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混合显-隐式时域有限差分方法的时间步长只由空间两个方向上的网格大小决定, 因而该方法被广泛应用于沿一个方向具有精细结构的电磁目标的模拟. 本文通过对传统时域有限差分方法基本公式进行近似, 给出适用于线性、非色散空间, 一维精细结构电磁目标模拟的通用混合显-隐式时域有限差分方法. 在通用混合显-隐式时域有限差分方法中, 通过媒质编号索引和迭代系数空间定位实现三对角矩阵的自动构建, 引入等效参数方法解决麦克斯韦方程微分形式在不同介质分界面失效的问题, 引入卷积完全匹配层边界条件对计算区域进行截断. 此外, 本文提出了一种缩减三对角矩阵数量的方法, 该方法可有效降低程序运行所需内存, 提高程序运行效率. 应用通用混合显-隐式时域有限差分方法仿真了平面波照射介质板和双频微带倒F天线两个模型, 数值计算结果与传统时域有限差分方法和CST软件的计算结果一致, 但与传统时域有限差分方法相比, 通用混合显-隐式时域有限差分方法的计算效率大大提高.
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关键词:
- 电磁目标/
- 混合显-隐式时域有限差分/
- 等效参数/
- 卷积完全匹配层
The hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is a weakly conditionally stable finite-difference time-domain (FDTD) method. The time step size of the HIE-FDTD method is only confined by the two coarse spatial cell sizes, so it is widely used in the simulation of electromagnetic targets with fine structures along one direction. In this work, the basic iterative formulations of the HIE-FDTD method are proposed by approximating the formulations of the FDTD method. In these formulations, the iterative coefficients are marked with spatial grid numbers. Therefore, the coefficients can be calculated automatically according to the medium parameters of the spatial cells by indexing the grid numbers. Since the triangular matrix which is used to calculate the electric field is based on the iterative coefficients, the triangular matrix can also be updated automatically. In addition, a method to reduce the number of tridiagonal matrices is proposed in this work, which can effectively reduce the calculation memory and improve the calculation efficiency. In the proposed HIE-FDTD method, equivalent parameters are employed at the interfaces of different media and the convolution perfectly matched layer boundary condition is used to truncate the computational region. Based on the proposed HIE-FDTD method, a series of programs are implemented, which can simulate arbitrary electromagnetic targets with fine structure in one dimension in linear and non-dispersive space. A dielectric plate irradiated by planar wave and a dual-frequency microstrip inverted F antenna are simulated by using these programs. The numerical results are in good agreement with those from the traditional FDTD method and CST software, and the computational efficiency of the proposed HIE-FDTD method is greatly improved in comparison with that of the traditional FDTD method. This study provides a reliable simulation tool for the wide application of the HIE-FDTD method.-
Keywords:
- electromagnetic target/
- hybrid implicit-explicit finite-difference time-domain/
- equivalent parameter/
- convolution perfectly matched layer
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计算方法 直接法 缩减法 1×1 5×5 10×10 1×1 5×5 10×10 三对角矩阵数量 684 11100 41760 12 12 12 程序运行时间/s 0.35 84.78 1299.4 0.02 0.20 0.51 程序所需内存/
MB1.40 24.14 90.80 0.98 15.77 59.27 
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