The total electric field E T induced by all the coils constituting the arrayed sensor is then obtained by (2), making a spatial translation and a superposition of the results obtained for the single coil. The electromagnetic problem formulation is given by (1), involving the magnetic vector potential A and the current source density Js. Firstly, the electric field induced by a single coil in the unflawed piece is calculated using the 2D axisymmetric finite element method. The direct problem is based on the generalization of the ideal crack model to an arrayed eddy current sensor, which we recall briefly in this section. On the other hand, a fast calculation of the incident field, produced by all the coils of the arrayed sensor, on the crack surface is achieved by making a translation and a superposition of the 2D axisymmetric finite element results obtained for one coil. The evaluation of the dyadic Green’s function matrix is made independently of the iterative procedure of inversion this makes the inversion to be very fast. The impedance variation of each coil is evaluated using the reciprocity principle. In the ideal crack model, the effect of the crack is represented by a current dipole layer on its surface, evaluated by an integral equation involving the electric dyadic Green’s functions and the normal incident electric field on the crack surface. In this work, we use the ideal crack model, generalized to arrayed eddy current sensors. On the other hand, the analytic models lack the flexibility to handle complex geometries. The use of the 3D finite element method would be very expensive in terms of memory space and CPU time. The inversion method proposed is based on the iterative solving of the direct problem it is thus important to have a fast tool to solve the latter.
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