Multipole theory solution of two-dimensional unbounded eddy current problems

Abstract

A new approach, the multipole theory (MT) method, is presented for the computation of two-dimensional (2D) unbounded eddy current problems. The essential concept is to represent the solution of the governing partial differential equation by the generalized MT formulae of the 2D Helmholtz equation and 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 constraint, is used to guarantee that the total net current is not changed due to the induced fields, and the radiation boundary conditions are satisfied. The eddy current problems of elliptic conductor, square conductor and a pair of circular conductors are considered as examples. The results obtained by the MT method are compared with experimental results and previously published work. It is shown that the MT method is an effective approach for computation of 2D unbounded eddy current problems.