Using Fdtd Time-domain Waveform Extrapolation Forecast And The Adi-fdtd

The finite-difference time-domain (FDTD) method is extensively applied in numerical calculation, simulation and design of electromagnetic structures because of its powerful capabilities. However, the FDTD method still has some limits. In this thesis , the intrinsic disadvantages of traditional FDTD are successfully overcome by studying classical FDTD methodology and foundations of mathematics.(1) To obtain complete time domain waveform, the number of the required time steps is often up to order of tens of thousand, hundreds of thousand, even more when applying FDTD to analyze highly resonant structures or discontinuous ones in MMIC. Data of complete time domain waveform is also needed in order to calculate accurate S-parameters of frequency domain via fast Fourier transform (FFT). If the time domain waveform is truncated in advance, the values of scattering parameters will deviate true ones. And the time cost is too great if one calculate the time waveform directly by using FDTD. In order to solve this problem, some approaches of other subjects can be used to accelerate the calculation in FDTD. Some feasible acceleration techniques are presented in this thesis by combining signal processing approach, modern spectral estimation techniques, sample learning. Only previous stage data of time domain waveform are calculated using FDTD. Based on these data, the extrapolation technique is then adopted to obtain complete time domain waveform so that accurate S-parameters of frequency domain can be obtained through FFT. This proposal can considerably reduce the computation time. The related foundations of mathematics and detailed measures are demonstrated in this thesis and compared with past literatures.(2) When a traditional explicit finite-difference time-domain (FDTD) method is used, fine geometric details dictate a small time step due to the Courant-Friedrichs-Lewy stability condition, which in turn could require an excessively large number of computation steps and significantly degrade the numerical efficiency. In this thesis the alternating-direction-implicit (ADI) scheme is introduced to eliminate the courant stability condition of traditional FDTD method by combining implicit difference equations with explicit ones. The ADI-FDTD is unconditionally stable and the size of the time step is based only on the desired accuracy so that the numerical efficiency is largely enhanced.Comparison of performance parameters such as computation time illustrates that ADI-FDTD has many advantages over traditional FDTD.Key words: FDTD, Extrapolation predictor, ADI-FDTD...