Development of split-step FDTD method with higher-order spatial accuracy
A split-step FDTD method with higher-order spatial accuracy is presented, which is proved to be unconditionally stable. From the dispersion analysis, it is justified that the method achieves improved accuracy compared with lower-order cases and its dispersion error is comparable with the higher-order ADI-FDTD method. Introduction: A split-step FDTD (SS-FDTD) method has been proposed to achieve arbitrary orders of accuracy in both space and time  . With the time increment sequences presented
... equences presented in , the method is anticipated to attain higher-order accuracy in time. To provide an approach for higher-order accuracy in space, an SS-FDTD method featuring second-order temporal accuracy and fourth-order spatial accuracy (denoted as SS-FDTD(2,4) here) is developed in this Letter. It will be seen that this method is unconditionally stable and achieves a lower dispersion error than SS-FDTD(2,2), which is the SS-FDTD based on the Crank-Nicolson approximation with second-order accuracy in both time and space  . Furthermore, the dispersion error of SS-FDTD(2,4) is also compared with that of the ADI-FDTD method with second-order accuracy in both time and space  (denoted as ADI-FDTD(2,2)), and the higher-order ADI-FDTD method with second-order accuracy in time and fourth-order accuracy in space  (denoted as ADI-FDTD(2,4)).