Survey on Symplectic Finite-Difference Time-Domain Schemes for Maxwell''s Equations

摘要

To discretize Maxwell''''s equations, a variety of high-order symplectic finite-difference time-domain $(p,q)$ schemes, which use $p$ th-order symplectic integration time stepping and $q$th-order staggered space differencing, are surveyed. First, the order conditions for the symplectic integrators are derived. Second, the comparisons of numerical stability, dispersion, and energy-conservation are provided between the high-order symplectic schemes and other high-order time approaches. Finally, these symplectic schemes are studied by using different space and time strategies. According to our survey, high-order time schemes for matching high-order space schemes are required for optimum electromagnetic simulation. Numerical experiments have been conducted on radiation of electric dipole and wideband S-parameter extraction of dielectric-filled waveguide. The results demonstrate that the high-order symplectic scheme can obtain satisfying numerical solutions under high Courant–Friedrichs–Levy number and coarse grid conditions.