A numerical study of the symplectic FDTD(p,q) method combined with matrix exponential technique for anisotropic magnetized plasma

A novel algorithm has been developed to simulate the electromagnetic properties of anisotropic magnetized plasma media, integrating the matrix exponential (ME) approach with the symplectic finite-difference time-domain (ME-SFDTD^(p,q)) method. The SFDTD^(p,q) method achieves p-th order accuracy in the temporal domain and q-th order accuracy in the spatial domain, providing a foundational numerical discretization of Maxwell's equations and the current density equation. Subsequently, the ME method is employed to accurately solve the matrix exponential coefficient terms that arise from the multi-stage symplectic integration of the governing equations. This leads to the successful establishment of a unified numerical framework for the ME-SFDTD^(p,q) method, capable of computing the field components in anisotropic magnetized plasma regions. In parallel, an efficient sub-grid technique is introduced to manage the air-plasma interface when employing a high-order spatial difference approximation. Following this, a thorough analysis of the numerical characteristics of the proposed method, including dispersion, stability, and computational complexity, is conducted. Additionally, two numerical examples are utilized to examine the computational characteristics of the ME-SFDTD^(p,q) method under different differential strategies. Finally, a comprehensive assessment of computational accuracy, efficiency, and memory usage observes that the ME-SFDTD^(4,4) method effectively reconciles the trade-off between these factors, establishing itself as a viable numerical solver for the accurate simulation of anisotropic magnetized plasmas.