电磁传播及散射的时域抛物线方程方法分析

发布时间：2018-03-15 21:00

本文选题：时域抛物线方程方法　切入点：电波传播　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：如何快速、精确分析电大尺寸目标的电磁特性一直是电磁系统的关键问题。常用的低频数值方法有矩量法(MoM)、时域有限差分法(FDTD)和有限元法(FEM)等。采用此类方法分析电小尺寸目标的电磁散射或电波传播问题时,具有计算精度高这一明显优势。但是在分析电大尺寸目标的电磁散射或长距离的电波传播问题时,计算量较大,计算效率低。高频近似方法对计算机配置要求较低,但其计算精度也会降低。抛物线方程是波动方程的一种近似形式,它可以利用较少的计算资源获得相对较好的精确度。本文主要对时域抛物线方程方法进行了研究,主要工作可分为以下几方面的内容:首先,介绍了标量抛物线方程、矢量抛物线方程和旋转抛物线方程方法的基本原理。详细阐述了抛物线方程方法的目标建模、边界条件的添加,并研究了窄角抛物线方程和宽角抛物线方程方法。其次,详细介绍了时域抛物线方程方法。采用时域抛物线方程方法对电波传播问题展开了深入研究,分别对单刃峰、多刃峰以及不规则地形等复杂环境下的电波传播时域电磁特性进行分析。最后,在时域抛物线方程方法的基础上,提出了宽角时域抛物线方程方法。采用宽角时域抛物线方程方法可以获得散射目标更大角度范围内的瞬态电磁特性,同时推导了基于Crank-Nicolson(CN)方法、交替方向隐式(ADI)方法以及交替方向显式(AGE)方法的宽角时域抛物线方程的离散格式。最后通过数值算例验证了该方法的正确性、稳定性和高效性。
[Abstract]:How quickly, Accurate analysis of electromagnetic characteristics of electrically large size targets has always been a key problem in electromagnetic systems. The commonly used low-frequency numerical methods are the method of moment (mom), the finite-difference time-domain method (FDTD) and the finite element method (FEMM). When the target's electromagnetic scattering or wave propagation is a problem, It has the obvious advantage of high accuracy. However, in the analysis of electromagnetic scattering of electrically large size targets or the propagation of radio waves over long distances, the computational complexity is large and the calculation efficiency is low. The high frequency approximation method requires less computer configuration. The parabola equation is an approximate form of wave equation, which can obtain relatively good accuracy with less computational resources. In this paper, the method of time domain parabola equation is studied. The main work can be divided into the following aspects: firstly, the basic principles of scalar parabola equation, vector parabola equation and rotational parabola equation method are introduced. The methods of narrow angle parabola equation and wide angle parabola equation are studied. Secondly, the time domain parabola equation method is introduced in detail. The time-domain electromagnetic characteristics of radio wave propagation in complex environments, such as single-edged peak, multi-edge peak and irregular terrain, are analyzed respectively. Finally, based on the method of time domain parabola equation, A wide angle time domain parabola equation method is proposed in this paper. The transient electromagnetic characteristics in a wider range of angles can be obtained by using the wide angle time domain parabola equation method, and the Crank-Nicolsonian method is also derived. The discrete scheme of the wide angle time domain parabola equation by alternating direction implicit method and alternating direction explicit age method is presented. Finally, the correctness, stability and efficiency of the method are verified by numerical examples.
【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

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