The Research On The Finite Difference Time Domain Methods In The Electromagnetic Fields

The finite-difference time-domain (FDTD) method is one of the most important methods in electromagnetic numerical simulations for its powerful capabilities. However, the FDTD method still has its disadvantages. In this thesis, the intrinsic characteristic of traditional FDTD are successfully improved by several new ideals through studying classical FDTD methodology and foundations of mathematics.To obtain complete time domain waveform, the number of the required time steps is sometimes up to tens of thousand's orders, even more than hundreds of thousand's orders when applying FDTD to analyze highly resonant structures or discontinuous ones in microwave integrated circuits. Meanwhile, data of complete time domain waveform is 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. In order to solve this problem, this thesis puts forward two acceleration techniques to combine direct FDTD method: Modified Matrix Pencil (MMP) method and Least-Square Support Vector Machines (LS-SVM). The complete time domain waveform could be obtained by the accelerated extrapolation techniques only based on the previous stage data of time domain waveform calculated by FDTD. Then accurate S-parameters of frequency domain could be obtained through FFT. This proposal can considerably reduce the computation time. Later, Particle Swarm Optimization (PSO) algorithm is suggested to help the LS-SVM to select the parameters γ and σ which should be selected in LS-SVM. This method reduces the human intervention and improve the robustness of original algorithm.The selection of the time steps' size in traditional finite-difference time-domain (FDTD) method is restricted to the Courant-Friedrichs-Levy stability condition. In this thesis the alternating-direction-implicit (ADI) scheme is introduced to eliminate the CFL stability condition of traditional FDTD method. The key techniques of ADI which leads to succcesful simulation results are discussed. Then ADI-FDTD method is adopted to analyse the electromagnetic characteristics of microstrip curcuits, patch antenna and waveguides. The simulation results indicates that the size of the time step could be selected larger in some extent when using ADI-FDTD, which improves the effiency of traditional FDTD method. Later, the MMP technique is combined with ADI-FDTD method and this hybrid method makes the calculation much more efficient when analysing electromagnetic...