基于空间滤波技术的高稳定度辛算法研究

发布时间：2018-07-05 03:09

本文选题：时域有限差分法 + 空间滤波　；参考：《安徽大学》2017年硕士论文

【摘要】：近年来,随着计算电磁学的蓬勃发展,计算电磁学方法不断的更新,在社会的众多领域做出了杰出的贡献,例如在现代无线电通讯、航天航空、超材料、色散媒质等领域得到了很好的应用和发展。期间,有关计算电磁学的学术项目,学术实验室,学术会议还有相应的学术论文大量的增加。同时,以计算电磁学为基础的商业软件和实际应用产品在社会的众多领域不断的涌现出来。计算电磁学可以说是取得了很高的成就。计算电磁学算法层出不穷,主要的杰出代表包括:离散麦克斯韦方程的时域有限差分法,离散矢量波动方程的有限元法,离散积分方程的矩量法。从1966年到Yee网格提出至今,经典的时域有限差分法以操作简单,便于并行,概念清晰,通用性强等优点在各个领域得到了很广泛的运用。经典的时域有限差分法最主要有一下有两大缺点:一,在网格方向上演进,所以在模拟一些不连续材质中存在一定的困难。二,由于各向异性、数值色散性、数值稳定性的影响,随着时间的积累时域有限差分法的数值误差会越来越大,导致了计算结果的失真。同时,传统的时域有限差分法必须始终满足时间和空间上的稳定性条件。为了打破传统稳定性条件的约束,实现显式的高稳定,本文采用空间滤波的方法。时域有限差分法在空间频域上对数值精度,数值色散有影响的是在低频部分,而高频部分的影响很小,可以忽略不计,所以通过在空间频域中滤除高频的部分,只保留低频部分,这样可是实现时间步的任意取值,完成显式的高稳定,极大的加快了运行速度和效率,并且不会影响到计算结果的精确度。为了解决上述问题,本文对高稳定度的辛时域有限差分法进行了系统研究。辛时域有限差分法依然必须要满足稳定性条件,时间和空间的交替差分依然受到严格的限制。本文在时间方向上,通过高阶辛积分和滤除空间高次谐波的方法,打破了传统的稳定性条件,实现显式的高稳定,同时能在长期仿真中保持麦克斯韦方程的辛结构,极大的提高了运行的效率,大大的缩减了运行时间,并且提高了计算结果的精度;在空间方向上,采用了高阶交错差分,提高了数值精度,减小数值色散;在网格剖分上,采用亚网格模型结合空间滤波的方法解决材质的不连续性问题。通过上述的算法和模型,来建立更加快速,高精度的时域解决方案。
[Abstract]:In recent years, with the vigorous development of computational electromagnetics, computational electromagnetics methods have been constantly updated, and have made outstanding contributions in many fields of society, such as modern radio communications, aerospace, metamaterials, Dispersive media and other fields have been well applied and developed. During this period, there has been a substantial increase in academic projects, laboratories and conferences on computational electromagnetism. At the same time, commercial software and practical application products based on computational electromagnetics are emerging in many fields of society. Computational electromagnetism can be said to have made great achievements. Computational electromagnetic algorithms emerge in endlessly. The main outstanding examples include the finite difference time-domain method for discrete Maxwell equation, the finite element method for discrete vector wave equation, and the moment method for discrete integral equation. From 1966 to now, the classical finite difference time-domain method has been widely used in various fields because of its advantages of simple operation, easy to parallel, clear concept and strong versatility. The classical finite-difference time-domain method has two main disadvantages: first, it evolves in the grid direction, so it is difficult to simulate some discontinuous materials. Secondly, due to the influence of anisotropy, numerical dispersion and numerical stability, the numerical error of the finite difference time-domain (FDTD) method will increase with the accumulation of time, resulting in the distortion of the calculation results. At the same time, the traditional FDTD method must always satisfy the stability conditions in time and space. In order to break the constraint of traditional stability condition and realize explicit high stability, the spatial filtering method is used in this paper. The finite-difference time-domain (FDTD) method has an effect on the numerical accuracy and dispersion in the spatial frequency domain, but the influence of the high-frequency part is too small to be ignored, so the high-frequency part is filtered out in the spatial frequency domain. Only the low frequency part is retained, which can realize the arbitrary value of the time step, complete the explicit high stability, greatly speed up the running speed and efficiency, and will not affect the accuracy of the calculation results. In order to solve the above problems, the symplectic finite-difference time-domain method with high stability is studied systematically in this paper. The symplectic finite-difference time-domain method still has to satisfy the stability condition, and the alternating difference between time and space is still strictly restricted. In this paper, by means of high order symplectic integration and filtering high order harmonics in time direction, the traditional stability condition is broken, and the explicit high stability is realized, and the symplectic structure of Maxwell equation can be maintained in the long term simulation. The efficiency of the operation is greatly improved, the running time is greatly reduced, and the accuracy of the calculation results is improved. In the spatial direction, the high order staggered difference is used to improve the numerical accuracy and reduce the numerical dispersion. The subgrid model combined with spatial filtering is used to solve the material discontinuity problem. Through the above algorithms and models, a faster and more accurate time domain solution is established.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O441

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