The implementation of connection boundary for the hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is discussed in this article. It shows that the incident field of the HIE-FDTD method must be split into two time steps. Compared with the implementation method commonly used in the conventionalThe finite-difference time-domain (FDTD) method [1] has been proven to be an effective means that provides accurate predictions of field behaviors for varieties of electromagnetic interaction problems. However, as it is based on an explicit finitedifference algorithm, the Courant-Friedrich-Levy (CFL) condition [2] must be satisfied when this method is used. Therefore, a maximum time-step size is limited by minimum cell size in a computational domain, which makes this method inefficient for the problems where fine scale dimensions are used.To overcome the Courant limit on the time-step size of the FDTD method, unconditionally stable methods such as the alternating-direction implicit FDTD (ADI-FDTD) scheme [3][4][5] have been studied extensively. Although the time-step size in the ADI-FDTD simulation is no longer bounded by the CFL criterion, the method exhibits a splitting error [6,7] that is proportional to the square of the time-step size and the spatial derivatives of the field. When field variation and/or the timestep size is large, the splitting error becomes pronounced. The accuracy of the ADI-FDTD method is limited. Besides, in the ADI-FDTD scheme, three time steps are used for defining the field components, and two subiterations are required for field advancement. It must solve six tridiagonal matrices and six explicit update for one full update cycle, which makes the ADI-FDTD computationally inefficient.Based on the theory of ADI-FDTD method, a novel threedimensional hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method has been developed recently [8][9][10][11][12][13]. In this method, the CFL condition is not removed totally, being weaker than that of the conventional FDTD method. The time step in this scheme is only determined by two space discretizations, which is extremely useful for problems where a very fine mesh is needed in one direction. In the HIE-FDTD method, only a single iteration (with two tridiagonal matrices and four explicit update) is needed for the field development. The HIE-FDTD method has better accuracy and higher computation efficiency than the ADI-FDTD method, especially for larger field variation. When the same timestep size is maintained, the CPU time for the HIE-FDTD method can be reduced to about half of that for the ADI-FDTD method [10].Because of the important impact of HIE-FDTD method on the electromagnetic computation, an accurate and efficient connection boundary condition must be developed to simulate electromagnetic interaction. This article gives two implementation strategies of the connection boundary, one uses split incident field and the other does not. By comparing the two implementation strategies, it shows that the split in...
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