A Butterfly-Based Direct Integral-Equation Solver Using Hierarchical LU Factorization for Analyzing Scattering From Electrically Large Conducting Objects

A butterfly-based direct combined-field integral-equation (CFIE) solver for analyzing scattering from electrically large, perfect electrically conducting objects is presented. The proposed solver leverages the butterfly scheme to compress blocks of the hierarchical LU-factorized discretized CFIE operator and uses randomized butterfly reconstruction schemes to expedite the factorization. The memory requirement and computational cost of the direct butterfly-CFIE solver scale as O(N log
²
N) and O(N
^1.5
log N), respectively. These scaling estimates permit significant memory and CPU savings when compared to those realized by low-rank decomposition-based solvers. The efficacy and accuracy of the proposed solver are demonstrated through its application to the analysis of scattering from canonical and realistic objects involving up to 14 million unknowns.