Modelling eddy currents in thin shields

The purpose of this paper is to present a simplified rigorous mathematical formulation of the problem of electric currents induced in thin shields with holes yielding more efficient numerical computations with respect to available methods.

A surface integral equation satisfied by the current density was constructed, which is, subsequently, represented at any point by linear combinations of novel vector basis functions only associated with the interior nodes of the discretization mesh, such that the current continuity is everywhere insured. The existence of the holes in the shield is taken into account by associating only one surface vector function with each hole. A method of moments is then applied to compute the scalar coefficients of the vector functions employed.

It was found that the induced current distribution for shields with holes having the complexity of real world structures can be determined with a satisfactory accuracy utilizing a moderate size processor notebook in a time of the order of minutes.

The originality of the proposed method consists in using specialized surface vector functions only associated with individual interior nodes of the shield, its multiply connected structure being efficiently accounted for by introducing one unknown for each hole, instead of unknowns for every node along the hole contours. The method presented is straightforward and highly efficient for mathematical analysis of thin shields with holes, and of other physical fields in the presence of multiply connected surface structures.