A novel machine-learning-based method for the fast solution of integral equations for electromagnetic scattering problems

Abstract

A novel method is proposed for the efficient and accurate iterative solution of frequency domain integral equations that can be used for large-scale electromagnetic scattering problems. The proposed method uses a novel group-by-group interaction scheme for the fast and accurate evaluation of far-zone interactions based on the one-box-buffer scheme during the matrix-vector multiplication at each iteration. Briefly, subdomain basis functions (that are used to model the scatterer) at each box are replaced by a fixed uniform distribution of Hertzian dipoles, and the dipole-to-dipole interactions are inferred in a group-wise manner by using machine learning algorithms. The efficiency and accuracy of the proposed method are assessed by comparing our results for scattering from several conducting geometries with those obtained by the Mie series and multilevel fast multipole algorithm (MLFMA) solutions.