The Study On The Symplectic Compact FDTD Method

The standard finite difference time-domain method of Maxwell equation, i.e. the Yee scheme, which uses the second-order center difference scheme in both time and space, is a low-order explicit scheme, with greater dispersion and dissipation errors. For electrically large domains and late-time analysis, it would result in the waveform distortion due to the accumulation of numerical errors. It is the intrinsic limitation for Yee scheme. In this paper, a temporal symplectic integrator propagator and a spatial compact difference scheme are combined into a new method, which is fourth-order accurate in both space and time, with no dissipation error, lower dispersive error and larger stability compared with other classic high-order difference schemes. First, dispersive error of compact difference scheme is discussed; Then, we introduce the application of symplectic method into Maxwell equation, and give the construction of symplectic FDTD scheme; later, we show the behavioral analysis for the symplectic compact FDTD method. At last, Numerical examples demonstrate the superior performance in late-time analysis of the method, and the electromagnetic scatting field calculation is agreed well with the analysis result.