Research On ADI-FDTD Algorithm For Waveguide Standing Wave Radiation

The thesis has studied alternating direction implicit finite difference time domain (ADI-FDTD) method as well as its application in the field analysis of a rectangular waveguide. The electromagnetic field distribution is computed when the rectangular waveguide irradiation cavity has no load or has load of lossy medium.Based on the unconditional stability of ADI-FDTD method, we use MATLAB programming to study the numerical dispersion of this method. On condition of the CFL stability, a comparison of numerical dispersion errors between ADI-FDTD method and the traditional FDTD method has been made to provide reference for the following study.C Programming is applied to implement both the ADI-FDTD and the FDTD algorithms before it is adopted to perform simulations of electromagnetic field distribution inside the rectangular waveguide radiation cavity with the TE102 mode. The comparison of simulation results leads to the conclusions. First, in case that CFL stability is fulfilled, the ADI-FDTD method requires more calculation time to finish a single iteration than that of the traditional FDTD method, which is approximately 4 times. As the time interval increases, the ADI-FDTD method keeps its stability, which has verified that the ADI-FDTD method has unconditional stability. Considering the impact of numerical dispersion error on the ADI-FDTD method, the increase of the time interval cannot achieve the ideal theoretical value, that is twenty times of the CFL definition. According to the field distribution, 6 times increase of the interval is the best one in the computation of rectangular waveguide radiation. Meanwhile, it is found that on a given grid condition, the increase of time-step size leads to the accumulation of the numerical dispersion error, thus impacting computation results including field variation with time or space. A water column is added into rectangular waveguide radiation cavity to imitate the radiation with a load of lossy medium. Analysis of field distribution on this condition reveals that the ADI-FDTD method still has unconditional stability, but results obtained are less accurate than the traditional FDTD method.