Multilevel fast multipole algorithm with multiple octrees for the solution of large-scale plasmonic problems with junctions

This paper presents an implementation of the multilevel fast multipole algorithm (MLFMA), which is used to solve large scattering problems formulated in terms of surface integral equations (SIE). The implementation is capable of handling multiple composite scatterers with multiple material junctions. Each scatterer defines an electromagnetic region in which a customized octree is created. In particular, for a fixed block size in each octree, the number of levels is always minimized. Therefore, the number of operations in terms of interpolations, anterpolations and translations is minimized. Furthermore, Kirchhoff's Law, relating the current flow across a junction edge, is imposed to ensure high accuracy on the electric field calculation. As a practical application example, the MLFMA with multiple octrees is discussed in this paper in order to design a composite dielectric substrate, which ultimately enhances the directivity of a plasmonic nanoantenna.