时域积分方程法分析导体的瞬态散射和辐射问题

【作者】 姜汝丹；

【导师】 陈如山；

【作者基本信息】 南京理工大学 ， 信号与信息处理， 2006， 硕士

【摘要】 相对于频域方法而言，时域积分方程法有这许多优势，因此，它是计算电磁学数值方法中一个重要的方法。本文全面系统地分析讨论了时域积分方程法。 本文中，基于电场方程形式的时域表面积分方程用来分析任意形状理想导体结构的瞬态散射和辐射问题。一种高斯平面波，或者时变的高斯电压源，被作为入射场或是激励源，用来分析它们的冲击响应。首先，对于时域电场积分方程，通过时间步进法(MOT，marching-on-in-time)，即空间变量部分用矩量法(MoM)离散，时间变量部分则采用差分法，求解任意形状导体结构的瞬态散射问题，其中，显式解法和隐式解法分别都被采用进行计算分析。但是，为了避免时间后期的振荡发散现象，时间步进法的时间步长的选取要受到Courant稳定条件的限制。然后，本文分析了使用基于Laguerre多项式的阶数步进法(MOO，marching-on-in-order)，它在求解时域电场积分方程时，可以将时间变量从中分离出来。这样，这种方法可以克服时间步进法的晚时不稳定的缺点，用于分析任意形状导体结构的瞬态散射问题，可以得到精确稳定的结果。此外，本文还分析了对原算法的改进，引入中心有限差分式的方案。考虑到阶数步进法的无条件稳定的特性，时域电场积分方程的阶数步进解法还在本文中用于分析一些导体天线的瞬态辐射问题。 本文推导分析了详细的算法过程，计算分析了一些典型的导体结构并且算法之间还做了比较分析。更多还原

【Abstract】 The time domain integral equation (TDIE) method is one of the important methods in electromagnetic numerical simulations for several advantages over conventional method in frequency domain. In this thesis, the TDIE methodology has been studied and disused systematically.A time domain surface integral equation based on the electric field formulation is utilized to calculation the transient scattering and radiation form arbitrary conducting structures in the thesis. The Gaussian plane wave or time-dependent Gaussian source voltage is used as an incident field or impressed generator to calculate impulse response. Firstly, the solution of the time domain electric flied integral equation (TD-EFIE) is based on the method of moments (MoM) and using the marching-on-in-time (MOT) technique, in which both explicit solution scheme and implicit solution scheme are used, to calculate the scattering form arbitrary shaped conducting structure. However, the time step in MOT is limited by the Courant condition to avoid the late-time oscillation. Secondly, by the marching-on-in-order (MOO) algorithm with Laguerre polynomials, time domain electric field integral equation can be solved without the time variables. Consequently this method, which can overcome the late-time instabilities in the MOT algorithm, is proposed to analysis the transient scattering from arbitrary shaped conducting structure to obtain the accurate and stable results. In addition, an improvement for the MOO methodology, using the central finite difference, is also presented in this thesis. Furthermore, considering the unconditional stable ability of the MOO method, TD-EFIE with MOO scheme is also used to calculate the transient radiation of some conducting antennas.Detailed mathematical steps are included, and several representative numerical results are presented and compared in the thesis.更多还原