Research On Unconditionally Stable Domain Decomposition Finite-difference Time-domain Methods In Electromagnetics And Their Applications

In the area of computational electromagnetics,the finite-difference time-domain(FDTD)method is still widely researched and investigated all over the world due to its prominent advantages over other numerical methods.With the fast development of the technology,the mutiscale problems to be solved in electromagnetics and microwave techniques are becoming more and more complicated.The unconditionally stable and fast numerical methods are very suitable for solving those multiscale problems with fine structures,while the unconditionally stable FDTD methods with high performance are still waiting for further study,which includes two aspects.Firstly,in terms of the theory and method,not only the implicit unconditionally stable FDTD based on the domain decomposition technique but also the explicit unconditionally stable FDTD based on the sub-gridding scheme should be thoroughly studied to propose accurate and efficient FDTD methods.Secondly,in terms of the engineering application,the fast numerical methods with high accuracy and efficiency should be applied to the simulation of the multiscale,electrically large and compelx problems in electromagnetics and microwave techniques.This thesis aims at investigating and researching the unconditionally stable and fast FDTD methods and their applications in electromagnetics.On the one hand,both the domain decomposition based implicit unconditionally stable FDTD methods and the sub-gridding based explicit unconditionally stable FDTD methods are thoroughly and systematically studied.On the other hand,the proposed fast FDTD methods are widely employed for numerically simulating the complicated and multiscale electromagnetic problems,such as the propagating properties of the time-reversed electromagnetic waves,the extraordinary optical transmission of the periodical metallic gratings and the ground penetrating radar in dispersive soils.The main contents in this thesis are summarized as follows.In the first part,the implicit unconditionally stable FDTD based on the weighted Laguerre polynomials(WLPs)is studied.Firstly,a vertex-based domain decomposition technique is proposed for WLP-FDTD,and the domain decomposition WLP-FDTD is applied to the calculation of S parameters of a two-dimensional(2-D)electromagnetic bandgap structure.Secondly,in order to accurately simulate the electromagnetic problems in open regions,the higher-order perfectly matched layer(PML)absorbing boundary condition is introduced into the domain decomposition WLP-FDTD,and the multi-objective genetic algorithm is used to choose optimal parameters in the higher-order PML.Thirdly,the proposed domain decomposition WLP-FDTD is used for solving the propagating properties of the time-reversed electromagnetic waves,including the time-space focusing and the super-resolution focusing in the far field.In the second part,the implicit unconditionally stable Crank-Nicolson(CN)FDTD method is investigated.Firstly,the domain decomposition technique is introduced into CN-FDTD to improve the efficiency in solving the complicated multiscale structures.The theoretical analyses of the domain decomposition CN-FDTD include the numerical solution of Drude dispersive model,the implementations of unsplit-field PML absorbing boundary condition and periodic boundary condition,and the realization of the domain decomposition technique.Secondly,the domain decomposition CN-FDTD is used to simulate and analyze the extraordinary optical transmission of the periodical metallic gratings in 2-D computational domains.In the third part,the explicit unconditionally stable FDTD method implemented with the spatial filtering process is researched.The spatially-filtered FDTD extends the time step with retaining the explicit updating nature of the conventional FDTD,and thus an efficient FDTD can be realized based on the sub-gridding scheme,which largely improves the computational efficiency in solving electrically large structures.Firstly,the spatially-filtered sub-gridded FDTD method is proposed,and the basic theory of the spatial filtering process,the numerical solution of Debye model and the implementation of unsplit-field uniaxial PML(UPML)absorbing boundary condition are presented in detail.Secondly,the proposed method is employed to model and simulate the threedimensional(3-D)practical ground penetrating radar scenarios in dispersive soils.Thirdly,based on the theory of time-reversed electromagnetic waves,the electromagnetic field shaping of arbitrary patterns are realized with perfectly electric conductor(PEC)boundary condition and PML boundary condition,respectively,by using the proposed 3-D spatially-filtered sub-gridded FDTD method.In the fourth part,the hybrid FDTD method based on the sub-gridding scheme is studied and investigated.Firstly,a 2-D hybrid method with the explicit FDTD and implicit CN-FDTD is presented,and the dispersion expressed by the Debye model is incorporated into both FDTD and CN-FDTD.Secondly,in the 3-D case,the hybrid sub-gridded method with explicit FDTD and implicit domain decomposition CN-FDTD is proposed.The numerical formulations of the Debye model,the implementations of the unsplit-field UPML absorbing boundary condition and the domain decomposition technique are presented.Thirdly,the efficient hybrid sub-gridded FDTD method is applied to the 2-D and 3-D ground penetrating radar simulations on dispersive soils,respectively.