ADI-FDTD On One-dimensional And Two-dimensional Electromagnetic Simulation And Its Applications

There is a long history for the development of electromagnetic field and electromagnetic wave theory, and it has been one of the fastest-growing fields which have almost permeated through all aspects of human being's life so far. The distribution of electromagnetic field is supposed to be acquired when engineers concern both theoretical and practical aspects of electromagnetic problems. It is common knowledge that most electromagnetic models are too complicated to get an analytical solution. Therefore, computer techniques have revolutionized the way in which electromagnetic problems are analyzed. Antenna designers and microwave engineers rely heavily on numerical methods based on computer techniques.It is well known that the core of a numerical method for electromagnetics is arithmetic. Finite-Difference Time-Domain method (FDTD) is a kind of simple and reliable method which is widely used for solving problems related to electromagnetics. As the traditional FDTD method is based on an explicit finite-difference algorithm, the Courant-Friedrich-Levy (CFL) condition must be satisfied. Therefore, a maximum time-step size is limited by minimum cell size in a computational domain, which means that if an object of analysis has fine scale dimensions compared with the wavelength, a small time-step sizewill lead to a significant increase in computation time.Alternating-direction Implicit Finite-Difference Time-Domain (ADI-FDTD) method was proposed in order to eliminate the limit of CFL condition in conventional FDTD method. Numerical formulation of the ADI-FDTD method for three dimensional waves is presented. Then the numerical stability of the formulation is also derived.The way to use connecting boundary in ADI-FDTD is discussed in details. A new kind of simplified calculating procedure of one dimension problems is proposed.A numerical example-- PBG structure is simulated, and the results of ADI-FDTD method are compared with those of analytical method and other numerical methods such as conventional FDTD and implicit FDTD. All the results agree well, and ADI-FDTD method requires the least CPU time.This paper designs a layered dielectric low pass filter, which is based on the design theory of stepped impedance filters. This kind of structure is simulated by three numerical methods, including ADI-FDTD method.An empty waveguide of BJ-22 and another waveguide where there is a water cylinder inside are modeled by FDTD and ADI-FDTD respectively. All results agree very well, and ADI-FDTD method requires much less CPU time than conventional FDTD method.