电流—电荷联立积分方程组及其矩量法模型的研究

发布时间：2018-05-28 16:51

本文选题：电磁散射 + 电流-电荷联立积分方程组(ECCIE)　；参考：《东南大学》2017年硕士论文

【摘要】：矩量法(MoM)是基于积分方程分析电磁问题的重要方法之一,具有较高的计算精度,已经被广泛应用于电磁散射、辐射问题。随着科技的发展以及制造工艺的不断进步,工程上对于复杂精细结构的电磁仿真、宽频带仿真等实际应用的需求越来越高。在这样的场景,由于几何特征的限制,目标的离散尺度远小于波长,传统的使用RWG函数的矩量法会出现数值不稳定、计算精度下降的低频问题。为了克服这个问题,学术界已经做了大量研究,提出了许多方法,例如,附加标量电荷未知量、标量势未知量或改善矩量法的离散过程等都能在一定程度上克服低频问题。本文是在前人关于附加电荷未知量的电流-电荷去耦合积分方程组(ECCIE)模型的基础上进行研究,包括基函数选择,离散策略的选取,矩量法矩阵方程加速求解等。本文的主要工作如下:1.引入电流-电荷联立的积分方程(ECCIE)及其矩量法模型来克服低频问题。此外,讨论了一个新的计算散射远场的方案,详细分析了它能够避免低频误差的原因。提供一些数值算例来验证目前的ECCIE的矩量法模型的正确性。2.研究了利用不同函数(RWG函数和/或BC函数)的离散与测试方案对ECCIE的矩量法模型数值精度的影响。使用BC函数和混合测试方案改善了 MFIE在低频时的数值精度。同时通过数值算例证实了这个方案用于ECCIE的从低频到中频的数值精度。3.建立组合场积分方程与电荷积分方程的联立系统(C-ECCIE)来避免在过度频段上的谐振。该方法的非谐振特性被研究。同时以数值算例证实了该方法从低频到中频的避谐振效果。4.把ACA压缩技术引入到电流-电荷联立积分方程矩量法模型中,实现了对系统矩阵的多层压缩,并加速了对应的矩阵-向量积的计算。数值算例验证了这个方案的可行性和加速效果。
[Abstract]:The method of moments (mom) is one of the most important methods for analyzing electromagnetic problems based on integral equations. It has high accuracy and has been widely used in electromagnetic scattering and radiation problems. With the development of science and technology and the continuous progress of manufacturing technology, the engineering demand for electromagnetic simulation of complex fine structures, broadband simulation and other practical applications is more and more high. In such a scenario, due to the limitation of geometric features, the discrete scale of the target is much smaller than the wavelength. The traditional method of moments using RWG function will cause numerical instability and the problem of low frequency with reduced accuracy. In order to overcome this problem, the academic circles have done a lot of research and put forward many methods, such as adding scalar charge unknowns, scalar potential unknowns or improving the discrete process of the method of moments, all of which can overcome the low frequency problem to a certain extent. In this paper, based on the previous models of current-charge decoupling integral equations with charge unknowns, including the selection of basis functions, the selection of discrete strategies, and the accelerated solution of matrix equations by the method of moments, etc. The main work of this paper is as follows: 1. The current charge coupled integral equation (ECCIEE) and its mom model are introduced to overcome the low frequency problem. In addition, a new scheme to calculate the scattering far field is discussed, and the reason why it can avoid the low frequency error is analyzed in detail. Some numerical examples are provided to verify the correctness of the current ECCIE mom model. 2. The influence of discrete and test schemes using different functions on the numerical accuracy of ECCIE's mom model is studied. BC function and mixed test scheme are used to improve the numerical accuracy of MFIE at low frequency. At the same time, the numerical accuracy from low frequency to intermediate frequency of ECCIE is proved by numerical example. The combined field integral equation and charge integral equation are set up to avoid resonance in the excessive frequency band. The non-resonant characteristics of the method are studied. At the same time, a numerical example is given to verify the effectiveness of the method from low frequency to intermediate frequency. 4. The ACA squeezing technique is introduced into the current-charge coupled integral equation of moments model. The multilayer compression of the system matrix is realized, and the calculation of the corresponding matrix vector product is accelerated. A numerical example is given to verify the feasibility and acceleration effect of this scheme.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O441

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