并行多层快速多极子算法中若干关键技术研究

【作者】 林云；

【导师】 聂在平；

【作者基本信息】 电子科技大学 ， 电磁场与微波技术， 2006， 硕士

【摘要】 由于强烈的工程应用背景,电大尺寸目标散射特性的计算越来越成为人们关注的焦点。其在雷达系统工程设计,目标识别,遥感遥测等领域中有着极其重要的应用。一方面传统的高频电磁分析方法虽然计算较快,内存需求较低。但是其存在的致命缺陷是计算结果精度较低,在许多场合下的计算结果的精度远远不能达到应用的要求。另一方面基于积分方程的多层快速多极子方法是一种求解电磁散射问题的快速算法。相对于一些传统的方法如几何光学方法,几何绕射方法,弹跳射线方法有着更高的精度和更广的适用范围。但是由于其基于积分方程方法,需要对全局中所有的子散射体之间的相互耦合加以考虑,从而导致在求解电大尺寸目标的散射问题时需要巨大的存储空间。同时由于其在谱域上严格积分导致计算量也很大。然而工程中又常常需要我们求解电大甚至超电大目标的散射问题,当前的计算条件难以满足工程需要。为了解决这一矛盾,有学者提出了采用并行技术提供较大的物理内存,并将任务合理地分解,并行计算的方式来解决这一问题。上世纪90年代锡拉丘兹大学(Syracuse University)首先在这方面做出了尝试,他们实现了并行矩量法程序。其后,伊利诺伊大学香槟分校(University of Illinois at Urbana-Champaign)的W.C.Chew教授实现了并行的多层快速多极子程序Scale ME(Scaleable MLFMA Engine),求解了未知量高达10,000,000的电磁散射问题。本文正是针对上述的问题,对并行多层快速多极子方法的关键技术进行研究。首先简要介绍了积分方程方法的发展及其数值实现,然后分析了多层快速多极子算法的推导过程,并分析了目前多层快速多极子算法的一些共性的问题,并针对上面的共性问题提出解决方案。然后探讨了多层快速多极子算法的并行化思路,以及在并行框架下对多层快速多极子算法的共性问题的解决方案的实现,其后讨论了在并行框架下实现混合场积分方程。最后对并行多层快速多极子算法的存储和通信的模式进行了研究。更多还原

【Abstract】 The problem of electromagnetic scattering from large-scale target has been being the focus of public for long time because of its strong engineering application requirement. It has very important use in the Radar system design, target identify, remote sensing and measuring.On one hand, although the traditional methods to solve the electromagnetic scattering form the target by the so called high frequency methods such as PO (Physical Optics), GO(Geometry Optics), have the less memory and computational requirement, they also have the fatal defection that the accuracy of these methods are too poor to use in real applications.On the other hand, the Multi-Level Fast Mutipole Algorithm (MLFMA) which based on the integral equation method can obtain the result with great accuracy, but this method accounts in all the couplings between every sub-scatter objects, it needs much more to store all of the information, and because of the rigorous integral on the spectrum space the computational complexity is also enormous. While the real applications usually need to solve the scattering problem form very large-scale target, even the recent computer can hardly satisfy the huge memory requirement and the enormous computational requirement.In order to solve this problem, some scholars presented the idea by utilizing the parallel techniques to provide the large accessible physical memory and by reasonable decomposition the whole problem to every compute node then making all the compute nodes work together to solve the whole problem. In the 90s last century the Syracuse University first implemented the parallel technique in the Moment of Method (MOM), and then Prof. W.C.Chew in UIUC successfully implemented this techniques into MLFMA, and with their code they solved the scattering problem with 10 million unknowns.In this paper, several key techniques in parallel MLFMA will be discussed.Firstly the development and the numerical implementation of Integral Equation Method are simply introduced, then the deduction of the MLFMA and some of the general difficulties in the MLFMA are discussed, several techniques to solve these difficulties are also presented.更多还原