局部特征值解的无条件稳定FDTD高效实施方案

doi:10.19665/j.issn1001-2400.2022.01.019

西安电子科技大学学报 ›› 2022, Vol. 49 ›› Issue (1): 188-193.doi: 10.19665/j.issn1001-2400.2022.01.019

局部特征值解的无条件稳定FDTD高效实施方案

赵斯晗¹(),魏兵^1,²(),何欣波^1,²()

1.西安电子科技大学物理与光电工程学院,陕西西安 710071
2.西安电子科技大学信息感知技术协同创新中心,陕西西安 710071

收稿日期:2020-12-18 出版日期:2022-02-20 发布日期:2022-04-27
通讯作者: 魏兵
作者简介:赵斯晗(1995—),女,西安电子科技大学博士研究生,E-mail: zshanzshan@163.com;|何欣波(1991—),男,西安电子科技大学博士研究生,E-mail: hxb_ak@163.com
基金资助:
国家自然科学基金(61901324);国家自然科学基金(62001345);电波环境特性及模化技术国防科技重点实验室基金(201903002);中国博士后科学基金(2019M653548);中国博士后科学基金(2019M663928XB);中央高校基本科研业务费(XJS200501);中央高校基本科研业务费(XJS200507);中央高校基本科研业务费(JB200501)

Efficient implementation of unconditionally stable FDTD with the local eigenvalue solution

ZHAO Sihan¹(),WEI Bing^1,²(),HE Xinbo^1,²()

1. School of Physics and Optoelectronic Engineering,Xidian University,Xi'an 710071,China
2. Collaborative Innovation Center of Information Sensing and Understanding,Xidian University,Xi'an 710071,China

Received:2020-12-18 Online:2022-02-20 Published:2022-04-27
Contact: Bing WEI

摘要/Abstract

摘要：

显式无条件稳定时域有限差分方法在未知量或不稳定模式个数很多时,求解全域矩阵特征值以及场值迭代的计算成本很高。针对这一问题,给出了一种基于局部特征值求解的显式无条件稳定时域有限差分方法的快速实现方案。该方案无需求解全域矩阵的特征值问题即可准确、高效地获得系统中所有的不稳定模式。在实施过程中,首先将计算域分为两部分:细网格和与之紧密相邻的粗网格为区域Ⅰ,其余粗网格为区域Ⅱ。之后原始系统矩阵可自然地被分为4个局域矩阵块,这4个小矩阵分别包含区域Ⅰ和区域Ⅱ的网格信息,以及两区域之间的耦合关系。由于不稳定模式仅存在于细网格和紧邻的粗网格中,因此只需求解区域I对应局域矩阵的特征值问题即可获得全域矩阵的不稳定模式。最后分别计算区域Ⅰ、Ⅱ的场值,两区域场值通过两个耦合矩阵块相关联,且耦合矩阵块中无不稳定模式。该方案降低了待求解矩阵维度,降低了运算复杂度,提高了计算效率。数值结果表明了该方案的准确性和高效性。

关键词: 时域有限差分, 显式, 无条件稳定, 不稳定模式, 局部特征值, 粗细网格

Abstract:

Due to the explicit and unconditionally stable finite difference time domain (US-FDTD) method has a high computational cost of solving eigenvalues of the global matrix and field iteration when there are a large number of unknown fields or unstable modes.To solve this problem,an efficient implementation scheme of US-FDTD based on the local eigenvalue solution (USL-FDTD) is given.All unstable modes in the entire system can be obtained accurately and efficiently without solving the eigenvalue problem of the global matrix by this scheme.In the implementation,first,the computational domain is divided into two parts.Region I contains all fine grids and the adjacent coarse grids.Region Ⅱ consists of the remaining coarse grids.Then the original global system matrix can be divided naturally into four local matrix blocks.These four small matrices contain the grid information on region I and region Ⅱ respectively,and the coupling relationship between region I and region Ⅱ.Since the unstable modes only exist in fine grids and the adjacent coarse grids,all unstable modes can be obtained by solving the eigenvalue problem of the local matrix corresponding to region I.Finally,the fields in region I and region Ⅱ can be calculated respectively.The fields of these two regions are associated by two coupling matrix blocks.In addition,there is no unstable mode in coupling matrix blocks.USL-FDTD not only decreases the dimension of the matrix to be solved,but also reduces the computational complexity and improves the computational efficiency.Numerical results show the accuracy and efficiency of this implementation.

Key words: finite difference time domain, explicit, unconditionally stable, unstable modes, local eigenvalue, coarse and fine grids

中图分类号:

O441

赵斯晗,魏兵,何欣波. 局部特征值解的无条件稳定FDTD高效实施方案[J]. 西安电子科技大学学报, 2022, 49(1): 188-193.

ZHAO Sihan,WEI Bing,HE Xinbo. Efficient implementation of unconditionally stable FDTD with the local eigenvalue solution[J]. Journal of Xidian University, 2022, 49(1): 188-193.

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参考文献 15

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方法	时间步长/s	求解矩阵维度	特征值计算时间或迭代时间/s	内存/MB
US-FDTD	1.67×10^-10	4 090	58.02/0.53	639.8
USL-FDTD	1.67×10^-10	526	0.12/0.15	268.1
传统FDTD	1.67×10^-11		0/20.68	261.2

局部特征值解的无条件稳定FDTD高效实施方案

Efficient implementation of unconditionally stable FDTD with the local eigenvalue solution

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