基于RKADE-SS-FDTD方法的无条件稳定高阶CFS-PML算法  

Unconditionally stable higher order CFS-PML algorithm based onRKADE-SS-FDTD method

作　　者：李建雄[1,2] 魏之栋 LI Jian-xiong;WEI Zhi-dong(School of Electronics and Information Engineering,Tiangong University,Tianjin 300387,China;Tianjin Key Labora-tory of Optoelectronic Detection Technology and Systems,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学电子与信息工程学院,天津300387 [2]天津工业大学天津市光电检测技术与系统重点实验室,天津300387

出　　处：《天津工业大学学报》2023年第2期55-60,共6页Journal of Tiangong University

基　　金：国家自然科学基金资助项目(51877151);天津市科技计划资助项目(20YDTPJC01090)。

摘　　要：为了提升完全匹配层(PML)算法的吸收效果,提出了一种用于截断非磁化等离子体的高阶复频率偏移PML(HO-CFS-PML)算法。该算法将龙格-库塔辅助微分方程(RKADE)算法和分裂步时域有限差分(SS-FDTD)算法相结合,来对非磁化等离子体进行仿真。在计算域边界处,引入了由辅助微分方程(ADE)算法实现的HO-CFS-PML用于截断开放区域中的等离子体,并通过一个数值算例进行模拟。结果表明:所提出的HO-RKADE-SS-CFS-PML算法在柯朗-弗里德里希斯-列维(CFL)数(CFLN)为8时,相比于传统CFS-PML算法,时间减少率可以达到79.2%,证明了该算法能够有效地消除柯朗-弗里德里希斯-列维(CFL)稳定性条件的约束,大大节省了计算时间;此外,HO-RKADE-SS-CFS-PML算法的最大相对反射误差可以达到-115 dB,明显小于其他算法的相对反射误差,并且随着CFLN的增大,该算法不会像RKADE-ADI-CFS-PML算法那样产生明显的误差增大现象,证明本文算法在大时间步长下拥有比其他算法更好的吸收电磁波的能力。In order to improve the absorbing performance of the perfectly matched layer(PML)algorithm,a higher order complex frequency shifted perfectly matched layer(HO-CFS-PML)algorithm for truncating unmagnetized plasma is proposed.This method combines the Runge-Kutta auxiliary differential equation(RKADE)algorithm with the split-step finite-difference time-domain(SS-FDTD)algorithm to simulate the unmagnetized plasma.At the boundary of computational domain,the HO-CFS-PML implemented by the ADE algorithm is introduced for truncating unmagnetized plasma in open region applications.Simulation is performed by a numerical example.The results show that the proposed HO-RKADE-SS-CFS-PML algorithm can achieve a time reduction of 79.2%compared to the conventional CFS-PML algorithm when the Courant-Friedrichs-Lewy number(CFLN)is 8.It is demonstrated that the algorithm can eliminate the Courant-Friedrichs-Lewy(CFL)stability constraint,which greatly saves the computation time.In addition,the biggest relative reflection error of HO-RKADE-SS-CFS-PML algorithm can reach-115 dB,which is significantly smaller than that of other algorithms,moreover,the biggest relative reflection error of this algorithm does not deteriorate significantly with the increase of CFLN like the RKADE-ADI-CFS-PML algorithm,which proves that the algorithm has better ability to absorb electromagnetic waves than other algorithms under large time steps.

关 键 词：高阶复频率偏移完全匹配层 分裂步时域有限差分法 龙格-库塔辅助微分方程 非磁化等离子体 

分 类 号：TD802[矿业工程—矿山开采] O441[理学—电磁学]