Implementation Of Efficient Algorithms In Finite-Difference Time-Domain Method

With the rapid development of the electronic and information industry,the computational electromagnetics(CEM)has developed into a technology closely related to human social life such as the electromagnetic compatibility(EMC)and signal integrity analysis(SI)of very large scale integration(VLSI),the evaluation of SAR value of wireless equipments,5G antenna and communication system design,and so on.Meanwhile,the increasing innovation of science and technology and the gradual improvement in theories of various disciplines have made CEM continue to intersect with other disciplines,such as cancer cell signaling identification in biological sciences,petroleum resource survey in earth remote sensing science,laser generation in physical science,design of new artificial materials and metamaterials in materials science,etc.The emergence of these cross-fields and the demand for solving complex electromagnetic systems have brought unprecedented opportunities and challenges to the development of CEM.One of the important methods used to solve the problems mentioned above is to develop accurate and efficient numerical calculation methods.Thus,this dissertation further developed the finite-difference time-domain(FDTD)method.In particular,in view of the defects and deficiencies in the existing perfectly matched layers(PMLs),a series of novel and efficient algorithms are proposed to improve the computational efficiency of FDTD simulations.Furthermore,this dissertation promotes the development of unconditionally stable FDTD algorithms and expands the theory of Crank-Nicolson FDTD(CN-FDTD)method.The main achievements of this dissertation are listed as follows.1.Based on the stretched coordinate PML(SC-PML)fomula and a new way to introduce the PML associated variables,this dissertation proposes three efficient PML implementations in non-split field forms.To be specific,they are respectively combined with the auxiliary differential equations(ADE),bilinear Z-transform(BZT)and matched Z-transform methods.The innovation lies in that each field component in the PML regions involves only on auxiliary variable,whereas other published SC-PMLs based on the first-order differential equation require two variables.Thus,the proposals have the advantage of saving memory.On the other hand,compared with the implementatons based on the second-order differential equation,these three new algorithms have fewer floating-point operands(FLOPS).2.Based on the complex frequency shifted PML(CFS-PML)formualtion and the matrix exponential difference(MED)method,this dissertation proposes an efficient PML algorithm in non-split field forms.Since the time asynchronization existed in the convolutional PML(CPML)is avoided,this new CFS-PML algorithm can achieve a better absorption effect.Meanwhile,via applying mature matrix theory to this new implementation makes it has more concise and compact forms.3.Based on CN-FDTD scheme and the CFS-PML formulation,this dissertation proposes two new unconditionally stable PML algorithms via the factorization-splitting(FS)and directsplitting(DS)methods.The innovation lies in that the proposals are the first proposed and verified three-dimensional CN-PML algorithms.Furthermore,unlike the commonly used ADIPML,LOD-PML and SS-PML,this new algorithm does not need to split a complete iterative time step into two or more sub-time steps.Thus,so it has more concise forms and higher efficiency.4.Based on the single-field CN-FDTD(SF-CN-FDTD)scheme and DS method,this dissertation proposes a new unconditionally stable FDTD algorithm.Compared with the alternating-direction-implicit FDTD(ADI-FDTD),locally one-dimensional FDTD(LODFDTD)and split-step FDTD(SS-FDTD),this new algorithm involves only the electric field E.Thus,it has much higher computational efficiency.