Multipole theory solution of two-dimensional unbounded eddy current problems

A new approach, the multipole theory (MT) method, is presented for the comp utation of two-dimensional (2D) unbounded eddy current problems. The essent ial concept is to represent the solution of the governing partial different ial equation by the generalized MT formulae of the 2D Helmholtz equation an d the 2D Laplace equation. The least squares method reduces the problem to the solution of a set of linear equations. Ampere's law, as an additional c onstraint, is used to guarantee that the total net current is not changed d ue to the induced fields, and the radiation boundary conditions are satisfi ed. The eddy current problems of elliptic conductor, square conductor and a pair of circular conductors are considered as examples. The results obtain ed by the MT method are compared with experimental results and previously p ublished work. It is shown that the MT method is an effective approach for computation of 2D unbounded eddy current problems.