One‐Step Leapfrog Locally 1D Theory with Higher‐Order Enhanced Absorption for Fine‐Details Simulation

Abstract

Based on a higher‐order concept and one‐step leapfrog formulation, an unconditionally stable leapfrog locally 1D (LOD) perfectly matched layer (PML) is proposed to not only enhance the absorbing performance in terminating an unbounded finite‐difference time‐domain (FDTD) algorithm but also improve the computational efficiency compared with the LOD‐FDTD algorithm. Most precisely, the PML is implemented by the auxiliary differential equations method. By applying the proposed scheme to a 3D electromagnetics simulation, the proposal can utilize the unconditionally stable algorithm, one‐step leapfrog formulation, and higher‐order concept in terms of attenuating low‐frequency propagation waves, enhancing the performance, and improving the computational efficiency. Numerical examples including the magic‐T waveguide model, very large‐scale integration circuits, and the structure of metamaterials are investigated to further demonstrate the efficiency, performance, and unconditional stability. The results help conclude that the proposed scheme can attain better performance and efficiency when the time step far surpasses the Courant–Friedrichs–Lewy limit. Most importantly, by employing the one‐step leapfrog formulation in the LOD algorithm, the memory requirements and simulation duration can be reduced significantly, indicating the improvement of the algorithm compared with the published LOD schemes.

One-Step Crank-Nicolson Direct-Splitting Algorithm with Enhanced Absorption to Evaluate Low-Pressure Discharge for Satellite Sensors in Outer Space

“…The original higher-order formulation holds six auxiliary variables which affect the efficiency and absorption [ 32 ]. Alternative higher-order formulation with four auxiliary variables is introduced to improve the entire performance, which has been extensively employed in massive problems [ 33 , 34 , 35 , 36 ].…”