Improvement Of Finite-Difference Time-Domain Method And Its Application In Multiple Physical Fields

The Finite-Difference Time-Domain(FDTD)method is a time-domain algorithm for the central differential discretization of the differential form of Maxwell's curl equation.This method can directly obtain the electromagnetic field at any time and space.After more than 50 years of continuous improvement and development,the FDTD method has become the most popular numerical algorithm in the field of computational electromagnetics,and it has been widely used in many engineering fields such as the design of microwave devices,antennas,metamaterials,the simulation of radar cross-section for the military targets,the analysis of circuit packaging,electromagnetic compatibility and signal integrity.However,the FDTD method also encounters some problems in the processing of practical problems that need to be improved and developed:the selection of the time and space discrete step size of the FDTD method is limited by stability and convergence,especially in the case of electrically large objects and the scatters which with a fine structural feature.The computational efficiency will be greatly reduced in this situations.Unconditionally and weakly stable FDTD methods have been proposed to solve the above problems,but the accuracy of this method is not satisfactory;The FDTD method can not only accurately solve the electromagnetic field in Maxwell's equation,but also show significant potential to deal with multiphysics problems by the combination of Maxwell's equation with other physical equations,but there are relatively few works was reported in this field.Based on the aforementioned problems existing in the FDTD method,the following innovative work has been carried out in this dissertation:1.Considering the material with statistical stochastic characteristics of dielectric parameters such as human tissues and organs,a stochastic hybrid explicit implicit time-domain finite difference method(S-HIE-FDTD)is proposed to apply the mathematical statistics theory to characterize the uncertainty of dielectric.The proposed random method can obtain the mean and variance of the broadband electromagnetic field by a single calculation.In the other hand,the time step of the proposed method is no longer limited by the size of the finest grid unit,so that it has higher computational efficiency when processing structure with high contrast spatial resolution.2.The unconditional and weakly stable implicit FDTD algorithm is proposed to improve the computational efficiency but the computational accuracy is sacrificed at the same time.Therefore,it is urgent and necessary to develop new algorithms which take both the computational efficiency and efficiency into account.In this dissertation,artificial anisotropy WCS-FDTD method and HIE-FDTD method are proposed based on weakly conditionally stable(WCS)and hybrid implicit-explicit(HIE)FDTD methods.The artificial anisotropy parameters are introduced into the implicit algorithm to optimize the numerical dispersion error and improve the calculation accuracy.At the same time,the computational complexity and the consumption of physical memory are not increased.3.In this dissertation,the FDTD method is extended to the simulation of multiphysics field:First,the engineering application of metamaterials is bounded by the ohmic loss in the system.The gain media can be employed to compensate for the ohmic loss caused by metal.The self-consistent mechanism of the Maxwell-Bloch equation is considered in this thesis to describe the four-level atomic system model of the gain medium.Based on the coupling mechanism of the gain medium and the extraordinary optical transmission,a novel structure is proposed to reduce the threshold when the ohmic loss is fully compensated.Second,due to the nonlinear characteristics of the material is difficult to be accurately described for the traditional numerical model.The self-consistent mechanism of a multi-physical framework for the Maxwell-hydrodynamic equation is considered in this dissertation to describe the nonlinear effects.The numerical example proves that the polarization of the second harmonic field can be controlled by the rotationally symmetric structure and the high dimensional angular momentum can be transferred by the quasi-periodic nonlinear metamaterials.