In this work we address the problem of modeling the response of an eddy current probe made by one or more coils on magnetic cores. The magnetic material is homogeneous and, moreover, it is assumed linear due to the "typical" low fields levels occurring in eddy current testing. The magnetization vector is, therefore, the gradient of an harmonic function. Here we exploit this by applying, to an Eddy Current Testing (ECT) problem, an innovative numerical formulation. The formulation involves a minimal representation for the magnetization made by a set of unknowns associated to a proper subset of edges of the boundary of the magnetic domain.
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