A Unified Arbitrary-Order Symplectic FDTD(p,q) Algorithm Based on Matrix Exponential Method for Anisotropic Time-Varying Plasma and PML

• Published in: IEEE transactions on microwave theory and techniques Vol. 73; no. 8; pp. 4630 - 4646
• Main Authors: Hou, Guilin, Xie, Guoda, Chen, Yi, Song, Kaihong, Deng, Xuesong, Fang, Ming, Li, Yingsong, Huang, Zhixiang, Elsherbeni, Atef Z.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Absorption; Accuracy; Anisotropic; Anisotropic time-varying plasma; arbitrary order; complex frequency-shifted perfectly matched layer (CFS-PML); Discretization; Dispersion; Electrons; Finite difference methods; Finite difference time domain method; Iterative methods; Mathematical analysis; Mathematical models; matrix exponential (ME) method; Maxwell equations; Maxwell's equations; Numerical stability; Perfectly matched layers; Plasmas; symplectic finite-difference time domain (SFDTD); Time-domain analysis
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2025.3547000

This study introduces a novel, unified arbitrary-order matrix exponential-symplectic FDTD<inline-formula> <tex-math notation="LaTeX">^{(p, q)} </tex-math></inline-formula> (ME-SFDTD<inline-formula> <tex-math notation="LaTeX">^{(p, q)} </tex-math></inline-formula>) 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<inline-formula> <tex-math notation="LaTeX">^{(p, q)} </tex-math></inline-formula> format, optimized for field components calculations in an anisotropic time-varying plasma medium. To effectively truncate the simulation space modeled by the ME-SFDTD<inline-formula> <tex-math notation="LaTeX">^{(p, q)} </tex-math></inline-formula> 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<inline-formula> <tex-math notation="LaTeX">^{(p, q)} </tex-math></inline-formula> 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.