标题： 一种用于电磁散射问题积分方程快速求解的新型高度可并行化机器学习方法 显示英文标题

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

摘要： 我们提出了一种新颖的方法，用于高效且准确地迭代求解用于大规模/多尺度电磁散射问题的频域积分方程（IEs）。 该方法在每次迭代中的矩阵向量乘法过程中，使用一种新颖的逐组相互作用策略，在单盒缓冲方案框架内准确评估远区相互作用。 简而言之，用于在每个盒子中建模散射体的子域基函数由固定数量的均匀分布且任意方向的赫兹偶极子（称为均匀基函数）表示，然后通过使用机器学习算法以分组方式预测偶极子到偶极子的相互作用，从而展现出效率、强大的并行化可扩展性和准确性，且没有低频崩溃（LFB）问题。 由于偶极子表示与散射体的底层材料特性无关，所提出的方法适用于所有类型的IEs（表面或体积）。 此外，由于训练是在离线状态下进行的，只要盒子的大小和盒子之间的距离保持不变，所得网络可以用于任何散射体在任何IE下，而无需额外训练。 通过将我们的结果与传统多级快速多极子算法在各种散射问题中得到的结果进行比较，评估了所提出方法的效率和准确性。 通过可扩展性测试展示了所提出方法的并行化性能，并证明了其对LFB的鲁棒性。 显示英文摘要

摘要： 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.