Fast Algorithms for Converting an FMM-Based Representation of Electrically Large Integral Operators to a Minimal-Rank ℋ2-Matrix

In this paper, we develop fast algorithms to convert an FMM-based representation to a new ℋ²-matrix whose rank is minimized based on accuracy. We then apply these algorithms to solve electrically large surface electric field integral equations for scattering analysis. The resultant new ℋ²-matrix is found to have a much reduced rank without sacrificing prescribed accuracy.