Volumetric Method of Moments and Conceptual Multilevel Building Blocks for Nanotopologies

On the basis of the relationship between charge dimensionality and singular field behavior, it is proven that in a volumetric description of a volume current carrying topology, half rooftops of different binary hierarchical level are allowed without introducing numerical difficulties. This opens the possibility to use a very efficient multilevel hierarchical meshing scheme in a volumetric method-of-moments (V-MoM) algorithm. The new meshing scheme is validated by numerical calculations and experiments. It paves the way toward a much more efficient use of MoM in the description of arbitrarily shaped nanostructures at infrared and optical frequencies.