用于电磁散射分析的积分方程快速直接求解法研究及进展  

The progress of integral-equation based fast direct solvers for electromagnetic scattering analysis

作　　者：胡俊[1] 荣志 郭翰 聂在平[1] HU Jun;RONG Zhi;GUO Han;NIE Zaiping(School of Electronic Science and Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China;Sigrity R&D US,Cadence Design Systems,Inc,San Jose 95134,USA)

机构地区：[1]电子科技大学电子科学与工程学院,成都611731 [2]Sigrity R&D US,Cadence Design Systems,Inc,San Jose 95134,USA

出　　处：《电波科学学报》2020年第1期26-33,共8页Chinese Journal of Radio Science

基　　金：国家自然科学基金杰青项目(61425010);国家自然科学基金创新群体项目(61721001)。

摘　　要：介绍了一系列用于电磁散射分析的积分方程快速直接求解方法,旨在显著缓解或避免积分方程迭代求解收敛缓慢甚至不收敛的问题,为积分方程提供一个快速稳定的数值求解手段.文中详细介绍了快速直接求解方法的优点、应用以及国内外的研究动态;重点讨论了几种不同的方法,分别为分级矩阵(hierarchical matrices,-matrices)以及分级非对角低秩矩阵(hierarchically off-diagonal low-rank matrices,HODLR),包括每种方法的构建以及分解求逆方式;对各个方法的优缺点展开了进一步讨论;给出了各个方法的分解以及内存复杂度和复杂飞机模型的电磁散射分析数值算例来证明各个方法的效率和精度.最后,对快速直接求解方法当前仍然存在的主要挑战和可能的策略进行了简略的讨论以及展望.This paper reviews a series of integral-equation based fast direct solvers for electromagnetic scattering analysis. The main contribution of fast direct solver is to alleviate the slow-convergence issue of iterative solver or even avoid it. This would provide a fast and stable numerical solution for the electromagnetic integral equations. The paper introduces the advantages and applications of fast direct solvers and the research review of the past few years in detail. The main part of the paper focuses on two different methods, namely hierarchical matrix and hierarchical off-diagonal low-rank matrix, including the construction of the compressed impedance matrix and the factorization of the inverse matrix. The advantages and disadvantages of each method are discussed in further. The effectiveness and accuracy are demonstrated through several numerical results which contain the time and memory complexities and scattering of complex airplane model. Finally, a concise discussion and explorations are drawn to the present challenges and possible remedy strategy for electromagnetic integral-equation based fast direct solvers.

关 键 词：电磁散射分析 电磁积分方程 快速直接求解方法 分级矩阵 分级非对角低秩矩阵(HODLR) 

分 类 号：O175.5[理学—数学]