SIE-DDM Based on a Hybrid Direct–Iterative Approach for Analysis of Multiscale Problems
SIE-DDM Based on a Hybrid Direct–Iterative Approach for Analysis of Multiscale Problems
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DOI：
10.1109/tap.2019.2932854
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发表时间：
2019-08
影响因子：
5.7
通讯作者：
M. Jiang;Zhi Rong;L. Lei;Xianjin Li;Yongpin P. Chen;Sheng Sun;Z. Nie;Jun Hu
中科院分区：
文献类型：
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作者：
M. Jiang;Zhi Rong;L. Lei;Xianjin Li;Yongpin P. Chen;Sheng Sun;Z. Nie;Jun Hu
本文提出了一种基于直接迭代混合算法的多尺度电磁场数值模拟的表面积分方程区域分解方法。SIE-DDM矩阵系统的求解通常采用内外环策略。因此，在每个分解域中，直接方法优于子求解器。在这里，一个快速的直接方法的基础上增强的层次非对角低秩（HODLR）格式，涉及扩展的容许条件（EAC）作为一种替代的子求解器，其中提出了一个重建和再压缩技术（RRT）。通过使用该技术，可以进一步提高效率和准确性。每个子区域的逆元采用Sherman-Morrison-伍德伯里算法（SMWA）求解，而全局系统仍采用迭代法求解。这种混合框架充分利用了迭代方法和直接方法的优势。另一方面，快速直接求解器为矩阵系统提供了一个鲁棒的预条件子，特别是对于病态的情况。几个数值例子将演示所提出的方法。
In this article, surface integral equation domain decomposition method (SIE-DDM) based on a hybrid direct–iterative approach is proposed for multiscale electromagnetic simulation. The solution of SIE-DDM matrix system is typically built on the strategy of inner-outer loop. Therefore, the direct approach is preferred to the subsolver in each decomposed domain. Here, a fast direct approach based on an enhanced hierarchically off-diagonal low-rank (HODLR) format involving extended admissibility condition (EAC) is present as an alternative subsolver, in which a reconstructing and recompression technique (RRT) is proposed. The efficiency and accuracy can be further improved by using this technology. The inverse of each subdomain is obtained by Sherman–Morrison–Woodbury algorithm (SMWA), while the global system is still solved by the iterative method. This hybrid framework makes full use of strengths of terative and direct approaches. On the other hand, the fast direct solver provides a robust preconditioner for the matrix system, especially for ill-conditioned cases. Several numerical examples will demonstrate the proposed method.