A Fast Plane Wave Expansion Algorithm for Rigorous Scattering Analysis From Swarm Targets

Swarm targets consisting of multiple aircraft, such as unmanned aerial vehicles (UAVs), have become an emerging tool in modern applications due to their agility and vast coverage. Because of the complicated coupling and shading effects among different units, accurate, flexible, and computationally efficient scattering analysis for this novel target remains challenging. To overcome this difficulty, in this work, a so-called plane wave expansion (PWE) algorithm is proposed. Unlike the multilevel fast multipole algorithm (MLFMA), which treats swarm targets as a single entity, PWE deals with individual units separately, allowing for the reuse of data structures for identical targets. The low computational complexity and the effectiveness of the proposed method are achieved by combining three calculation strategies: 1) evaluating the coupling effects between two close units using a rigorous fast PWE technique and ignoring those of well-separated units; 2) determining the threshold defining “well-separated” through an adaptive procedure so that the overall accuracy is controllable; and 3) quickly estimating the initial solution (IS) to accelerate convergence. Extensive numerical simulations, including one with up to 56 electrically large UAVs, are carried out to demonstrate the accuracy, effectiveness, and robustness of the proposed method.