Nested Reduction Algorithm for Generating \mathcal^-Matrix Representation of Electrically Large Surface Integral Operators from FMM - Yang, Chang; Jiao, Dan (Digest - IEEE Antennas and Propagation Society. International Symposium (1995), 2020)
In this paper, we develop a fast algorithm to generate a rank minimized \mathcal{H}^{2} -matrix from multi-level FMM to represent electrically large surface integral equations (SIEs). The rank of the new \mathcal{H}^{2} -matrix is determined based on prescribed accuracy and is found to be much smaller than the original FMM's rank. The resultant rank-minimized \mathcal{H}^{2} -matrix can be used to accelerate both iterative and direct solutions. Numerical experiments on large-scale surface IE-based scattering analysis having millions of unknowns on a single CPU core have demonstrated its accuracy and efficiency.