Research Of Three-Dimensional Unconditionally Stable Five-step LOD-FDTD Method

Due to the finite difference time domain(FDTD) method can be intuitive description of the calculated electromagnetic problems and easy to program while in electromagnetic calculation, it has become an important numerical method in the electromagnetic simulation field. However, along with the development of science and technology, the calculation efficiency and precision are required higher and higher. Due to the limitation of Courant-Friedrich-Lewy(CFL) stability condition, efficiency of the traditional FDTD method algorithm is serious impact when applied in electromagnetic simulation in practical. Therefore, in order to improve the computational efficiency and breakthrough the CFL stability limit conditions, three dimensional unconditionally stable five-step locally one-dimensional finite difference time domain algorithm(LOD5-FDTD) is researched in this paper. Whose time step is not restrict by the CFL stability condition combined with the locally one dimensional(LOD) finite difference time domain characteristics.Firstly, this paper reviews and summarizes the research progress of LOD5-FDTD algorithm and the algorithm in normal medium is derived and iterative formulas of the electric and magnetic components are given in detail. The accuracy of the algorithm is researched and analysized based on the computation resonant frequency of a resonant cavity(include filling with no media and partly filled with media).Then, the derivations of LOD5-FDTD algorithm UPML absorbing boundary conditions are given. And the specific form of the iterative formula and iterative flow chart of the electromagnetic field components are given, when the UPML absorbing boundary conditions are introduced into the LOD5-FDTD algorithm. The relative error of an electric dipole and the spatial phase distribution of a sinusoidal source are analyzed to verify of the efficiency and stability of the absorbing boundary. The numerical results show that the UPML absorbing boundary has good absorption efficiency when led into the LOD5-FDTD algorithm, and the algorithm could maintain unconditional stability.Finally, in order to apply the algorithm to scattering computation, this paper presents the boundary conditions of the LOD5-FDTD algorithm. Firstly, the specific implementation method of Total Field/Scatter Field(TF/SF) connection boundary and modify iterative formulas of the electromagnetic field components are given around the connect boundary. The spatial amplitude distribution of a sinusoidal field is analyzed, which shows the feasibility of the introduction of the TF/SF connection boundary and its capability of maintaining the characteristic of the unconditional stability of the algorithm. Then, the radar cross section(RCS) of the metal plate is simulated and calculated, which further verifies the feasibility and unconditionally stability of the algorithm.