基于快速多极子方法的高效迭代方法及其工程应用

【作者】 温剑；

【导师】 聂在平；

【作者基本信息】 电子科技大学 ， 无线电物理， 2005， 硕士

【摘要】 军用目标的隐身设计、反隐身技术研究,雷达系统设计与雷达目标识别等工程技术的最新发展,迫切需要对复杂目标电磁散射特性的精确快速求解。基于矩量法的快速多极子方法(FMM)和多层快速多极子方法(MLFMA)是积分方程的高效算法,其计算精度高,满足复杂目标散射特性分析的要求。然而,面对复杂的工程问题,还必须对多层快速多极子方法作进一步改进和优化。本文在快速多极子方法的基础上,进一步采取一系列有效的算法,加速矩阵方程的迭代求解。这些方法与一般的快速多极子方法相比,结果精度没有变差,但求解速度大大提高,更适合实际工程中对复杂结构目标RCS 计算的要求。本文首先介绍快速多极子方法的基础——矩量法的关键技术,包括复杂目标的几何建模,基函数和权函数的选择等。接着详细了介绍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。然后,本文了总结使用MLFMA 程序计算目标RCS 过程中影响结果精度的关键因素,如几何剖分、电磁建模、积分方程类型的选择,等等,为工程用户提供技术规范,保证计算结果的精度。本文还完成了大量工程实例,证明了文中方法和程序的有效性和正确性。本文也指出工程应用中面临的挑战,从实际工程应用的方面对方法的改进提出了要求。在此基础上,本文围绕加速迭代求解这个目标,从两个方向展开研究。(1) 在给定精度前提下减少迭代步数,采用适合于快速多极子方法的矩阵预条件技术,改善矩阵的条件数,加快迭代收敛。(2) 减少每次迭代过程的计算时间,本文采取了一种新的角谱数的计算准则,大大减少角谱空间中积分的计算量。以上两种方法都是严格的,不会降低快速多极子方法的精度。本文所有实例的数值结果均与相应文献结果或已获验证的数值程序计算结果吻合良好,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】 With the development of the stealth and anti-stealth of the military targets, the radar system design and the radar recognition technology, the electromagnetic scattering property of the complex targets needs to be solved accurately and efficiently. The fast multipole method (FMM) and the Multilevel fast multipole algorithm (MLFMA) based on the method of moment (MOM) are the efficient algorithm for solving integral equation. For its high accuracy, it meets the analysis of the EM scattering property of the complex targets. The MLFMA must be further optimized to cope with the complex engineering. Firstly, the differential equation methods, the integral equation methods and the hybrid methods used for analysis of scattering are reviewed. As the basis of FMM, the key techniques of MOM such as geometry modeling and the choice of basis/weight functions are discussed. The FMM and the MLFMA are studied in detail. Secondly, the key points for RCS accuracy in MLFMA have been summarized. Including geometry modeling, electromagnetic modeling, the selection of integral equation, detailed technical requirement is provided to assure the accuracy. The challenges raise from the application are present, and advice for the optimization of the algorithm are list. At last, several highly efficient iterative algorithms based on MLFMA are extensively studied. Such as use preconditioned conjugate gradient (PCG) algorithm to reduce the iterative steps, use modified multipole numbers method to reduce the computation of each step. 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 engineering.更多还原