Fast computation of scattering from (near-)resonant structures

The direct solvers of this paper are recursive in nature: i.e., they introduce (sub)scatterers to the geometry one at a time and obtain the complete solution for a partial geometry at each recursion. As a new (sub)scatterer is added, its interaction with all the existing ones need to be computed. The existing (sub)scatterers are divided into two groups: near neighbors and distant neighbors with respect to the most recently added (sub)scatterer. The near-neighbor interactions are computed using the recursive aggregate interaction matrix algorithm (RIMA), whereas the distant-neighbors are aggregated and their wholesale interaction with the recently added (sub)scatterer is efficiently computed using the recursive aggregate T-matrix algorithm (RATMA).