Improved Fdtd Algorithms And Their Applications For Solving Complex Electromagnetic Problems

With the rapid development of information science and technology,the focus on computational electromagnetic(CEM)research is being shifted to multi-scale problems.To solve these complex EM problems,one of the most widely used numerical methods is the finite-difference time-domain(FDTD)method.However,due to the Courant-Friedrich-Levy(CFL)stability condition which imposes an upper limit on the time-step size,it often takes long computational time in simulating electrically large structures containing fine features.Therefore,this dissertation is devoted to developing some improved FDTD algorithms for solving different EM problems.The main academic contributions of this dissertation are summarized as follows:(1)The unconditionally stable Leapfrog alternately-direction-implicit(ADI)-FDTD method is analyzed,with its stability and numerical dispersion verified in theroy.Improved reformulations with higher efficiency and no memory increasement is proposed.Different source implementations for Leapfrog ADI-FDTD including current source,hard source and incident plane wave are investigated.Moreover,the convolutional perfected layer(CPML)is incorporated into Leapfrog ADI-FDTD to handle radiation problems.(2)An improved Leapfrog ADI-FDTD method is provided for computing lossy materials.Its unconditional stability,high computational efficiency and accuracy are verified through numerical experiments.The improved formulations are applied for simulating UWB wireless communiction systems and predicting channel parameters like multi-path fading constant and path loss exponent(PLE),while good agreement is abtained in comparison with theoretic model.(3)The weakly conditional stable(WCS)-FDTD method is analyzed,with its stability and numerical dispersion verified in theroy.As its CFL stability condition is only determined by the largest space step instead of the smallest one,much less computational time is required than that of conventional FDTD in handling problems which are discretized finely in only two directions.An efficient implementation of PML,based on the stretched coordinate(SC)-PML and digital signal processing(DSP)techniques,is proposed to truncate the WCS-FDTD lattices.With its implementation,energy leakage from small cross-slots on the common wall of a rectangular waveguide coupler is predicted accurately,which agrees very well with that of other methods.(4)The hybrid implicit explicit(HIE)-FDTD method is analyzed,with its stability and numerical dispersion verified in theroy.As its CFL stability condition is only determined by two space discretization instead of the smallest one,much less computational time is required than that of conventional FDTD in handling problems which are discretized finely in only one direction.In addition,an improved one-step Leapfrog HIE-FDTD scheme is also provided,where its field updating is implemented in the same manner as that of traditional FDTD and its CFL stability condition is relaxed significantly.The CPML is implemented for Leapfrog HIE-FDTD to handle radiation problems with its stability verified semi-analytically and its high absorption efficiency proven numerically.(5)An improved HIE-FDTD method is proposed for simulating Terahertz(THz)graphene structures,where the Drude model of monolayer graphene and the associated auxiliary differential equation(ADE)technique are implemented.Numerical results are presented for the transmission coefficient of a THz plane wave normally incident on an infinite monolayer graphene sheet and S-parameters of some THz graphene-based devices like couplers,filters and absorbers which can be adjusted effectively by changing the chemical potential or layer number of graphene patch.Good agreement is abtained in comparison with those of analytical solution and simulation software HFSS.(6)An improved Leapfrog HIE-FDTD method is proposed for simulating graphene-based structures over an ultra-wide THz.The conductivity of graphene can be described by a closed-form approximate expression,which can be expanded into a rational sum of complex-conjugate pole-residue pairs using the vector-fitting techniques and then implemented into FDTD by an ADE formulation.Numerical results are presented for the transmission coefficient of a ultra-wide THz plane wave normally incident on an infinite monolayer graphene sheet and graphene-based frequency selective surfaces,which can be adjusted effectively by changing the chemical potential,operating temperature or the layer number of graphene patch.