A Novel Highly Parallelizable Machine-Learning Based Method for the Fast Solution of Integral Equations for Electromagnetic Scattering Problems

We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel group-by-group interaction strategy to accurately evaluate far-zone interactions within the framework of 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 represented by a fixed number of uniformly distributed and arbitrarily oriented Hertzian dipoles (referred to as uniform basis functions), and then the dipole-to-dipole interactions are predicted in a group-wise manner by employing machine learning algorithms, thereby showcasing efficiency, strong scalability for parallelization and accuracy without the low-frequency breakdown (LFB) problem. Since the dipole representation is independent of the underlying material properties of the scatterer, the proposed method is valid for all types of IEs (surface or volume). Moreover, because the training is performed offline, the resulting networks can be used for any scatterer under any IE, without extra training, as long as the size of, and the distances among the boxes are preserved. The efficiency and accuracy of the proposed method are assessed by comparing our results with those obtained from the conventional multilevel fast multipole algorithm for various scattering problems. The proposed method's parallelization performance is showcased through scalability tests, and its resilience to LFB is demonstrated.