Research On Unconditionally Stable ADI-EDTD Algorithm For Dispersive Media

The finite difference time domain(FDTD)method is an effective numerical algorithm for solving electromagnetic problems in contemporary microwave engineering.The algorithm needs to meet the time stability condition,its time step is mainly limited by the minimum mesh size in the simulation area,which makes the method has no obvious advantages in simulating dispersion media with fine structure division.In order to overcome the limitation of time stability,this paper studies the application of unconditionally stable alternating direction implicit finite difference time domain(ADI-FDTD)algorithm in dispersion media.In addition,the FDTD algorithm often uses different discrete methods when simulating different media regions,which cannot give a unified numerical discrete process.Therefore,this paper combines the recursive integration(RI)method with the FDTD algorithm to realize the unified integrated modeling of the FDTD algorithm when simulating different dispersion media.Firstly,the basic theoretical knowledge of the FDTD algorithm and the derivation process of some formulas are introduced,including: basic difference equations,numerical dispersion of the FDTD algorithm,and excitation source settings.Introduced common dispersion media models,such as Debye dispersion model,Lorentz dispersion model,and the realization of their corresponding numerical discrete process.Secondly,in order to improve the efficiency of time domain numerical algorithm simulation of dispersion media.A three dimensional unconditionally stable ADI-FDTD algorithm for efficiently and quickly simulating wave propagation in dispersion metal structures is proposed.Based on the critical point dispersion model,the ADI-FDTD algorithm is developed to study the electromagnetic characteristics of one dimensional plasma models and three dimensional metal resonator structures.The numerical results are in good agreement with the traditional FDTD algorithm simulation results,which verifies the correctness and effectiveness of the proposed numerical algorithm.Next,the unconditionally stable ADI-FDTD algorithm is applied to the simulation of biological tissue based on the quadraticcomplex rational function(QCRF)model,and the electromagnetic characteristics of biological muscle tissue in the range of 400 mHz ~ 3GHz are analyzed to further verify The unconditional stability of the ADI-FDTD algorithm is introduced.Finally,under the framework of the FDTD algorithm,the recursive integration method is applied to the simulation application of dispersion media based on N-pole Debye dispersion media.When dealing with frequency domain dispersion terms,order reduction is used to avoid complex discrete terms caused by higher order time derivatives.At the same time,the method can implement an integrated numerical discrete framework to model dispersion media and absorption boundary conditions in the simulation area.Numerical simulation results verify the correctness and effectiveness of the method.