旋转对称体宽带电磁散射的快速算法研究

发布时间：2018-01-16 07:20

本文关键词：旋转对称体宽带电磁散射的快速算法研究　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：在计算电磁学领域,如何高效分析电大尺寸目标的电磁特性一直是人们研究的重要课题,而旋转对称体(BoR)由于其特殊的几何外形,也一直都是研究的热点。采用时域矩量法对旋转对称体目标分析时,可精确求解其全向的电磁散射特性。旋转对称体空间上的离散只需要在其母线上进行,一般采用三角基函数,若采用高阶基函数,离散尺寸可以选取的较大,求解计算的未知量变少,在保证计算精度的同时效率就会提高。若只需求解旋转对称体目标的前向散射特性或电磁波的传播特性时,抛物线方程方法能够以极少的计算资源完成对此类问题的求解。抛物线方程(PE)是波动方程的一种近似,与矩量法(MoM)等积分方法相比,抛物线方程方法求解得到的结果精度较低,但计算资源的消耗会很少,在分析旋转对称体时若结合其周围的场分布特性简化标准的三维抛物线方程,可大幅减少计算资源的消耗。本文研究的是旋转对称体宽带电磁散射的快速算法,分别为基于阶数步进的时域积分方程方法以及抛物线方程方法。文章首先介绍了旋转对称体结构的特殊性及基于阶数步进的时域积分方法的理论基础,考虑到旋转对称体目标在空间上剖分是对线型结构剖分,引入了一阶、二阶、三阶曲线基函数,详细推导了基于这三类基函数的旋转对称导体时域积分方程和旋转对称介质体时域积分方程,实现对旋转对称导体及介质体电磁特性的快速分析。同时,在本文方法中加入自适应交叉近似(ACA)方法,进一步降低了计算机资源的消耗。最后介绍了旋转对称导体的抛物线方程方法,抛物线方程方法的求解是利用迭代推进的方法,根据旋转对称体周围场可展开成傅里叶级数的形式,简化标准的三维抛物线方程,使需要求解的三维问题最终简化成一系列的一维问题,计算消耗的时间和内存自然大幅减少。
[Abstract]:In the field of computational electromagnetics, electromagnetic characteristics, how to analyze the electrically large target has been becoming an important research topic, and the body of revolution (BoR) because of its special geometrical shape, it has always been a hot research. The analysis of rotationally symmetric targets using time domain method of moments, the exact solution of the electromagnetic scattering characteristics of omnidirectional the discrete rotational symmetry. The body space only in the bus, generally use the trigonometric function, if the higher order function, discrete size can be selected larger, unknown quantitative computing, in ensuring the accuracy and efficiency will be improved. If only needs to solve rotational symmetry target before scattering characteristics or propagation characteristics of electromagnetic waves, parabolic equation method can be completed with very little computational resources to solve the problem. The parabolic equation (PE) is a kind of approximate wave equation And with the method of moments (MoM) and integral method for solving parabolic equations method compared to results obtained with low accuracy, but the computational resource consumption will be small in three-dimensional parabolic equation in the analysis of rotationally symmetric body if combined with the field distribution around the simplified criteria, can significantly reduce the consumption of computational resources. This paper studies the body of revolution is a fast algorithm of broadband electromagnetic scattering, respectively. The order of the step time domain integral equation method and parabolic equation method. Firstly, based on the introduction of special rotational symmetry structure and theoretical basis of order step time integration method based on considering the rotational symmetry target in space section is on the linear structure partition, introduced one order, two order, three order curve function, with rotational symmetry conductors of these three types of basis functions in time domain integral equation and rotational symmetry are deduced based on media Time domain integral equation, realize the fast analysis of electromagnetic characteristics of rotational symmetric conductor and dielectric bodies. At the same time, in this method with adaptive cross approximation (ACA) method, to further reduce the computer resource consumption. Finally introduces the parabolic equation method of rotation symmetric conductor, solving parabolic equation method is a method of using iterative push. According to the rotational symmetry field can be expanded into Fu Liye Series in the form of three-dimensional parabolic equation simplified standard, the three-dimensional problem to solve the final simplified into a series of one-dimensional problems, the calculating time and significantly reduce the memory consumption.

【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011

【相似文献】