An 3-D Unconditionally Stable CDI-FDTD Method Based on the Conformal Technique for Simulating Complex Curved PEC Objects

The conventional Yee grid modeling approach employed within the unconditionally stable complying-divergence implicit finite-difference time-domain (CDI-FDTD) technique commonly encounters substantial staircasing errors when simulating objects with curved PEC structures. In response to this challenge, a novel conformal CDI-FDTD (C-CDI-FDTD) method is introduced, which integrates the conformal mesh technique with the CDI-FDTD methodology to refine the Yee mesh region involving surface structures in the model. This refinement aims to more accurately simulate curved surface features and mitigate computational errors arising from staircase approximations. Additionally, the method's numerical stability is assessed through the Von Neumann analysis, establishing its inherent unconditional stability. In contrast to the conventional conformal finite-difference time-domain (C-FDTD) approach, the proposed C-CDI-FDTD method circumvents the necessity of reducing the Courant–Friedrichs–Lewy (CFL) condition for ensuring numerical convergence. Moreover, a numerical analysis demonstrates that the incorporation of conformal grid techniques has no impact on the divergence characteristics of the CDI-FDTD technique. Finally, the accuracy and efficiency of the proposed C-CDI-FDTD method are validated through three classical numerical instances.