【作者】 杨阳；

【导师】 陈如山；

【作者基本信息】 南京理工大学 ， 电磁场与微波技术， 2005， 博士

【摘要】 时域有限差分方法(FDTD)由于其强大的功能，已经成为电磁场数值模拟的最重要方法之一。但是对于任何一个具体的方法而言，总是优点和缺点并存的。本文通过对时域有限差分方法的研究，针对传统FDTD算法本身的固有特点提供了若干改进方案。 FDTD分析谐振结构、微波集成电路中的不连续性结构等问题时，为了获得完整的时域波形，所需的时间步数有时可能会达到几万，甚至几十万次。而要通过快速傅立叶变换(FFT)获得准确的频域参数，又必须得到完整的时域波形数据。如果过早地中断时域波形，会使频域结果偏离真实值。为了解决这一问题，本文将FDTD分别与改良的矩阵束(MMP)方法及最小二乘的支持向量机(LS-SVM)方法相结合，提出了两种可行的加速算法，只需获取FDTD的早期部分时域波形，通过外推技术即可获得准确的完整时域波形，再经过FFT得到准确的频域参数，从而能够大幅度的增加FDTD的计算效率。文中还对LS-SVM算法在应用中需要选择参数γ，σ的问题，提出应用粒子群优化算法进行优化选取参数，减少了人工干预，进一步提高了鲁棒性。 传统FDTD时间步长的选取受到Courant-Friedrich-Levy(CFL)稳定性条件的约束。本文又研究了三维的基于变替方向隐格式的时域有限差分(ADI-FDTD)方法，详细讨论了ADI-FDTD方法成功实现仿真的几项关键技术。并将其应用于分析平面微带电路、贴片天线和波导等三维结构的电磁特性。数值结果证明ADI-FDTD可以在一定程度上增大时间步长，从而提高传统FDTD算法的计算效率。同时把ADI-FDTD与MMP外推预测技术相结合为分析电磁结构提供了一种更为迅速有效的方法。 本论文最后研究了ADI-FDTD算法存在的随着时间步长的增大，其数值色散误差也增大的问题，提出了三维的基于Crank-Nicolson差分格式的FDTD(CN-FDTD)算法。通过运用该算法对谐振腔和平面微带电路的电磁特性分析，显示出在时间步长的取值远大于CFL稳定性条件，而CN-FDTD和ADI-FDTD的时间步长相同的情况下，CN-FDTD的计算精度远高于ADI-FDTD。由于在场的更新中需要求解大型稀疏矩阵方程，文中采用了对称超松弛预处理的双共轭梯度法对CN-FDTD方程组进行迭代求解，并利用前一时刻所求出的E值作为迭代算法的初始值，保证了较高的求解速度和迭代算法的稳定性。但进一步寻求高效求解大型稀疏矩阵方程的方法是CN-FDTD方法取得广泛应用的关键技术。更多还原

【Abstract】 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更多还原