The Research On Finite Difference Time Domain Methods In The Computational Electromagnetics

The computational electromagnetics (CEM) is the combination of several courses including computer technology, computational mathematics, electromagnetics and etc. As the result of its rapid development, various commercial EDA sofwares based on different algorithms have been presented for the use by engineers, for example, HFSS, CST, Magic, ADS and etc. Those softwares offer great help to engineers in shortening research periode, reducing cost and improving stability. In addition, the development of CEM is also advantageous to the solution of more complex electromagnetic problem.This dissertation mainly deals with the research on the finite-difference time-domain (FDTD) method, which is one of the most important methods in CEM. After the comprehensive study of the previous work by people, some effective FDTD methods are presented by the author.The breakthroughs of this dissertation are as follows:1,The careful study shows that the conventional error measures used to evaluate the performance of the FDTD method's numerical dispersion is deficient. This dissertation presents new error measures which can be applied in general cases.2,This dissertation presents a new low-dispersive H-FDTD method based on hegxagon grid. In the H-FDTD method, Hegxagon grid is used for the spatial discretization by virtue of peridodical sampling theorem based on arbitrary geometry. Unlike the conventional treatment, the definition of the directional derivative is introduced for the construction of the finite difference scheme. Compared with that of the conventional FDTD method, the numerical dispersion of the H-FDTD is reduced to some extent.3,This dissertation presents a new unconditionally-stable FDTD method named the US-FDTD method. Such US-FDTD method is based on the weighted Finite difference scheme. In comparison with that of the ADI-FDTD mthod based...