New Energy Analysis of ADI-FDTD for the Two Dimensional Maxwell Equations

Several new energy identities of the 2D Maxwell equations with the perfectly electric conducting boundary conditions are first proposed and proved by the energy methods. Then, the energy identities of the 2D ADI-FDTD method in the discrete
$L^2$
and
$H^1$
norms are derived. By these identities it is proved that the 2D ADI-FDTD method is unconditionally stable and energy conserved in the discrete
$L^2$
and
$H^1$
norms. Numerical experiments are carried out and confirm the analysis on stability and energy conservation.