The eddy current model as a low-frequency, high-conductivity asymptotic form of the Maxwell transmission problem

摘要

We study the relationship between the Maxwell and eddy current (EC) models for three-dimensional configurations involving bounded regions with high conductivity sigma in air and with sources placed remotely from the conducting objects, which typically occur in the numerical simulation of eddy current nondestructive testing (ECT) experiments. The underlying Maxwell transmission problem is formulated using boundary integral formulations of PMCHWT type. In this context, we derive and rigorously justify an asymptotic expansion of the Maxwell integral problem with respect to the non-dimensional parameter gamma := root omega epsilon(0)/sigma. The EC integral problem is shown to constitute the limiting form of the Maxwell integral problem as gamma - 0, i.e. as its low-frequency and high-conductivity limit. Estimates in gamma are obtained for the solution remainders (in terms of the surface currents, which are the primary unknowns of the PMCHWT problem, and the electromagnetic fields) and the impedance variation measured at the extremities of the excitating coil. In particular, the leading and remainder orders in gamma of the surface currents are found to depend on the current component (electric or magnetic, charge-free or not). These theoretical results are demonstrated on three-dimensional illustrative numerical examples, where the mathematically established estimates in gamma are reproduced by the numerical results. (C) 2018 Elsevier Ltd. All rights reserved.