电磁散射时域快速偶极子方法的研究

发布时间：2018-07-27 15:50

【摘要】：通信、医疗、国防等许多领域都需要用到信息技术,而信号的传播主要依赖于电磁波。尤其在国防科技,谁能够准确、快速地获取目标信息,谁就能掌握主动权。计算电磁学能够获取和识别目标的信息,这在微波领域的有着重要的作用,因此计算电磁学的快速发展对国防科技技术的进步有着重要的意义。本论文以电磁场时域积分方程(TDIE)为基础,以时间步进法(MOT)为数值求解方法。论文内容分为三个部分:第一部分是本文的基础部分,研究了TDIE的基本原理、MOT算法及其等效偶极子的基本原理。首先建立求解理想导体的目标时域电场、磁场和混合场积分方程。然后介绍了时间插值基函数、空间插值基函数以及激励源的设置。然后在时间步进的时域积分方程(TDIE)基础上,采用等效偶极子(EDM)方法来简化阻抗元素形式,降低计算复杂度和节省填充时间。第二部分是本文的核心部分,在EDM的基础上,继而使用了一种新的方法来加速矩阵矢量乘——时域快速偶极子(TD-FDM),并且取得了很好的效果。第三部分研究了快速偶极子算法的并行算法。为了进一步加速电大尺寸问题求解过程,本文进行了并行方案的开发,使其可以计算一些大规模未知量的工程应用问题。最后通过一些数值算例结果,统计了TD-FDM算法计算复杂度和峰值内存,证明了其精确性和有效性。
[Abstract]:Information technology is needed in many fields, such as communication, medical treatment, national defense and so on. The transmission of signals is mainly dependent on electromagnetic waves. Especially in national defense science and technology, who can acquire the target information accurately and quickly, who can grasp the initiative. The rapid development of computational electromagnetics is of great significance to the progress of national defense technology. Based on the time domain integral equation (TDIE) and time stepping (MOT) as the numerical solution, the content of this paper is divided into three parts: the first part is the basic part of this paper, and the basic principle of TDIE, the MOT algorithm and its etc. The basic principle of the effective dipole. First, the time domain electric field, the magnetic field and the mixed field integral equation are established to solve the ideal conductor. Then the time interpolation base function, the spatial interpolation basis function and the setting of the excitation source are introduced. Then the equivalent dipole (EDM) method is used to simplify the impedance on the basis of the time domain integral equation (TDIE) step. The second part is the core part of this paper. On the basis of EDM, a new method is used to accelerate matrix vector multiplication - time domain fast dipole (TD-FDM), and has achieved good results. The third part studies the parallel algorithm of fast dipole algorithm. In order to further accelerate the problem solving process of the size of TVU, the parallel scheme is developed in this paper so that it can calculate the engineering application problems of some large-scale unknown quantities. Finally, the computational complexity and the peak memory of the TD-FDM algorithm are calculated by some numerical examples, and the accuracy and effectiveness of the algorithm are proved.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN011

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