiconductor systems

The eddy current problems of multiconductor systems are considered for those cases in which we are interested to know the magnetic field distribution over selected conductors only. For these problems the classical approach to reduce the number of unknowns in the formulation of the numerical procedure is to replace other current-carrying conductors by fictitious current filaments carrying the same total currents. The error due to this approximation is estimated in relation to the kind of symmetry of the problem. It is shown that the factor governing the approximation error is the number of antisymmetric lines, namely, the error is smaller the greater the number of antisymmetric lines in the problem. In problems with double antisymmetry the error is reduced by two orders of magnitude as compared with the formulations of the problems without symmetry. Some examples are included to illustrate the theory.