A Robust Preconditioned GMRES Method for Electromagnetic Scattering From Dielectric Rough Surfaces
A Robust Preconditioned GMRES Method for Electromagnetic Scattering From Dielectric Rough Surfaces
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DOI：
10.1109/tgrs.2012.2184291
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发表时间：
2012-03
影响因子：
8.2
通讯作者：
Guangdi Yang;Yang Du
中科院分区：
文献类型：
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作者：
Guangdi Yang;Yang Du
在本文中，我们提出了一种广义最小残差程序，该程序使用前向-后向方法（FBM）进行正确预处理，用于分析一维电介质随机粗糙表面的电磁散射。还结合了谱加速（SA）技术来加速矩阵矢量乘积的计算。对于有损电介质，格林函数是衰减的并适当截断，不需要对较低介质应用SA技术。所应用的预处理将原始线性系统从接近奇异的系统转变为具有良好条件数的稳定系统。发现预处理矩阵的谱集中在复平面中点 1 附近，这说明预处理器对原始矩阵具有良好的逼近质量。此外，预处理器的构造不需要了解阻抗矩阵谱的分布，这意味着所提出的方法可以用作通用迭代求解器。所提出的方法证明了数值算法的理想特性：稳健且高效。在鲁棒性方面，所提出的方法显着提高了 FBM-SA 的收敛性，特别是对于指数相关的粗糙表面。在效率方面，所提出的方法在水平 (HH) 偏振方面比 FBM-SA 快两到四倍，在垂直 (VV) 偏振方面大约快两倍。这些特征表明，所提出的方法可以有效地用于分析具有高斯谱和指数谱的一维介电高斯表面的电磁散射。
In this paper, we propose a generalized minimal residual procedure which is right preconditioned with the forward-backward method (FBM) for the analysis of electromagnetic scattering from 1-D dielectric randomly rough surfaces. The spectral acceleration (SA) technique is also combined to expedite the computation of matrix-vector product. For lossy dielectric, the Green's function is attenuative and suitably truncated, without the need to apply the SA technique for the lower medium. The applied preconditioning transforms the original linear system from near singular to stable with a good condition number. The spectrum of the preconditioned matrix is found condensed in the vicinity of the point 1 in the complex plane, which speaks of the good approximation quality of the preconditioner to the original matrix. Moreover, the construction of the preconditioner does not require the knowledge of the distribution of the impedance matrix spectrum, which means that the proposed method can be used as a general purpose iterative solver. The proposed method has demonstrated the desirable properties of a numerical algorithm: robust and efficient. Regarding robustness, the proposed method significantly improves convergence over the FBM-SA, in particular, for exponentially correlated rough surfaces. Regarding efficiency, the proposed method runs two to four times faster than the FBM-SA for horizontal (HH) polarization, and is about twice faster for vertical (VV) polarization. These features indicate that the proposed method can be effectively used to analyze electromagnetic scattering from 1-D dielectric Gaussian surfaces with both Gaussian and exponential spectra.