Application of Dirichlet-to-Neumann Map Boundary Condition for Low-Frequency Electromagnetic Problems

Abstract

In this article, we present a differential formulation combined with an exact boundary condition based on a Dirichlet-to-Neumann (DtN) operator, and its applications to eddy current problems. A numerical model for the eddy current problem is derived using a reduced vector potential formulation combined with analytic expression of a DtN operator on an appropriate canonical boundary. The main advantage of this method is the improved accuracy and reduced computational cost compared to conventional approaches. The effectiveness of the proposed formulation is demonstrated in eddy current nondestructive testing applications for predicting the induced current density distribution. The numerical results for two model problems are presented: a conducting sphere in a uniform magnetic field and an eddy current probe inspection of a conducting plate with a volumetric defect.