三维柱坐标下ADI-WLP FDTD算法的CPML实现  

CPML Implementation for ADI-WLP FDTD Algorithm in Three-Dimensional Cylindrical Coordinate System

作　　者：朱大伟 陈海林[1] 杨洁 陈彬[1] ZHU Da-wei;CHEN Hai-lin;YANG Jie;CHEN Bin(National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering,Army Engineering University of PLA,Nanjing 210007,China;Communication Engineering College,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]陆军工程大学电磁环境效应与光电工程国家级重点实验室,南京210007 [2]南京工程学院通信工程学院,南京211167

出　　处：《微波学报》2019年第3期1-6,共6页Journal of Microwaves

基　　金：国家自然科学基金(51477182,61701221)

摘　　要：提出一种三维柱坐标系下交变方向隐式(ADI)的加权拉盖尔时域有限差分(WLP-FDTD)算法,并利用卷积完全匹配层(CPML)实现。通过引入微扰项可将大型稀疏矩阵的CPML形式分解为6个三对角矩阵,之后结合高斯-赛德尔思想,将6个三对角矩阵划分为两部分迭代计算,可进一步提升计算效率和收敛速度。在柱坐标模型的应用算例中,数值计算结果显示该算法的CPML吸收边界对比Mur吸收边界有较好的吸收效果。In this paper, a weighted Laguerre finite-difference time domain(WLP-FDTD) algorithm of alternating direction implicit(ADI) in three-dimensional cylindrical coordinate system is presented, and the convolution perfect match layer(CPML) is used to implement it. By introducing the perturbation term, the CPML form of large sparse matrix can be decomposed into six tri-diagonal matrices. Then, by combining the thought of Gauss-Seidel, six tri-diagonal matrices can be divided into two parts for iterative calculation, which can further improve the calculation efficiency and convergence speed. In the application example of the cylindrical coordinate model, the numerical results show that the CPML absorbing boundary of the algorithm has good absorption effect compared with the Mur absorbing boundary.

关 键 词：时域有限差分法 拉盖尔多项式 交变方向隐式 卷积完全匹配层 高斯-赛德尔 轴上特殊处理 

分 类 号：O241.3[理学—计算数学]