Novel Techniques to Improve Numerical Accuracy of the Finite Difference Time Domain Method

• Main Authors: Shu-Hai Sun, 孫樹海
• Other Authors: Charles Choi
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/68944479261054503266

博士 === 義守大學 === 電機工程學系博士班 === 94 === The finite difference time domain (FDTD) method is useful to analyze the propagation of the electromagnetic wave. In FDTD method, Maxwell’s curl equations are discretized by utilizing central-difference equations with second-order accuracy, and the electric and magnetic field components are located at the suitable positions on the Yee cell. Since the cell size is restricted by the size of the smallest object in the computation domain and the maximum temporal increment is limited by the Courant-Friedrich-Levy (CFL) stability condition, the simulation of the model with fine components can cost enormous memory and computation resources. In this research, several techniques are proposed to improve the numerical accuracy and efficiency of the FDTD method. The subgridding scheme is a useful technique which deals with models with fine components, but the instability limits the numerical resolution. By utilizing the finite-difference Laplacian interpolation scheme (FDLIS) to the FDTD method and coupling with the subgridding scheme, the new subgridding and multilevel subgridding schemes for the FDTD and FDTD(2, 4) methods were proposed, and the stability and efficiency of the method were validated by solving a scattering problem. Although the temporal increment is free of the CFL stability condition and the computational domain can be discretized in non-uniform mesh distribution using the alternating-direction implicit FDTD (ADI-FDTD) method, the numerical error grows with the increase of the temporal increment. By coupling wave-envelope technique with the ADI-FDTD method, it is found that the envelope ADI-FDTD method in two- and three-dimensional domains maintain good numerical accuracy for a large temporal increment. In this thesis, the numerical performances of the envelope ADI-FDTD and ADI-FDTD methods are discussed in two- and three-dimensional domains, respectively. A two-dimensional waveguide problem and a three-dimensional cavity problem were also solved by the envelope ADI-FDTD, ADI-FDTD, and FDTD methods, and the solutions showed the good performance of the envelope ADI-FDTD method in this thesis.