High-Order ADI-FDTD Schemes for Maxwell's Equations with Material Interfaces in Two Dimensions

In this paper, we apply the immersed interface method (IIM) and the hierarchical derivative matching (HDM) method, respectively, to restore the accuracy of the high-order alternating direction implicit finite-difference time-domain (ADI-FDTD) scheme of the 2D Maxwell's equations with material interfaces. For the case of discontinuous permittivity epsilon and continuous permeability mu, we propose four high-order schemes. Two of them are of second order in time and fourth order in space (ADI-IIM-FDTD(2,4) scheme and ADI-HDM-FDTD(2,4) scheme). Others are of fourth order both in time and space (ADI-IIM-FDTD(4,4) scheme and ADI-HDM-FDTD(4,4) scheme). For the case of discontinuous permittivity epsilon and permeability mu, the (2,4) scheme and the (4,4) scheme are constructed as well (ADI-HDM-FDTD-X(2,4) scheme and ADI-HDM-FDTD-X(4,4) scheme). The proposed six schemes maintain the advantages of ADI-FDTD method such as unconditional stability and computational efficiency. Numerical examples are given to verify the performance of the proposed schemes.