Author(s)

Rengang Shi^1,2, Haitian Yang³

¹Department of Applied Mathematics, Dalian University of Technology, Dalian, China.
²College of Science, China University of Petroleum, Qingdao, China.
³Department of Engineering Mechanics, Dalian University of Technology, Dalian, China.

In this paper, a new kind of energy identities for the Maxwell equations with periodic boundary conditions is proposed and then proved rigorously by the energy methods. By these identities, several modified energy identities of the ADI-FDTD scheme for the two dimensional (2D) Maxwell equations with the periodic boundary conditions are derived. Also by these identities it is proved that 2D-ADI-FDTD is approximately energy conserved and unconditionally stable in the discrete L² and H¹ norms. Experiments are provided and the numerical results confirm the theoretical analysis on stability and energy conservation.

Stability, Energy Conservation, ADI-FDTD, Maxwell Equations

Shi, R. and Yang, H. (2015) Energy Identities of ADI-FDTD Method with Periodic Structure. Applied Mathematics, 6, 265-273. doi: 10.4236/am.2015.62025.