基于面中心立方体（FCC）网格的FDTD算法的研究

发布时间：2018-06-13 17:48

本文选题：时域有限差分方法 + FCC网格　；参考：《江苏大学》2017年硕士论文

【摘要】：自从时域有限差分(FDTD)方法提出以来,由于其具有表述简单、易于理解,在时域中能直观描述电磁特性等特点,该方法的应用范围越来越广。而且,随着计算机技术的快速发展和算法本身计算效率和计算精度的不断提高,FDTD方法已逐渐发展为一种成熟、高效的电磁计算方法。然而,传统基于Yee元胞的FDTD方法,易造成各向异性效应,从而导致计算精度的降低。本文针对这一问题,重点研究了一种新的计算网格(面中心立方体网格,FCC网格)FDTD方法;其相比于Yee元胞的FDTD方法,具有良好的各向同性效果,较宽松的稳定性条件,且计算精度较高。论文研究了基于FCC网格的FDTD(FCC-FDTD)方法,并应用该方法分别对填充有空气和等离子体的两个矩形谐振腔进行仿真计算,得出相关结论。同时,分析研究了FCC-FDTD方法的连接边界条件,并给出算例验证。首先,本文详细地介绍了FCC网格中场的空间分布,并在此基础上,重点分析推导了FCC-FDTD方法在一般介质情况下的电场、磁场分量的离散迭代式。同时,给出了此方法的稳定性条件,并与基于Yee元胞的FDTD方法的稳定性进行了比较。随后,利用了FCC-FDTD方法仿真计算了普通谐振腔的111TM模的谐振频率,并将其与基于Yee元胞的FDTD方法的计算结果进行比对,结果验证了FCC-FDTD方法的正确性和准确性。其次,又将FCC网格应用到等离子体中,推导出电场分量、磁场分量和电流密度的离散迭代关系式;并通过卷积算法和拉普拉斯变换方法离散本构方程得出电流密度的计算迭代式。同时,为了验证应用FCC网格处理等离子体方法的正确性,本文计算了一个填充非时变等离子体的谐振腔的电磁谐振特性,与模式匹配原理结果相符。结果验证了此方法的正确性,同时表明了此方法具有计算等离子体目标电磁问题的能力。最后,为了将FCC-FDTD方法应用到电磁散射问题的计算中,论文还对此方法的连接边界条件进行研究分析,并给出了连接边界处的电场、磁场分量的离散迭代式;并通过仿真计算正弦场在整个计算区域内的幅值分布图,验证FCC-FDTD方法的连接边界条件的可行性及正确性。综上所述,本文所研究的FCC-FDTD方法为以后计算复杂目标提供了一种新的可行性方法。
[Abstract]:Since the finite-difference time-domain (FDTD) method was proposed, it has been widely used because of its simple expression, easy to understand and intuitive description of electromagnetic characteristics in time domain. Moreover, with the rapid development of computer technology and the continuous improvement of computational efficiency and accuracy of the algorithm itself, FDTD method has gradually developed into a mature and efficient electromagnetic calculation method. However, the traditional FDTD method based on Yee cell is easy to cause anisotropic effect, which leads to the decrease of calculation accuracy. In order to solve this problem, this paper focuses on a new computational grid (FCC mesh FDTD method), which has better isotropic effect and looser stability condition than that of Yee cell FDTD method. And the calculation accuracy is high. The FCC-FDTD method based on FCC grid is studied in this paper, and the simulation results of two rectangular resonators filled with air and plasma are obtained by using this method. At the same time, the connection boundary conditions of FCC-FDTD method are analyzed and verified by an example. Firstly, the spatial distribution of FCC meshes is introduced in detail, and on this basis, the discrete iterations of the electric and magnetic field components of the FCC-FDTD method in general media are analyzed and deduced. At the same time, the stability conditions of the method are given and compared with the FDTD method based on Yee cell. Then, the resonance frequency of 111TM mode of the common resonator is simulated by using FCC-FDTD method, and compared with the calculation results of the FDTD method based on Yee cell. The results verify the correctness and accuracy of the FCC-FDTD method. Secondly, the FCC grid is applied to plasma, and the discrete iterative equations of electric field component, magnetic field component and current density are derived. By convolution algorithm and Laplace transform method, the iterative formula of current density is obtained by discretization of constitutive equation. At the same time, in order to verify the correctness of the FCC grid plasma treatment method, the electromagnetic resonance characteristics of a cavity filled with time-invariant plasma are calculated, which is consistent with the results of mode matching principle. The results verify the correctness of the method and show that the method has the ability to calculate the electromagnetic problems of plasma targets. Finally, in order to apply the FCC-FDTD method to the calculation of electromagnetic scattering problem, the connection boundary conditions of this method are studied and analyzed, and the discrete iterative formulas of the electric field and magnetic field components at the connecting boundary are given. The feasibility and correctness of the FCC-FDTD method are verified by simulating the amplitude distribution of the sinusoidal field in the whole calculation region. To sum up, the FCC-FDTD method studied in this paper provides a new feasible method for the computation of complex targets in the future.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN011

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