宽带电磁散射的频域高效算法

【作者】 马文敏；

【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， 2007， 硕士

【摘要】 现代目标识别、目标隐身技术、微波成像及微波遥感等工程领域均需要对目标的宽带电磁散射特性进行分析。为满足工程需要并突破目前国内外大多数宽带电磁散射方法所受到的目标几何结构和电尺寸限制,本文从频域角度出发,先将利于宽带计算的高阶矢量基函数(基于修正勒让德多项式)应用于多层快速多极子算法(MLFMA)中,以求解采样频点处目标的电磁散射特性,再使用改进的宽带插值方法(基于高斯点处的归一化感应电流)对已获得的采样频点处的电磁散射信息进行共享,以方便地求得其他未知频点处的电磁散射特性,从而实现对复杂电大尺寸目标宽带电磁散射特性的高效精确分析。将高阶矢量基函数应用于MLFMA之前,本文先介绍了涉及到的几个关键技术,包括目标的几何建模、高阶基的正交化和处理阻抗元素奇异性积分的Duffy变换方法,之后详细分析了高阶MLFMA中几个基本参数的选取原则及其对内存需求、计算效率、精度等性能指标的影响,并给出了高阶MLFMA的一般应用原则。典型的数值算例表明,由于高阶基函数可以极大地降低未知量的数目,在求解复杂电大尺寸目标的电磁散射特性时与低阶MLFMA相比高阶MLFMA可以大幅度地降低存储量和计算量。当将高阶MLFMA应用于宽带电磁散射分析中时,整个频带范围内所有采样频点处的计算统一采用最低频率处的几何建模剖分,随着频率的升高只需适当增加基函数的阶数,从而不但大大减少了几何建模的工作量,而且各频点处的计算也比传统方法更加节约计算量和存储量。改进后的宽带插值方法(基于高斯积分点处而非基函数定义中心处的归一化感应电流)不但可以提高精度,同时适用于低阶基函数和高阶基函数情形,而且不要求所有采样频点处的计算中具有相同的未知量数目,从而很好地与基于高阶MLFMA的采样频点处电磁散射特性高效求解方法结合起来共同完成复杂电大尺寸目标的宽带电磁散射特性分析。本文中典型的数值算例表明基于高阶MLFMA和归一化感应电流插值的宽带电磁散射频域方法具有通用、高效、精确、内存需求小、适用带宽大的优点,为复杂电大尺寸目标的宽带电磁散射分析提供了有效的工具。更多还原

【Abstract】 The wide band electromagnetic scattering is very important in many fields such as modern radar target recognizing, microwave imaging and microwave remote sensing. However most traditional wide band methods are not valid when the object is complex in structure or electrically large. In order to meet the practical engineering requirement, the multilevel fast multipole algorithm (MLFMA) and the higher order vector basis function, which is based on modified Legendre polynomials and good for the rapid frequency sweep, are first combined to calculate the electromagnetic scattering at frequency samples. Then an improved interpolation method based on the normalized induced current is used to share the above calculated information to obtain the scattering at other frequencies. In this way the wide band electromagnetic analysis from the scatter with complex structure and large electrical size is performed accurately and efficiently in the frequency domain.There are several related techniques to be presented, such as the geometrical modeling, the orthogonalization of the higher order basis functions and the skill to deal with the singular integral met in the computation of the impedance matrix, before the higher order basis functions are used in MLFMA. Then the effect of several basic parameters on the memory cost, accuracy and efficiency is discussed, and the referenced principle is given. Because the number of unknowns is greatly reduced when the higher order basis fuctions are used, much less memory and CPU time are needed when the higher order MLFMA is used to calculate the electromagnetic scattering from the object with complex structure and large electrical size, compared with the low order MLFMA.When the higher order MLFMA is used to solve the wide band electromagnetic scattering problem, only one invariant mesh system, usually got at the lowest frequency, is required for all different frequency samples at which the scattering should be calculated, and only the order of the basis function has to be adjusted with frequency change. Therefore this method requires much less geometrical modeling work and less unknowns to be solved at each frequency sample than traditional wide-band methods, so the memory cost and computational complexity are both decreased. The interpolation method for the rapid frequency sweep, which is based on the normalized induced current at the Gauss integral points located in the basis domain instead of at the center of the basis domain, is not only more accurate but also valid in the higher order method. Moreover, it does not require the same number of unknowns at different frequency samples, so it is easy to be combined with the higher order MLFMA to solve the wide band scattering problem efficiently and accurately.The typical numerical examples in this paper have shown that the frequency domain method presented here, based on the higher order MLFMA and the interpolation of the normalized induced current, is more universal, more efficient and more available for wide band scattering analysis compared with other wide band methods.更多还原