The Unconditionally Stable CNAD-PML Algorithm For Truncating Dispersive Media

Due to the exsitance of Courant-Friedrichs-Lewy(CFL)condition,the space size of the mesh and the time step is severely limited in the conventional Finite-Difference Time-Domain(FDTD)algorithm.If they surpass the CFL limit,the conventional FDTD algorithm is no longer stable,thus the conventional FDTD algorithm is a conditionally stable algorithm.With the development of information transmission technology,the integration of components become higher than ever before.Therefore,fine structures should be simulated in the simulation during design.When analyzing complex fine structures,large amount of FDTD time steps are formed resulting in the unacceptable calculation time.In order to alleviate such problem,unconditionally stable algorithms are proposed.Among several unconditionally stable algorithms,the 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.However,large sparse matrices should be calculated in the origin CN-FDTD algorithm resulting in higher occupation of computational source.In order to solve such problem,the Approximate-Decoupling(AD)is proposed by Sun et al to transform the complex sparse matrix into the tri-diagonal matrices,and then to acquire the value of electromagnetic field components by the Thomas algorithm.In order to simulate the infinite computational domain in finie space,an absorbing boundary(ABC)must be employed to truncate the mesh.The perfect matched layer(PML),proposed in 1994,is regarded as one of the best ABCs.Among several ABCs,the complex frequency shifted perfectly matched layer(CFS-PML)is one of the most powerful implementations.However,the low-frequency propagation wave cannot be absorbed by using the one order CFS-PML,the higher order PML is employed to alleviate such problem.The magnetized plasma plays an important part in radio frequency industry,satellite network and so on.With its unique anisotropic property,magnetized plasma is a reliable medium for frequency-shifting and so on.Research on magnetic plasma by using the FDTD algorithm has become a frontier science in electromagnetism.The main content of this paper is to propose an auxiliary differential equation method(ADE)algorithm to simulate wave transmission in the magnetized plasma,CNAD-PML to truncate the magnetized plasma and higher order CNAD-PML implementation for truncating vacuum,lossy,Debye,Drude,left-handed materials and magnetized plasma.These media models can simulate most dispersive media.The propagation methods of electromagnetic waves in the isotropic dispersive media and the anisotropic dispersive media are mainly the piecewise linear recursive convolution method(PLRC)and ADE,respectively.The implementation methods of the PML mainly are the ADE method and the bilinear transform method(BT).The specific arrangements are as follows:1.An ADE method to simulate wave transform in magnetized plasma.2.The CNAD-PML algorithm to truncate the magnetized plasma,The ADE method is used to analyze the propagation of fields in the magnetized plasma and the truncation of the PML is realized by the BT method,donated as BT-CNAD-SC-PML and BT-CNAD-CFS-PML for short.3.The higher order CFS-PML based on the CNAD algorithm to truncate the dispersive media.The PLRC and ADE method are used to analyze the propagation of fields in the media and the truncation of the CFS-PML is realized by the ADE and the BTmethod,donated as 2nd-CNAD-CFS-PML.The proposed CNAD-PML algorithms are used to truncate dispersive media and the corresponding numerical examples are given to verify them.The absorption effect of the higher order PML algorithms based on CNAD is compared to that of the CFS-PML algorithms based on the conventional FDTD and the one order CNAD-PML under the same conditions separately.Numerical examples show that the proposed algorithm are effective and these algorithms have the advantages of unconditional stability and high precision which can greatly save simulation time and improve calculation efficiency by expanding the time step.