| In these years, with the improvement of the performance and the reduction of the cost, the computer has been applied to practical problem for large-scale simulation, which has become one of the important research domains in various scientific fields. In the field of Computational Electromagnetic, the application of computer simulation is indispensable. Thus, it also promoted the emergence of various numerical algorithms. The finite-difference time-domain (FDTD) algorithm has been widely applied for the numerical simulation for its unique advantage and suitability in Computational Electromagnetic. At the same time, using FDTD to solve the electromagnetic problem has become a hot research direction. More delicate grids are used to obtain the required accuracy by the condition of numerical dispersion, which is not conducive to improve the calculation efficiency. For this reason, scholars have put forward various methods to improve the algorithm. Among these methods, the high order FDTD has been widely applied.Firstly, a high order FDTD method based on Discrete Singular Convolution (DSC) and Symplectic Integration Propagator (SIP) theory is introduced in this paper. This method can improve the traditional difference form of electromagnetic equations. The difference accuracy of the space can be improved to2M (M>2) order. And the precision of the time domain will be increased to4order. By analyzing the dispersion characteristics of the high order FDTD, this algorithm can obviously decrease the numerical dispersion error. At the same time, it can introduce bigger size grid than traditional FDTD method to meet the same accuracy.Secondly, according to the characteristic of the electromagnetic field varying strongly on the border of different material surface, the non-uniform grid is generated by applying the coordinate map method. The gird on the area of changing rapidly will be refined. Then the non-uniform grid will be introduced into the high order FDTD. The scattering parameter of the waveguide will be simulated by this method.The conclusion is drew that the amount of compute is significantly reduced and the more accurate result will be obtained.Thirdly, in the three dimensional electromagnetic scattering problems, the computational domain will be divided for the high order method. The key technology for the scattering problem will be solved. The high order algorithm will be expanded to the PML domain directly. The reflection of PML is effectively decreased and the absorption performance is increased. At the same time, according to the characteristic of the high order algorithm, the calculation formulas of the total and scattering field will be fixed. After the incident wave has been put on the connect boundary. The RCS of the target will be obtained by the near-filed to far-field transformation.Fourthly, the non-uniform grid will be introduced into the high order FDTD to solve the three dimensional scattering problem. The electromagnetic distribution and RCS of the target will be obtained by programming the3D high order simulation algorithm. It will be concluded that the non-uniform grid algorithm can effectively solve the electromagnetic problem. Also this algorithm can achieve the same accurate as the uniform delicate grids. And after the coordinates mapped, the number of grid will be reduced. As this reason, the proposed algorithm can effectively save memory space and improve the computational efficiency.A larger grid can be used to divide the computation domain by the high order FDTD introduced in this article. Combining with the non-uniform grid, the conflict of the calculation efficiency and accuracy can be solved much more effectively. Therefore, applying this theory to research the scattering problem of electrically large and complex structure target is of certain practical value. |
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