时域有限差分中的色散媒质问题研究

发布时间：2018-05-01 03:31

本文选题：FDTD + 色散媒质　；参考：《东南大学》2015年硕士论文

【摘要】：自然界的电磁材料往往随频率呈现复杂变化,即具有电磁色散特性。本文结合数字信号处理相关技术和时域有限差分算法(FDTD)相关知识,对色散媒质的电磁散射问题进行了深入研究,并在所提出的方法上加以改进和完善,此外还对一些实际应用问题进行了具体分析。首先,本文简单介绍了FDTD理论知识和常见的三种色散媒质模型。在其基础上给出了三种较为少见的色散媒质模型,并对其频域本构关系进行了理论研究。利用频域电磁参数拟合,自然界色散媒质的电磁散射问题大都可以基于以上六种色散媒质模型进行分析。其次,对这六种色散媒质模型的电色散和磁色散特性分别进行了理论研究。结合其物理意义和频域特征,介绍了色散媒质FDTD的阶梯近似Z变换算法(Z-FDTD)。Z变换算法通过将连续的频域本构关系变换到z域,再通过逆变换得到其本构关系的离散时域差分形式,然后应用到修正过的FDTD算法当中进行迭代计算。通过常见的三种色散模型算例的数值实验结果,验证了Z变换算法的通用性、可行性。最后,介绍了色散媒质阶梯近似移位算子算法(SO-FDTD)。SO-FDTD算法通过将时间微分算子变换成离散时域移位算子构建色散媒质的频域本构关系,使得复杂的色散媒质模型能够较好地应用时域算法对其进行研究。在其基础上,为了提高计算精度,还对SO-FDTD算法进行了进一步的完善工作。本文引入了色散媒质共形技术,在目标边界上对其电磁参数进行均值等效处理以修正阶梯近似带来的目标特性失真。在可得到的相同条件下,通过多个典型算例的数值实验结果表明了共形SO-FDTD算法能够更为准确地分析色散媒质的电磁散射问题。从而,进一步将SO-FDTD算法发展和完善成为一种处理各向同性色散媒质的精确且通用方法。
[Abstract]:Electromagnetic materials in nature often show complex variation with frequency, that is, electromagnetic dispersion. In this paper, the problem of electromagnetic scattering in dispersive media is deeply studied by combining the correlation technology of digital signal processing and the FDTD algorithm of finite-difference time-domain (FDTD), and the proposed method is improved and improved. In addition, some practical application problems are analyzed in detail. Firstly, FDTD theory and three kinds of dispersive media models are briefly introduced. On the basis of these models, three rare dispersive media models are presented, and their constitutive relations in frequency domain are studied theoretically. By using frequency-domain electromagnetic parameters fitting, the electromagnetic scattering problems of dispersive media in nature can be mostly analyzed based on the above six dispersion media models. Secondly, the electrodispersion and magnetic dispersion characteristics of the six kinds of dispersive media models are studied theoretically. Combined with its physical meaning and frequency domain characteristics, the step approximation Z transform algorithm of dispersive medium FDTD is introduced. By transforming the continuous constitutive relation in frequency domain to z domain, the discrete difference form of constitutive relation in time domain is obtained by inverse transformation. Then it is applied to the modified FDTD algorithm for iterative computation. The results of numerical experiments of three kinds of dispersion models show that the Z transform algorithm is universal and feasible. Finally, a step shift operator algorithm for dispersive media is introduced. The time differential operator is transformed into a discrete time-domain shift operator to construct the frequency-domain constitutive relation of dispersive media. The complex dispersive media model can be well studied by time domain algorithm. On this basis, in order to improve the accuracy of the calculation, the SO-FDTD algorithm is further improved. In this paper, the conformal technique of dispersive media is introduced to deal with the mean equivalent of the electromagnetic parameters at the target boundary to correct the characteristic distortion of the target caused by the step approximation. Under the same conditions, the numerical results of several typical examples show that the conformal SO-FDTD algorithm can more accurately analyze the electromagnetic scattering problem of dispersive media. Thus, the SO-FDTD algorithm is further developed and perfected as an accurate and general method for dealing with isotropic dispersive media.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN011

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