The Research On 3D Artificial Anisotropic HIE-FDTD Algorithm

Hybrid Explicit Implicit Finite-Difference Time-Domain(HIE-FDTD)method has been widely used in computational electromagnetics to study electromagnetic problems of lossless media.HIE-FDTD combining explicit and implicit methods degrades the stability condition of FDTD,and has higher computational efficiency when calculating electromagnetic problems with a compact size structure in a single direction.However,the existing HIE-FDTD method is only applicable to lossless media,and is not applicable to lossy media widely existing in nature,so it is very meaningful to adopt appropriate methods to extend the scope of application of HIE-FDTD while ensuring the calculation accuracy.Based on the study of the traditional FDTD method,combined with the existing lossless three-dimensional HIE-FDTD method,and the analysis of the introduction of artificial anisotropy parameters HIE-FDTD,this paper proposes a suitable for both lossy media and lossless media Three-dimensional artificial anisotropy HIE-FDTD method.First,the existing FDTD and HIE-FDTD theory in lossless media are analyzed.By introducing artificial anisotropy parameters,the artificial anisotropy HIE-FDTD algorithm is discussed in detail on the basis of retaining electrical conductivity and magnetic permeability.While optimizing the numerical dispersion of the algorithm,the application range of the HIE-FDTD method is expanded from lossless media to lossy media.In addition,the stability condition of the artificially anisotropic HIE-FDTD algorithm is given by the growth matrix.It can be seen that the time step of the method is independent of the value of the spatial step in the direction of the compact structure.Secondly,the program flow of the anisotropic HIE-FDTD method with CPML boundary conditions is designed,and the specific implementation scheme is given.Based on the realization of the sub-grid-based FDTD method,by comparing the calculation results of two different methods,with the same accuracy,the efficiency is improved several times.Finally,on the basis of completing theoretical analysis derivation and program implementation,the method is applied to two types of calculation examples of broadband filters with lossy dielectric substrates and absorbers with graphene coating for analysis and calculation,The results show that the method proposed in this thesis can achieve the same accuracy as the traditional FDTD when simulating media with lossy and non-lossy media,and can be improved several times to thousands of times compared with the traditional FDTD method under different meshing density conditions.The above calculation efficiency fully validates the effectiveness and efficiency of the proposed HIE-FDTD method.