有耗介质中时域精细积分方法的数值色散分析  

Numerical dispersion of precise integration time domain method in lossy media

作　　者：孙刚[1] 马西奎[1] 白仲明[1] Sun, Gang[1]; Ma, Xi-Kui[1]; Bai, Zhong-Ming[1]

机构地区：[1]西安交通大学,电气工程学院,电力设备电气绝缘国家重点实验室,陕西西安710049

出　　处：《电波科学学报》2012年第2期209-215,共7页Chinese Journal of Radio Science

基　　金：国家自然科学基金资助项目(No.50877055)

摘　　要：分析了时间步长、空间步长、电导率和电磁波传播方向对时域精细积分(PITD)方法的数值损耗和数值色散的影响。结果表明:PITD的数值损耗大于电磁波的真实损耗,其数值波速可以大于电磁波的真实波速。PITD的数值损耗和数值色散都基本上不受时间步长的影响。随着空间步长的减小,PITD的数值损耗和数值色散的误差都逐步减小。当电导率较小时,PITD的数值损耗和数值色散的误差比时域有限差分(FDTD)方法的大。但当电导率较大时,PITD的数值波速却比FDTD的数值波速更加接近于电磁波的真实波速。PITD的数值损耗和数值色散的各向异性在三维情况下的值要大于其在二维情况下的值。数值算例表明:对良导体而言,PITD比FDTD拥有更高的计算精度和更快的计算速度。In this paper, both numerical loss and numerical dtsperslon m precxse in- tegration time domain （PITD） method are investigated. It is shown that numerical loss in PITD method is always larger than the physical value, and numerical phase velocity in PITD method can be larger than the physical value. Both numerical loss and numerical dispersion in PITD method can be made nearly independent of time step size. The smaller spatial step size always gives smaller numerical loss error and smaller numerical dispersion error in PITD method. With smaller electric conduc- tivity, both numerical loss error and numerical dispersion error in PITD method are larger than those in finite difference time domain （FDTD） method. With larger electric conductivity, numerical phase velocity in PITD method is closer to the physical phase velocity as compared with FDTD method. The anisotropies of PITD method in 3D case are usually larger than those in 2D case. The numerical results show that for good conductors, PITD method gives better accuracy and is more effi cient in execution time than FDTD method.

关 键 词：有耗介质 时域精细积分方法 数值损耗 数值色散 

分 类 号：TM15[电气工程—电工理论与新技术]