Zooming into the near field: A novel formulation of the BEM as applied to EMC modelling and simulation problems

The Boundary Element Method is a versatile and powerful numerical technique which has been successfully applied to EMC problems in device modelling at various scales and frequency ranges. The underlying system of surface integrals involve (dyadic) Green´s functions and their spatial derivatives which are as a rule singular with varying degree of singularity. While the arising singularities are in principle integrable, sophisticated regularization techniques are required to assure reliable numerical results in terms of accuracy and robustness. In particular in the near-field region the calculations may turn out to be prohibitively complicated. In this paper, utilizing simplest possible models, a novel technique for treating near-field problems has been presented. An easy-to-use, and, at the same time, conceptually systematic recipe has been developed which is applicable to a myriad of modelling and simulation problems in computational engineering. The presented method enables zooming into the near-field systematically and facilitates obtaining numerical results with arbitrary degree of precision.