h‐ and b‐conform finite element perturbation techniques for nondestructive eddy current testing

The aim of the present paper is to compare the performances of a finite‐element perturbation technique applied either to the h‐ conform magnetodynamic formulation or to its b‐ conform counterpart in the frame of nondestructive eddy‐current testing problems.

In both complementary perturbation techniques, the computation is split into a computation without defect (unperturbed problem) and a computation of the field distorsion due to its presence (perturbation problem). The unperturbed problem is conventionally solved in the complete domain. The source of the perturbation problem is then determined by the projection of the unperturbed solution in a relatively small region surrounding the defect. The discretisation of this reduced domain is chosen independently of the dimensions of the excitation probe and the specimen under study and is thus well adapted to the size of the defect.

The accuracy of the perturbation model is evidenced by comparing the results of the two counterpart formulations to those achieved in the conventional way for different dimensions of the reduced domain. The size of the reduced domain increases with the size of the defect at hand. This proposed sub‐domain approach eases considerably the meshing process and speeds‐up the computation for different probe positions.

At a discrete level, the impedance change due to the defect is efficiently and accurately computed by integrating only over the defect itself and a layer of elements in the reduced domain that touches its boundary. Therefore, no integration of any flux variation in the coils is required.