Nonlinear least squares optimization applied to the method of fundamental solutions for eddy current problems

Abstract

The authors describe the use of a nonlinear least squares optimization technique for adaptively determining the equivalent source locations when the method of fundamental solution is used for 2D eddy current problems. The main advantage of the method is that guesswork in locating the sources is eliminated. Two examples of applying the method are given. One is the case of two circular conductors (one magnetic and the other nonmagnetic). The second is the case of a single conductor having a rectangular cross section. In both cases, the conductors carry an impressed current. Results are compared with those obtained without the use of nonlinear least squares optimization. It is shown that in both cases the source points can easily go across the boundaries during the optimization procedure. >