Numerical dispersion analysis of symplectic and ADI schemes

In this paper, Maxwell´s equations are taken as a Hamiltonian system and then written as Hamiltonian canonical equations by using the functional variation method. The symplectic and ADI schemes, which can be extracted by applying two types of approximation to the time evolution operator, are explicit and implicit scheme in computational electromagnetic simulation, respectively. Since Finite-difference time-domain (FDTD) encounter low accuracy and high dispersion, the more accurate simulation methods can be derived by evaluating the curl operator in the spatial direction with kinds of high order approaches including high order staggered difference, compact finite difference and scaling function approximations. The numerical dispersion of the symplectic and ADI schemes combining with the three high order spatial difference approximations have been analyzed. It has been shown that symplectic scheme combining with compact finite difference and ADI scheme combining with scaling function performance better than other methods. Both schemes can be usefully employed for simulating and solving the large scale electromagnetic problems.