A Comprehensive Study on the Stability and Implementation of the Conformal LCDI-FDTD Method

Compared with the conventional finite-difference time-domain (FDTD) method, the conformal FDTD (C-FDTD) method incorporates additional geometric parameters such as edge lengths and surface areas, which significantly complicates its three-dimensional (3D) stability analysis. The stability of current unconditional conformal algorithms has not been fully analyzed theoretically, with many validations limited to parameter-based numerical experiments. This paper presents a systematic investigation into the stability of the conformal leapfrog complying divergence implicit FDTD (C-LCDI-FDTD) method. By integrating von Neumann analysis with the Jury criterion, a comprehensive theoretical proof of the method’s unconditional stability in 3D is established. Then, the detailed implementation procedure is elaborated. Finally, the stability is validated through three representative numerical examples, demonstrating excellent agreement with the theoretical stability analysis and further confirming the robustness of the C-LCDI-FDTD method.