Implementation Of The Periodic Boundary Condition In The Tdfit Method

Since the finite-difference time-domain (FDTD) method is proposed, it has been developed into a mature numerical method during the past 50 years. With the characteristic of simplicity, generality, and flexibility, FDTD has many advantages in dealing with electromagnetic prob-lems. Many structures of electromagnetic problems possess a periodicity in one or more di-mensions. For example, a frequency selective surface (FSS) is commonly used in a radome to control the energy that reaches the antenna. Another type of structure that can be considered as periodic is an antenna array. If large enough, many of the important parameters of an an-tenna array can be analyzed by assuming that the structure is periodic. Based on the method of FDTD, the dissertation details the theoretical overview of a special FDTD method named as time-domain finite-interal (TDFIT) and its periodic boundary condition, and introduces how to realize it. The main contributions of the thesis include:1. The function of periodic boundary condition is presented using the TDFIT software frame-work.2. With the periodic boundary condition, a discrete grid model of radiation is developed to calculate the active pattern of the element cell within an infinite antenna array, which is val-idated by the example of horn antenna. An element far-field pattern, which is obtained from a rectangular waveguide antenna in the periodic boundary condition, is used to synthesize an array pattern. Compared with the array pattern in real size, a good agreement is observed.3. To develop further application of PBC (periodic boundary condition), we realize a technique to calculate the reflection and transmission coefficients for planar periodic structures lit by plane wave. The method refered to as spectral finite-difference time-domain (SFDTD) re-places the conventional single-angle incident wave with a constant transverse wavenumber (CTW) wave. Because the transverse wavenumbers are constant, the fields have no delay in the transverse plane (x-y plane), and PBC can be directly implemented in the time domain for both oblique and normal incident waves.