基于电磁散射的大规模连续线性系统的高性能算法

本项目旨在加强计算电磁学领域的重要基础矩阵计算问题研究，设计高性能迭代算法以降低计算复杂度。针对电磁散射计算中大规模连续线性系统的系数矩阵规模大、求解难度高以及右端向量个数多带来的算法不稳定性等因素，以离散电磁散射频域中麦克斯韦方程组的边界元方法作为切入点，拟深入挖掘应用特征，并转化成数学上可描述的特点，构造高效求解多个右端向量同时给定和分时给定两种情形的大规模线性系统的块Krylov子空间方法和预条件技术，发展子空间方法的随机化算法，并运用强化学习算法的思想研究相应最优参数选取问题。

This project aims to strengthen the study of important fundamental matrix computational problems in the field of computational electromagnetics, and to design high-performance iterative algorithms to reduce the computational complexity. Taking into consideration the factors of large scale of the coefficient matrix, high difficulty of system solving, and algorithm instability caused by the large number of right-hand vectors, we plan to deeply exploit application features based on the boundary element method for discretizing the Maxwell equations in electromagnetic scattering in the frequency domain, and characterize them mathematically for the purpose of constructing block Krylov subspace methods and preconditioning techniques for solving large-scale linear systems with both cases of simultaneously given right-hand sides and right-hand sides given in sequence. Furthermore, we will develop randomized algorithms associated with subspace methods, and handle the optimal parameter selection problem using the idea of reinforcement learning algorithm.