【作者】 潘灿林；

【导师】 薄亚明； 高美凤；

【作者基本信息】 江南大学 ， 检测技术与自动化装置， 2007， 硕士

【摘要】 积分方程法是求解电磁散射问题的重要方法之一,积分方程的矩量法的系数矩阵是一个满矩阵,求解该线性方程组是一个耗时的过程,通常采用迭代求解。基于积分方程的快速算法主要通过对系数矩阵的处理降低计算量和存储量。相对于数值解法,高频近似法在求解电磁散射问题,往往更有效率,但精度和对复杂结构适用性受限。研究将高频近似有机融合于数值求解方法中的数值近似法,将能在解决问题的效率与适用性方面取得更好的折衷。本文研究基于高频照射照明区和阴影区概念、电磁场积分公式与数值迭代技术的混合算法。利用电磁场表面积分公式、高频近似和数值近似,提出了一种新的迭代方法,称为加窗测试迭代法。首先,加窗测试迭代法应用于求解导体柱电磁散射问题:以表面感应电流为未知量建立积分方程求解散射场,在散射体表面构造单点测试方程,由电磁场边界条件与场关系式建立迭代式。依据高频近似概念在阴影区用实窗函数压缩迭代中产生的误差电流,窗函数应可根据散射体尺寸变化调整下降速度,故可利用凯塞窗的可调参数。文中讨论了窗函数参数的选取,并提出了改进的汉宁窗。区分不同的入射波情况,分别分析了柱体对TM和TE入射波的散射。在新方法中,迭代初始值选用物理光学电流,迭代过程中采用快速多极子法可加速矩阵向量乘积,减少计算开销。数值实验表明该方法快速、有效,仅需几次迭代就可收敛至足够精度,且迭代次数与散射体尺寸无关,适合于求解电大尺寸物体的电磁散射问题。其次,加窗测试迭代法推广到均匀介质柱的电磁散射中。根据介质柱性质,提出了单测试方程和双测试方程两种情形下的加窗测试迭代法,并给出了单测试方程情形下的结果。研究结果表明,本文提出的混合技术,有效融合了数值法和高频近似法的混合法,具有满意的精度、较好的适应性和较快的计算速度。更多还原

【Abstract】 Integral equation method is one of important methods for solving electromagnetic scattering problems. Because the coefficient matrix of moment method (MM) is a dense matrix and solving the linear system is time-consuming, iterative methods are generally used for the solution. Fast algorithms based on integral equations are concentrating on dealing with the coefficient matrix to reduce the time consuming and memory space. Comparing with the numerical methods, high frequency approximation techniques are much more efficient in solving electromagnetic scattering problems, but it is limited in lower precision and applicability for scatterers with complex structures. Hybrid methods combined numerical methods with high frequency approximation would be better tradeoff between efficiency and applicability.In this thesis, a hybrid technique using electromagnetic integral formulae and numerical iterative technique is investigated based on the regions of illumination and shadow in high frequency approximation. A novel iterative method is presented by combining numerical technique, high frequency approximation and surface integral formulae of the fields, which is called windowed iterative technique.Windowed iterative technique is firstly applied to solve electromagnetic scattering problems of conducting cylinder. A single point measuring equation of a field is determined near the scatterer surface, and the iterative formula is established by use of the boundary conditions and field relationships. A window function is introduced to compress the error of current distribution in the shadow region. The descendent rate should be adjusted according to the scatterer sizes, so Kaiser window function is employed for its adjustable parameter. Parameter determination is discussed. Furthermore, a modified Hanning window is proposed. The scattering from cylinders under the TM and TE incidences are analyzed respectively. In the new technique, the solution is initialized with the physical optical current, and then is modified with the fast multipole method (FMM) to accelerate the matrix-vector multiplication and reduce computational costs. The numerical results demonstrate the efficiency and effectiveness. Sufficient accuracy can be reached after only several iterations which is independent of the sizes of the scatterers. It is can be employed to solve electromagnetic scattering problems of electrically large bodies.Secondly, windowed iterative technique is extended to solve the scattering from homogeneous dielectric cylinders. Both single and double measuring equations are proposed. The results with the former are given.It is concluded from the results that numerical methods and high frequency approximation can be syncretized in the hybrid technique proposed which possesses satisfactory precision, good applicability and less computational operations.更多还原