Near-field phenomena in EMC applications

The application of the Boundary Element Method (BEM) to real-life electromagnetic field problems is generally plagued by numerical difficulties which can be traced back to the singularities of the involved dyadic Green´s functions. As a rule, the calculation of the self-actions of the boundary elements (diagonal entries in the impedance matrix), and the interactions between the nearby-located boundary elements (near-diagonal entries of the impedance matrix), lead to numerically ill-posed slowly convergent Fourier-type integrals. This fact may severely limit the applicability of this otherwise almighty and elegant method. In this paper we show that numerically divergent integrals in the BEM applications can be evaluated in a way akin to the integration of generalized functions. Thereby, the involved exponentially decaying terms automatically emerge from our formulation, as opposed to the conventional schemes, where they are constructed rather arbitrarily in an ad hoc fashion. The proposed technique leads to a myriad of novel integral representations for Dirac´s delta function in one- and two dimensions, which are presented here for the first time. Since the derived integral representations are associated with physically realizable problems, they are problem-tailored, and can be readily used. The paper concludes with the formulation of a number of challenging problems for future development along with hints to tackling them. The underlying ideas have been presented in great detail.