| The finite-difference time-domain(FDTD)method has been widely used in electromagnetic simulations because of its simplicity,versatility,ease of control,and high computational efficiency.However,its time step size is limited by Courant-Friedrich-Levy(CFL)stability condition.The Newmark-Beta algorithm was used to discrete the time-domain governing equations in structural dynamics firstly.Then,it was applied to the time-domain finite element method and became the mainstream method in discrete finite element equations due to its unconditional stability.In this dissertation,based on the traditional FDTD method and Newmark-Beta algorithm,a new unconditionally stable time-domain finite-difference method,Newmark-Beta-FDTD method,is proposed。In this method,the spatial and temporal derivatives in Maxwell’s equations are discretized by the central difference technique and Newmark-Beta algorithm,respectively,resulting in an implicit iterative equation.The time step size of the new method is not limited by the CFL stability condition any more,so it has great advantages in computational efficiency when an electromagnetic problem with the fine or multi-scale structure is simulated.In this dissertation,the numerical theory of Newmark-Beta-FDTD method and its application in practical simulations are mainly studied,including the following aspects:1.The two-dimensional formula systems of the Newmark-Beta-FDTD method based on wave equation and Maxwell’s equations are derived in detail.The formula of the Newmark-Beta-FDTD method with three-dimensional Maxwell’s equations is derived,and the stability of the Newmark-Beta-FDTD method is proved.At the same time,the numerical dispersion of the three-dimensional Newmark-Beta-FDTD method is analyzed.2.The key techniques of Newmark-Beta-FDTD method are studied.The Mur’s and perfectly matched layer(PML)absorbing boundary conditions matching for the Newmark-Beta-FDTD method are derived,so that the Newmark-Beta-FDTD method can be used in open space.At the same time,the reverse Cuthill-Mckee(RCM),a matrix bandwidth compression technology,is introduced into the solution of the Newmark-Beta-FDTD matrix equation,which greatly improves the efficiency of the lower-upper decomposition of the coefficient matrix.The domain decomposition technique is introduced into the Newmark-Beta-FDTD method.The entire computational domain is decomposed into several subdomains,and thus the large sparse matrix equation produced by the Newmark-Beta-FDTD method can be divided into some independent small ones,which further improve the computational efficiency of the proposed method,and reduce the computational cost.The subgridding technique is introduced into the hybrid method combined with Newmark-Beta-FDTD and FDTD.3.The auxiliary differential equation(ADE)technique,which represents the characteristics of dispersive media,is introduced into the Newmark-Beta-FDTD method,and the ADE-Newmark-Beta-FDTD method suitable for simulating the dispersive media is obtained.At the same time,the periodic boundary conditions of Newmark-Beta-FDTD method are studied,which extends the application area of the Newmark-Beta-FDTD method.4.The method proposed in this dissertation is employed to simulate the time-reversal system.The super-resolution focusing of electromagnetic waves in twoand three-dimensional multipath space are achieved by loading some sub-wavelength scatterers and a fine wire array near the source antenna.By comparing the calculation results and computational resources of Newmark-Beta-FDTD with traditional FDTD,the accuracy and efficiency of the proposed method are proved.5.The proposed method is applied to an anisotropic dispersion medium.Through the analysis of properties in metamaterials,the relationship between parameters and spatial positions of the metamaterial is studied in detail.The FDTD method and Newmark-Beta-FDTD method with auxiliary difference equations are used to simulate the invisible metamaterials.The phenomenon of ―invisible‖ is achieved.Comparing the results between FDTD and Newmark-Beta-FDTD,the superiority of the proposed method is validated. |
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