Leapfrog ADI-FDTD Method And Its Theory Of Berenger Perfectly Matched Layer Equation

The perfect matched layer is a technique initially proposed by Berenger for solving unbounded electromagnetic problems with the finite-difference time-domain method.The time step of the alternate-direction-implicit finite-difference time-domain method is not con-strained by the courant-friedrichs-levy limit,which is unconditionally stable.Based on these two methods,we investigate Maxwell’s equations from a theoretical point of view.Firstly,for the three-dimensional electromagnetic wave,we set the PML boundary in the unbounded electromagnetic field in the free space.We formulate an equivalent PML model from the original Berenger PML model,and prove the stability of the model.The quivalent PML model is further discretized by using the leapfrog alternate-direction-implicit finite-difference time-domain method.With the help of the energy norm,a strict stability and convergence analysis is obtained.The error optimal convergence order of the scheme is(T~2+h~2).Finally,numerical experiments are used to verify the validity of the theoretical analysis.