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Research Of Efficient Algorithms On Solving Time Domain Electromagnetic Differential Equations

Posted on:2019-10-06Degree:DoctorType:Dissertation
Country:ChinaCandidate:H G BaoFull Text:PDF
GTID:1360330575469835Subject:Electromagnetic field and microwave technology
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In order to adapt to a growing number of engineering applications with broadband,high speed signals and nonlinear systems,the technology of transient electromagnetic analysis has got a rapid development,and become one of the research hotspots in the field of computational electromagnetics.As an important means of transient electromagnetic analysis,time domain differential equation methods have their unique advantages on analyzing the electromagnetic problems with inhomogeneous mediums,complex systems or multi physical variables.Considering the difficulties and challenges from the analysis of practical electromagnetic problems with time domain differential equation methods,this dissertation concentrates on the development of efficient electromagnetic analysis technology based on conformal finite difference time domain(CFDTD)method and discontinuous Galerkin finite element time domain(DG-FETD)method,which are the two representative methods with broad application prospects.Firstly,in order to make the unconditional stability and high parallelism compatible,a flexible and universal domain decomposition parallel scheme is proposed for the time domain differential equation methods in this dissertation.This proposed noniterative domain decomposition method takes profit of the causality of electromagnetic waves.A buffer region is introduced to decouple the interactions between neighboring subdomains at each time step.In consequence,the data communications just occur between adjacent processors and involve the data in b uffer regions.Hence,it is suitable for parallel computing.With the Message Passing Interface(MPI)library,the proposed domain decomposition parallel implementations of the leapfrog ADI-FDTD method and CN DG-FETD method have been achieved,respectively.Secondly,in view of the challenges on the multi-scale electromagnetic analysis with traditional time domain differential equation methods,this dissertation focuses on their fast algorithms.The subgridding scheme with CFDTD method has been introduced in this dissertation.The energy transmission between coarse grids and fine grids is implemented with the Huygens principle.The ratio of the size of coarse grid and fine grid can be selected as arbitrary odd number,technically.The conformal algorithm has been introduced to improve the accuracy furtherly.A modified implicit-explicit time stepping scheme with DG-FETD method is proposed for multi-scale electromagnetic simulations.The leapfrog scheme is employed for electrically coarse regions and Crank-Nicholson scheme for electrically fine ones.In particular,just the elements adjacent with implicit regions are handled with the variant of classical leapfrog scheme.Furthermore,the noniterative domain decomposition method is introduced to decouple the original system at each time step and improve the parallel performance of the proposed scheme.Thirdly,considering the fact that there is a lack of efficient method for uncertainty analysis of electromagnetic problems in the current situation,this dissertation concentrates on the efficient uncertainty analysis technology with time domain differential equation methods.The conformal FDTD method with polynomial chaos expansion is introduced for uncertainty analysis.For the electromagnetic problems with random input variables which satisfy the random Gaussian distribution characteristics,Hermite polynomials are used to expand the random variables.Combined with the exponential time differencing Runge-Kutta method,the PCE-CFDTD method has been introduced to analyze the hypersonic targets with random electron concentrations.An efficient DG-FETD method with polynomial chaos expansion is proposed for uncertainty analysis of plasma characteristics.The DG-FETD method with recursive convolution(RC)technique is proposed to analyze the Drude model of plasma.The PCE method is used to represent the stochastic variables of the electromagnetic wave.This proposed method maintains the advantages of DGTD method which is a spatially explicit algorithm and has the merit of easy parallelization.Finally,for a practical complex electromagnetic problem,if using a single method,the computational precision and efficiency will not be the best.Therefore,the hybrid algorithms with time domain differential equation methods are investigated.A hybrid discontinuous Galerkin finite-element finite-difference time-domain method with hybrid hexahedral and tetrahedral elements is proposed for electromagnetic simulations.The discontinuous Galerkin method is employed to improve the efficiency in dealing with non-conforming meshes.This proposed hybrid method takes full advantage of the efficiency of FDTD method with the traditional Yee's grid and the flexibility of FETD method in modeling complex geometry,and it inherits the powerful ability in parallelism.
Keywords/Search Tags:Time domain differential equations, conformal FDTD method, discontinuous Galerkin FETD method, domain decomposition method, parallel computing, subgridding scheme, implicit-explicit time stepping scheme, uncertainty analysis, polynomial chaos expansion
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