Research On Locally One-dimensional Finite-difference Time-domain

The Finite-Difference Time-Domain(FDTD)method is a numerical method which has been gradually improved and used in computational electromagnetic.In this paper,after describing the basic principle of the traditional FDTD method,an unconditionally stable FDTD method based on the traditional FDTD method-Locally One-Dimensional Finite-Difference Time-Domain(LOD-FDTD)method is introduced.First of all,according to Maxwell's equations,this thesis introduces the procedure of numerical discrete differential treatments in spatial and time domain.In order to discuss the stability of numerical solution,this thesis discussed the principle by which the discrete intervals in spatial and time domain are set and numerical dispersion and numerical anisotropic properties caused by numerical discrete differential treatments.Then,the absorbing boundary condition essential to simulate the electromagnetic field by the FDTD method and the extrapolation based on the principle of Huygens from near-field to far field are explained.Finally,the basic iterative formula of the LOD-FDTD algorithm is derived,and the stability of the algorithm is proved,and the correctness of this algorithm is verified by two-dimensional resonator.The Mur's first order absorption boundary conditions and LOD-PML of the algorithm are given,and their reflection error is calculated by an example.