The Force-Gradient Symplectic Finite-Difference Time-Domain Scheme for Maxwell's Equations

Abstract

In this paper, a novel force-gradient explicit symplectic finite-difference time-domain (SFDTD) algorithm based on the T + V type Hamiltonian decomposition is derived to investigate the propagation characteristics of electromagnetic waves, in which Maxwell's equations are numerically integrated by third-order symplectic map combined with force gradient in the time direction. The numerical stability and dispersion analyses are presented. The numerical results effectively confirm that the force-gradient SFDTD (F-SFDTD) method is reliable for electromagnetic wave computation; its accuracy is superior to the non-force-gradient SFDTD method and the traditional FDTD method. The implementation of F-SFDTD method is easily applied to compute the back scattered radar cross sections (RCS) using 2-D TM mode for a perfectly conducting cylinder.