Research On Unconditionally Stable FDTD And Its High-order PML Algorithm Based On Plasm

The traditional Finite-difference time-domain(FDTD)method is limited by Courant-Friedrichs-Lewy(CFL)stability condition,so the time step cannot be too large.In order to overcome the restriction of CFL conditions,scholars have developed some unconditionally stable FDTD algorithms.Such as the Alternating Direction Implicit(ADI)FDTD,the split-step(SS)FDTD and the Crank-Nicolson Approximate Decoupling(CNAD)FDTD.In addition,in order to simulate the open space model,it is necessary to set up the Perfect Matched Layer(PML)at the boundary of the FDTD computational domain.Among many PML algorithms,Complex Frequency Shifting(CFS)PML is good to absorb outward wave,Especially,higher order CFS-PML(HOCFS-PML)is one of the hot issues in current research.The FDTD algorithm based on plasma medium is also an important research issue.It has many important applications in scientific research and industrial production.We use a FDTD algorithm based on plasma medium in this thesis,which is called Runge-Kutta Auxiliary Differential Equation(RKADE)algorithm.Based on the traditional ADE-FDTD algorithm,this algorithm not only improves the calculation accuracy,but also keeps the advantages of simple calculation of the original algorithm.In this thesis,the algorithm is combined with various unconditionally stable FDTD algorithms,and the HO-CFS-PML algorithm based on these algorithms is studied.The specific content includes the following three parts:1.The HO-CFS-PML algorithm based on RKADE-ADI algorithm is proposed in two-dimensional.Two numerical examples are used to analyze the effectiveness,absorption effect and required time of this algorithm.The results show the HORKADE-ADI-CFS-PML algorithm not only achieves unconditional stability,but also has better absorption effect than first-order CFS-PML(FO-CFS-PML).2.This thesis adopts a Strang split based SS(St-SS)algorithm,by combining the RKADE algorithm with the St-SS-FDTD algorithm,the unconditional stable HORKADE-St-SS-CFS-PML algorithm is proposed in two-dimensional.The accuracy of RKADE-St-SS algorithm is analyzed by numerical conductivity error,and it is proved that RKADE-St-SS algorithm has higher computational accuracy than RKADE-ADI.At the same time,two numerical examples are used to analyze the effectiveness and absorption performance of the proposed algorithm.It is proved that this algorithm has better absorption effect than FO-RKADE-St-SS-CFS-PML.Compared with HORKADE-ADI-CFS-PML algorithm,this algorithm has higher absorption ability and calculation accuracy,but also needs more calculation time.3.The HO-CFS-PML algorithm based on RKADE-CNAD algorithm is proposed in two-dimensional.Two numerical examples are used to prove the effectiveness of the proposed algorithm.It is proved that the proposed algorithm has better computational accuracy than FO-RKADE-CNAD-CFS-PML.At the same time,compared with HORKADE-ADI-CFS-PML and HO-RKADE-St-SS-CFS-PML,the algorithm has higher computational efficiency.