Unconditionally Stable CRANK-NICOLSONDOUGLAS-GUNNCFS-PML Algorithm For Truncating Dispersive Media

Due to the limitation of Courant-Friedrichs-Lewy(CFL)condition,Finite-Difference Time-Domain(FDTD)is not suitable for simulating some fine structure devices.Therefore,some unconditionally stable algorithms are proposed,where Crank-Nicolson FDTD(CN-FDTD)algorithm does not need to split a time step into several sub time steps,which saves memory and simplifies the steps,but it needs to compute large sparse matrices.In order to improve the computational efficiency,Sun et al.used Douglas-Gunn(DG)method to transform the complex sparse matrix into the three diagonal matrices,and then to acquire the value of electromagnetic field components by catch up method.At the same time,Perfect Matched Layer(PML),as the best absorption boundary condition,has become more and more mature through the development of more than 20 years.the complex frequency shifted perfectly matched layer(CFS-PML)is a perfect match layer with the best performance at present,which has a wide application prospect.The main content of this paper is to propose two CFS-PML algorithms based on CNDG to truncate the Debye,the Lorentz and the Drude media models.These three media models can simulate most isotropic dispersive media.The propagation methods of electromagnetic waves in the isotropic dispersive media are mainly the piecewise linear recursive convolution method(PLRC),the trapezoidal recursive convolution method(TRC)and the auxiliary differential equation method(ADE).The implementation methods of PML mainly are the ADE method and the bilinear Z transform method(BZT).The specific arrangements are as follows:1.A new unconditionally stable CFS-PML algorithm based on CNDG and BZT methods is proposed to truncate the Debye media model.The PLRC method is applied to analyze the propagation of the electric field component in the Debye media model.The algorithm does not need to split a time step into several sub-time steps,which greatly simplifies the derivation process and improves the computational efficiency.The absorption effect,the simulation time and the memory of the algorithm are compared to that of the algorithm based on the traditional FDTD.Numerical examples show that the absorption effect of the CFS-PML based on CNDG algorithm is as good as that of the CFS-PML based on the traditional FDTD algorithm.Furthermore,it can save time greatly by expanding time step,and the absorption effect is not affected at the same time.2.A new unconditionally stable CFS-PML algorithm based on CNDG and ADE methods is proposed to truncate the Lorentz and the Drude media models.The ADE method is used to analysis the Lorentz media model and the TRC method is used to analysis the Drude media model.This algorithm does not need to split a time step into several sub time steps,simplifies the derivation process and improves the computational efficiency.The absorption effect,the simulation time and the memory of the CFS-PML algorithm based on CNDG are compared to that of the CFS-PML algorithm based on traditional FDTD.Numerical examples show that the algorithm is effective,and it can save time greatly by expanding the time step and the absorption effect is not affected.