【作者】 刘磊承；

【导师】 吴先良； 陈明生；

【作者基本信息】 安徽大学 ， 电磁场与微波技术， 2011， 硕士

【摘要】 由于积分方程有着自动满足辐射边界条件,并且只需要在目标表面进行离散等优点,因而受到了广泛地关注。随着计算机的发展,其研究范围和应用领域也随之不断扩大。成为分析电磁场问题的一个重要手段。本文首先介绍了矩量法(MOM)的基本原理和频域积分方程的基本情况,推导了一维情况下的海伦方程,接着分析了二维情况下的电场、磁场以及组合场积分方程,并对三种积分方程的计算效果进行了比较。然后简单地介绍了矩量法结合离散傅里叶逆变换求解瞬态响应的问题。其次,介绍了时域积分方程基本情况,通过对一维细直导线的分析介绍了时间步进(marching on in time)算法的基本求解原理,接着,我们着重介绍了二维无限长导体情况下的时域电场、磁场以及组合场积分方程,分别分析了TM波和TE波入射下的三种积分方程的显式与隐式算法,并将结果进行了比较。另外,本文还将三种积分方程通过数值算例进行了比较。针对MOT(marching on in time)算法在求解时域积分方程中的后时不稳定性,我们通过对均值方法的进一步的研究,提出了一种改善方案,在一定程度上改善、延缓了后时振荡的发生。然后,介绍了二维无限长介质体的计算,我们采用PMCHW方程来计算介质体,推导了两种形式的用于求解二维介质体的PMCHW方程。最后,因为分析不同时间基函数在MOT算法中的计算效果也是MOT算法中研究的一个方面,所以,我们探讨了两个时间基函数对MOT算法稳定性的影响与时间基函数自身频谱成分之间的关系。接着,我们把二阶子域时间基函数加入到PMCHW方程的数值求解之中,其数值结果验证了其可行性。更多还原

【Abstract】 The integral equation attracted extensive attention since it can satisfy the radiation boundary conditions automatically and only the target surface is required to be discretized. With the development of computer, the field of research and application of integral equation is expanded. And the integral equation method has being an important tool to analysis the electromagnetic problems.Firstly, we introduce the theory of moment of methods (MOM) to study the basis functions of frequency domain integral equation. And then the solution for Hallen’s equation, and the electrical field integral equation (EFIE), magnetic field integral equation (MFIE) and the combined field equation (CFIE) for two-dimensional are deduced. The inverse discrete Fourier transform in conjugation with MOM for analysis the transient scattering problems is also introduced.Secondly, time domain integral equation (TDIE) method based on marching on in time (MOT) is introduced to analysis the thin straight wire. And the explicit and implicit scheme of the TD-EFIE、TD-MFIE and TD-CFIE is deduced, which is used to scattering analysis of two-dimensional objects illuminated by a Gaussian plane wave pulse. Both the TM and TE mode are discussed. For the later-time oscillation problems, an improved solution scheme based on further study of averaging techniques is proposed.Thirdly, for the transient field analysis of dielectric objects, PMCHW equations of two forms are deduced for the calculation of two-dimensional dielectric objects.Finally, considering analyzing the effect for different kinds of the temporal basis functions is also an important aspect of MOT in time scheme optimization, the relationship between the frequency distributions of temporal basis with the stability of MOT is discussed for two kinds of temporal basis. Based on the discussion, the second order sub-domain time basis is proposed for the solution of PMCHW equation, and numerical results and analysis shows that the proposed method is practicable.更多还原