High Order Compact Scheme FDTD Method

In recent years, with the development of science and technology, the electromagnetic numerical methods as a new interdisciplinary have made great progress. The traditional finite difference time-domain method(FDTD), as a typical full-wave analysis of time-domain numerical algorithm has been the broad of applications in the many electromagnetic fields, and shows the broad prospects in development. However the traditional FDTD method also has its own shortcomings, which uses the second-order center difference scheme in both time and space, so the method has a low-order explicit scheme and greater dispersion. For electrically large domains and late-time analysis, along with the increase of time step, the dispersion errors resulted from the discretization will slowly accumulate. It would lead to a serious distortion of the calculated waveform. According to the limitation of the traditional FDTD method, this thesis presents a new numerical method-High Order Compact Scheme FDTD method. This method not only improves accuracy, but also has the advantages of fewer grid nodes, less memory consumes and CPU time, etc. A detailed study and research on aspects of the basic principle are analyzed; the specific implementation details and typical applications of this method are also included in this thesis. Specific studies are as follows:●Aimed at the deficiency of the traditional FDTD method. Firstly, in order to improve the space difference scheme, a new difference method, namely compact difference schemes, has been proposed. Then the Compact difference scheme based on the discrete form of Maxwell equation is proposed in detail. And the basic characteristics of the methods, including the numerical stability, absorbing boundary conditions were presented. ●Making use of the Compact-FDTD method, numerical simulation of the waveguide system of lossless and lossy medium are obtained. Compact format FDTD method has improved greatly in the area of memory space and CPU time compared with the traditional FDTD method, which is confirmed by calculating a concrete example. Using the high-order compact-FDTD method, the specific process of electromagnetic wave propagation in photonic crystals and photonic crystal fibers is also included in this thesis.●Finally, the thesis elaborates the advantages and disadvantages of high-order compact-FDTD method, and possibility of combining this method with symplectic algorithm. The thesis also makes a prospect to the many aspects where need energy conservation of the system, improve stability of the algorithm and conquer waveform distortion.