Study Of Runge-kutta High-order Finite Difference Time-domain Method And Its Application In Electromagnetic Scattering

Recently, fast and accurate analysis of three dimensional(3D) large scale and complicated objects has always been of great importance in computational electromagnetic fields. Firstly, the thesis has studied the multiresolution time-domain(MRTD) method and the high order finite differnce time-domain(HO-FDTD) method. Based on them, a novel high accuracy Runge-Kutta High order Finite-Differnce Time-Domain(RK-HO-FDTD) method is proposed. The numerical characteristics of the new method as well as its application fundamentals has been studied and analyzed in detail and a framework for the study of complex 3D objects has been built. In order to further improve the efficience and accuracy of the RK-HO-FDTD method, the modifications have been made to the method. The analysisi of the radar cross section(RCS) of complicate object has been performed by the method and the results show that the accuracy has been greatly improved.The main works and contributions of this thesis are summarized as follows:1. The basis theories of the MRTD and HO-FDTD methods have been fully studied in detail, and their numerical characteristics, including dispersion error, stability and convergence. Firstly, the dispersion equation has been derived by the Fourier’s analysis method. The results show the HO-FDTD method has the better dispersion error than MRTD. Secondly, the stability and the maximum stability factor of the two methods have been solved and analyzed. Based on the convergence, the two methods are both limited by the temporal convergence. At last, the computational cost and memory requirments have been studied.2. In order to handle the convergence limitation of the MRTD and HO-FDTD methods, a high order convergence both in the spatial domain and temporal domain method, the RK-HO-FDTD method has been proposed. The theory and update equations of the new method has been built and derived. Its characteristics including the dispersion error, stability, convergence, dissipation and computational cost and CPU requirement have been fully studied. The conclusion is that the new method is better than the MRTD and HO-FDTD method.3. The main techniques used in the application of the RK-HO-FDTD method are studied including how to induce the plane wave, how to set excitation source, how to deal with the perfectly electrical conductor(PEC) interface, how to set anisotropic perfectly matched layer(APML) and how to handle with the dielectric interface. The full electromagnetic system of the RK-HO-FDTD method has been built.4. The RK-HO-FDTD method is applied to the electromagnetic scattering analysis of complex objects.The near-to-far-field transformation method is imployed in the RK-HO-FDTD method as well as under the circumstances of time-harmonic and transient field for the RCS. The results of the numerical experiments show the great accuracy and the effcience of the method.5. In order to improve the further accuracy of the method, the modifications have been taken to it. The conformal RK-HO-FDTD method has been proposed to decrease the stair error. The optimal technique has been proposed for the weighten parameter of the RK-HO-FDTDmethod. The numerical example has been used to validate the modified method is more accuracy than the old one.