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) used for large/multiscale electromagnetic (EM) scattering problems. The proposed method uses a novel group-by-group interaction strategy to accurately evaluate far-zone interactions, defined within the framework of the one-box-buffer scheme, during the matrix-vector multiplication at each iteration of the matrix solution. Briefly, the 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). Then, the dipole-to-dipole interactions are predicted in a groupwise manner by employing machine learning (ML) algorithms. Consequently, the proposed method is effi cient, strongly scalable for parallelization, accurate, and does not exhibit the low-frequency breakdown (LFB) problem that is inherent to the conventional multilevel fast multipole algorithm (MLFMA). 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) as well as the corresponding subdomain expansion functions. Moreover, because the training is performed offline, the resulting ML networks can be used for any scatterer under any IE without extra training, as long as the sizes and the relative distances among the boxes are preserved. The efficiency and accuracy of the proposed method are assessed by comparing its results with those obtained from the conventional MLFMA for various scattering problems. The proposed method’s parallelization performance is showcased through scalability tests, and its resilience to LFB is demonstrated.