A Unified Arbitrary-Order Symplectic FDTD(p,q) Algorithm Based on Matrix Exponential Method for Anisotropic Time-Varying Plasma and PML - Hou, Guilin; Xie, Guoda; Chen, Yi; Song, Kaihong; Deng, Xuesong; Fang, Ming; Li, Yingsong; Huang, Zhixiang; Elsherbeni, Atef Z. (IEEE transactions on microwave theory and techniques, 2025)
This study introduces a novel, unified arbitrary-order matrix exponential-symplectic FDTD ^{(p, q)} (ME-SFDTD ^{(p, q)} ) method tailored for simulating anisotropic time-varying plasma medium. The governing equations, comprising both current density and Maxwell's equations, are reformulated into a compact first-order differential matrix form and then discretized in the temporal domain using a multistage p-order symplectic integrator. Meanwhile, the matrix exponential (ME) coefficients arising from the symplectic discretization are efficiently computed utilizing the ME method, while spatial derivatives are approximated by a q-order central-difference scheme. These processes yield a complete numerical iteration framework specific to the ME-SFDTD ^{(p, q)} format, optimized for field components calculations in an anisotropic time-varying plasma medium. To effectively truncate the simulation space modeled by the ME-SFDTD ^{(p, q)} method, a high-performance complex frequency-shifted perfectly matched layer (CFS-PML) technique is proposed, which shares the same primary iteration formulas as the ME-SFDTD ^{(p, q)} method, exhibiting excellent absorption performance and high compatibility. In addition, a comprehensive numerical stability and dispersion analysis is conducted to confirm the feasibility of the proposed method. Finally, several numerical examples are presented to thoroughly validate the accuracy and efficiency of the approach.