Study On Improved Fdtd Methods In The Computational Electromagnetics

With the rapid development of semiconductor fabrication techniques, modern electronic devices trend to become more and more complex and smaller along with the electromagnetic environment. Thus, the electromagnetic effects must be paid special attention to. Although certain outcomes have been obtained in this field, challenges, such as electric-large objects and multi-scale problems, always exist. In this thesis, the leapfrog ADI-FDTD method based on the original FDTD method is investigated systematically and main work has been summarized as follows:1. Brief Introduction to the FDTD method:A brief introduction to the original FDTD method including the main iterative equations, the perfect matched layer (PML) (especially for the convolutional perfect matched layer (CPML)). the stability condition, and numerical dispersion, is given. Since the main work focuses on the implicit FDTD methods, the original ADI-FDTD method is presented. At last, the numerical dispersion formulations for the ADI-FDTD method and LOD-FDTD method are given.2. Arbitrary order leapfrog ADI-FDTD method:Arbitrary order one-step leapfrog ADI-FDTD method with high efficiency and unconditional stability is proposed. The stability is verified in theory and by numerical results. In addition, the ADI-FDTD method, LOD-FDTD method and leapfrog ADI-FDTD method have the same numerical dispersion relation in theory. Studies on the changes of the dispersion along with several parameters are given. The convolutional perfected layer (CPML) is incorporated into the leapfrog ADI-FDTD method to handle the radiation problem. Detailed efficiency comparison with other implicit schemes is given. Furthermore, improved reformulations with higher efficiency and no memory increasement have been proposed.3. Hybrid FDTD methods:Two hybrid FDTD methods are proposed to improve the efficiency. The first one is the local subgridding technique and the second one is the global nonuniformal grids. In addition, the detailed theory and coding process are given.