基于多层快速多极子方法的高效快速算法研究

【作者】 胡劼；

【导师】 聂在平； 胡俊；

【作者基本信息】 电子科技大学 ， 无线电物理， 2004， 硕士

【摘要】 实现复杂目标电磁散射的高效求解对于雷达系统设计与雷达目标识别具有十分重要的意义。而日趋频繁的工程应用对求解的速度和效率提出了迫切要求。即使是使用近年来最令人瞩目的一种电磁散射高效求解方法——快速多极子方法和多层快速多极子方法,往往在分析一些电大尺寸目标电磁散射问题时,也会耗费过长的计算时间,不能满足工程应用的要求。本文基于多层快速多极子方法,采用了渐进近似的原理,开发出了几种高效快速方法来分析复杂目标的三维矢量散射。这些方法与传统多层快速多极子方法相比具有计算速度快,精度可控制的特点,特别适合于工程应用。本文还给出了多种三维电大尺寸目标电磁散射的计算结果,并与多层快速多极子方法的结果作了比较,证明在保证精度的前提下,可以大大节省了计算时间。本文首先回顾了用于散射分析的积分方程方法,介绍了快速多极子方法的基础—矩量法的关键技术,例如目标体的几何建模,基函数和权函数的选择。接着,详细介绍了快速多极子方法和多层快速多极子方法的基本原理和数值实现过程,并且用计算实例证明了方法和程序的有效性和正确性,为下一步的工作打下了良好的基础。最后,在上述方法的基础上,深入研究了自适应射线传播多层快速多极子方法、快速远场近似多层快速多极子方法和快速远场近似-局部耦合多层快速多极子方法等高效快速计算方法。在保证了计算精度的前提下,利用电磁散射的物理机制,对多层快速多极子方法中的最粗层上组进行了分区,对其转移因子作了一系列合理近似,当未知数特别庞大时,应用这些方法可以获得更高效率。本文所有数值结果均与文献结果或已获验证的数值程序计算结果吻合<WP=5>良好,充分说明了这些算法的高效性和正确性。本文研究工作为电大尺寸复杂三维目标的矢量电磁散射高效分析提供了有效的手段,为越趋频繁的工程应用提供了强有力的支持。更多还原

【Abstract】 To realize efficient solution of electromagnetic (EM)?scattering from complex target has very practical value for the design of radar system and identify of radar targets. Nowadays, more and more engineering projects need faster and more efficient methods to solve such problems. Even though two most attractive solvers—fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are used, they are still time consuming in solving the scattering problems of large objects. Based on MLFMA, this paper uses several approximate methods, and implement some highly efficient and fast methods to analyse EM scattering of complex 3D targets. Compared with the traditional algorithms, they can work much faster still with a reasonable accuracy. This characteristic makes them suitably to be implemented into engineering projects. This paper gives numerical results to compare with those of MLFMA , which prove the efficiency of the algorithms.Firstly, the integral equation methods used for analysis of scattering are reviewed. As the basis of fast multipole method, the key techniques of moment of method such as target modeling and the choice of basis/test functions are discussed.Secondly, the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA) are studied in detail. After expatiating their principles and numerical computing process, the paper gives some results to affirm their correctness.At last, several highly effcient algorithms based on MLFMA are extensively studied, such as adaptive ray-propagation MLFMA <WP=7>(ARP-MLFMA) , fast far-field approximation MLFMA (FAFFA-MLFMA) and fast far-field approximation partial coupling MLFMA (FAFFA-PC-MLFMA). Using physical principle of scattering, these methods divide the groups in the coarsest level into different regions, and simplify the translator of MLFMA. Hence, the computational cost is reduced greatly, especially when the number of unknowns is very large.All numerical results in the paper agree well with the results in the references and those computed by confirmed numerical programs. It proves well their high efficiency and accuracy. The research work in this paper provides a useful means for fast analysis of scattering from complex 3D targets with large electrical size and gives strong support to more and more engineering projects.更多还原