An efficient numerical model for a magnetic core eddy-current probe

In this paper, we study the problem of modeling the response of an eddy-current probe made by one or more coils mounted on magnetic cores. The numerical model is based on an integral formulation in terms of the induced eddy-current J and the magnetization vector M. In terms of numerical modeling, the presence of the magnetic material has a major impact on the computational cost when, as in usual eddy current test operations, the probe is moved on the surface of the test specimen. Here, we propose an efficient numerical method, based on an integral formulation, to model the response of eddy-current testing probes with a magnetic core. The magnetic material is supposed to be homogeneous and linear. This last assumption is motivated by the circumstance that the fields levels occurring in typical eddy-current testing operations are low. The magnetization vector is, then, the gradient of an harmonic function and it admits a minimal representation made by a set of unknowns associated to a proper subset of edges of the boundary of the magnetic domain. An experimental test shows the accuracy of the method and the foundation of the underlying hypothesis.