-
针对时域非连续伽略金(discontinuous Galerkin time-domain, DGTD)算法中的阻抗边界条件问题开展研究. 阻抗边界条件中的频域算符
${\rm{j}}\omega $ 一般在根号内部, 其在时域数值算法中的实现有一定难度. 另一方面, DGTD算法中数值通量表达式也含有阻抗边界条件, 这也进一步增加了频时转换难度. 为了能给出简化的DGTD阻抗边界算法, 本文首先针对数值通量表达式进行推导, 得到一个特定函数$ {\tilde Z_R} $ , 该函数包含频域算符${\rm{j}}\omega $ , 函数以外表达式不含频域算符${\rm j}\omega$ , 这样就可以仅处理$ {\tilde Z_{\rm{R}}} $ 的频时转换问题. 由于$ {\tilde Z_{\rm{R}}} $ 形式复杂, 对$ {\tilde Z_{\rm{R}}} $ 进行矢量匹配处理, 得到关于${\rm{j}}\omega$ 的一阶有理分式, 进而得到其时域迭代式. 这一过程简明、易于实施, 还可避开矩阵计算. 本文方案经一维及三维算例验证, 精度很好, 针对特定电磁问题如涂覆层问题可大幅降低计算时间.-
关键词:
- 阻抗边界条件/
- 矢量匹配/
- 时域非连续伽略金算法
Large-size conductive targets or coated targets are difficult problems in computational electromagnetics. In general, these problems can be classified as multi-scale problems. Multi-scale problems usually consume a large quantity of computational resources. A lot of efforts have been devoted to seeking for fast methods for these problems. When the skin depth is less than the size of a conductive target, the tangential component of the electric field and magnetic field over the surface of the target can be correlated by the surface impedance $ \tilde Z $ . The$ \tilde Z $ is usually a complex function of the frequency, and it can be used to formulate an impedance boundary condition (IBC) to describe iterative equations in time domain methods, avoiding the volumetric discretization of the target and improving computational efficiency. This condition is commonly known as the surface impedance boundary condition (SIBC). Similarly, for a conductor whose thickness is in the order of skin depth or less, it also has high resource requirements, if the target is of direct volume discretization. The transmission impedance boundary condition (TIBC) can be utilized instead of a coated object to reduce resource requirements. Therefore, there is no need to discretize volume.There are few studies on the IBC scheme by using the discontinuous Galerkin time-domain (DGTD) method. Li et al. (Li P, Shi Y, Jiang L J, Bağcι H 2015 IEEE Trans. Antennas Propag. 635686 ; Li P, Jiang L J, Bağcι H2015 IEEE Trans. Antennas Propag. 633065 ; Li P, Jiang L J, Bağcι H2018 IEEE Trans. Antennas Propag. 663590 ) discussed the IBC scheme by using the DGTD, which involves complex matrix operations in the processing of IBC. In the DGTD method, numerical flux is used to transmit data between neighboring elements, and the key to the IBC scheme in DGTD is how to handle numerical flux. We propose a DGTD method with a simple form and matrix-free IBC scheme. The key to dealing with IBC in DGTD is numerical flux. Unlike the way in the literature, the impedance$ \tilde Z $ is not approximated by rational functions in our study. A specfic function$ {\tilde Z_R} $ obtained after the derivation in this work is approximated by rational functions in the Laplace domain through using the vector-fitting (VF) method, and its time-domain iteration scheme is given. This approach avoids matrix operations. The TIBC and SIBC processing schemes are also given. The advantage of the proposed method are that the upwind flux’s standard coefficients are retained and the complex frequency-time conversion problem is implemented by the vector-fitting method. The one-dimensional and three-dimensional examples also show the accuracy and effectiveness of our proposed method in this work.-
Keywords:
- impedance boundary condition/
- vector-fitting method/
- discontinuous Galerkin time domain method
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] -
通量系数 $ k_E^e $ $ k_H^e $ $ v_H^e $ $ v_E^e $ 迎风通量表达式(upwind flux) $\dfrac{{{{\tilde Y}^{e + }}}}{{{Y^e} + {{\tilde Y}^{e + }}}}$ $\dfrac{{{{\tilde Z}^{e + }}}}{{{Z^e} + {{\tilde Z}^{e + }}}}$ $\dfrac{1}{{{Y^e} + {{\tilde Y}^{e + }}}}$ $\dfrac{1}{{{Z^e} + {{\tilde Z}^{e + }}}}$ 
下载:
导出CSV
离散尺度/m 四面体数量 时间步/(10–11s) 计算时间/min 均方根误差/dB DGTD (SIBC) 0.05 402094 0.328972 54 0.6237 DGTD (standard) 0.05 487677 0.328447 61 0.5836 下载:
导出CSV
-
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
下载:
计量
- 文章访问数:2683
- PDF下载量:65
- 被引次数:0