A Stability Extensible Symplectic FDTD(4,4) Method and Its Application in Subgrid Technique for Arbitrary Grid Ratios

This communication presents a novel algorithm, namely, the 3-D stability extensible spatial-filtering symplectic finite-difference time-domain method (SF-SFDTD
$^{\mathrm {(4,4)}})$
algorithm, as an enhancement to the traditional finite-difference time-domain (FDTD
$^{\mathrm {(2,2)}})$
method. The symplectic FDTD
$^{\mathrm {(4,4)}}$
method, which exhibits higher-order numerical accuracy in both temporal and spatial domains, is utilized as the basis for this algorithm. The primary objective of this research is to overcome the limitations imposed by the Courant–Friedrich–Levy (CFL) condition. To achieve this, the study leverages the SF technique to establish an enlarged CFL condition within the proposed SF-SFDTD
$^{\mathrm {(4,4)}}$
algorithm. Additionally, a novel hybrid subgrid technique is introduced to accommodate arbitrary coarse/dense grid ratios within the simulation domain. Specifically, the standard FDTD
$^{\mathrm {(2,2)}}$
method is employed in the coarse grid region, while the proposed SF-SFDTD
$^{\mathrm {(4,4)}}$
method is applied to the dense grid region. This approach ensures that the entire simulation can employ the same time increment determined by the stability condition of the coarse grid, owing to the highly stable characteristic of the SF-SFDTD
$^{\mathrm {(4,4)}}$
method. To confirm the accuracy and advantages of the proposed SF-SFDTD
$^{\mathrm {(4,4)}}$
algorithm and its extended method of hybrid subgrid technique, some numerical examples are carried out. The results demonstrate the efficacy of the algorithm in terms of both efficiency and memory requirement.