A Stable Subgridding Technique Based on ADE FDTD for Problems With Drude Media

This paper proposes a novel subgridding technique based on the auxiliary differential equation finite-difference time-domain (ADE FDTD) method for accurate modeling and simulation of geometric structures with dispersive media. An enhanced ADE-FDTD formulation is developed, leading to the construction of a novel dissipative system characterized by an energy matrix. It is rigorously demonstrated that the derived storage equations satisfy the mathematical form of the Poynting theorem for dispersive materials. In particular, a generalized Courant-Friedrichs-Lewy (CFL) stability condition is analytically established for the Drude model, under which the dissipative property of the ADE-FDTD system is proven, ensuring long-term numerical stability. Numerical experiments confirm the stability and flexibility of the subgridding scheme, supporting arbitrary grid refinement with minimal boundary reflection. Simulations of the NASA standard almond model further demonstrate significant accuracy and efficiency improvements over conventional methods, validating the effectiveness of the proposed approach for complex electromagnetic problems in dispersive media.