The Research On High Order Accurate FDTD Method In The Saltation Media Region

The standard Finite Difference Time Domain (FDTD) method is second order accuracy in the homogeneous media. The main problem is the issue of the treatment of the grids containing the dielectric interface, when the region filled with different media is investigated. Many kinds of theory and methods are introduced in this thesis, such as method with effective permittivity based on uniform grids, area integration method, the subgridding method, subgrid modeling method with dielectric curved surface and the enlarged cell technique at metallic curved. A further research is made and a variety of improved algorithms are proposed in this thesis on the basis of the existing methods above. In this paper, the issue of planar dielectric interface is discussed firstly, and then extended to the case of angular dielectric interface; finally the curved dielectric surface is investigated for the practical considerations.At first, the TE mode and TM mode in the two-dimensional case is analyzed, and the several approximate methods to deal with the grids filled with different media in the standard FDTD algorithm are introduced, including scheme of arithmetic average of permittivities and the effective permittivity. But only the first order accuracy can be obtained in these efforts. The rigorous second-order accurate FDTD equations at planar dielectric interfaces are straightforwardly derived though the discretization of the integral forms of Maxwell's curl equations on the non-uniform Yee's lattice and Taylor series expending of continuous field components over finite volumes including the interfaces. In the new method, the accuracy is improved effective by the appropriate arrangement of the coarse grids and fine grids in the regions filled with different media based on the requirement of research. The better accuracy is demonstrated by the calculation of the error in the numerical electric fields from the proposed method. The second-order accurate FDTD technique of TE mode and TM mode is applied into three-dimensional case, by the analysis of a FDTD modeling with nonuniform grids.The second-order accurate FDTD equations are derived, and the distance parameters and effective permittivities are obtained for the second-order condition. Numerical simulations of microstrip circuits are carried out and the return and reflection characteristic are analyzed to demonstrate the validity of the proposed methods.In the subgridding method, the dielectric regions with different attentions are divided with coarse grids and fine grids, and the mesh size of coarse grid is the treble or double of that fine grid. The subgidding method could save the computational resource and improve the performance, but only first order accuracy of the electric fields at the boundary of coarse grids and fine grids can be obtained when the traditional subgridding method is deal with the regions with different media. Thus an improved subgridding method is proposed to obtain the second-order accuracy of the electric at the interface by the construction of the nonuniform grids and the introduction of the auxiliary magnetic fields. Some ridged waveguides are simulated to compare the different results from the proposed method and the standard method.The devices with curved dielectric surface often used in practical applications, and a series of conformal FDTD algorithms are produced to accurately model the curved surface. From the relative simple staircase method, the subgrid modeling method to the complex area integration method, and the novel enlarged cell technique, all of them are trying to pursuit the perfect agreement of algorithm accuracy with computational cost. But the result always is not perfect, neither bad accuracy nor complex calculation process. An enlarged cell method at the curved dielectric surface is presented in this thesis. This improved method is simple and effective and the accuracy is improved without the additional computational cost.