共形HIE-FDTD方法的稳定性分析及改进

Stability analysis and improvement of conformal HIE-FDTD method

提出一种金属共形混合隐显式时域有限差分方法(conformal hybrid implicit explicit finite difference time do-main,CHIE-FDTD),与传统FDTD方法相比,该方法用于计算不能与网格共形的金属目标时,既能克服阶梯近似法带来的误差和引起的虚拟表面波,又能提高计算效率。但由于Dey-Mittre金属共形方法本身要求减小柯朗-弗里德里希斯列维(Courant-Friedrichs-Lewy,CFL)条件来增加稳定性,将其引入HIE-FDTD会导致时间步长的减小或使得仿真波形发散提前(降低算法的稳定性)。针对该问题开展了研究,给出了改进方法,并进行了数值验证。

In this paper, a conformal HIE （hybrid implicit explicit）-FDTD method is proposed to analyze the irregular me- tallic object whose boundary cant match the orthogonal mesh. Compared with the convention FDTD method, the proposed method can overcome the error caused by staircase and allow larger step-size. However,the conformal technology needs to reduce step-size to ensure stability, and HIE-FDTD with application of conformal technology may lose the stability expected with the HIE-FDTD schemes. In this paper, instability factor in CHIE-FDTD is analyzed, and an improved method is pro- posed, the accuracy and efficiency of the proposed method are verified by numerical simulation results.