A Hybrid Conformal/Nonconformal Domain Decomposition Method for Multi-Region Electromagnetic Modeling
A Hybrid Conformal/Nonconformal Domain Decomposition Method for Multi-Region Electromagnetic Modeling
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DOI：
10.1109/tap.2014.2300149
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发表时间：
2014-01
影响因子：
5.7
通讯作者：
M. Xue;Jianming Jin
中科院分区：
文献类型：
--
作者：
M. Xue;Jianming Jin
本文提出了一种求解大规模多区域电磁场问题的统一框架--共形/非共形混合区域分解方法。在这种方法中，一个原始的电大问题首先根据它的几何形状被划分成几个区域。然后对每个区域进行网格化，并进一步分解成更小的子域。因此，分解问题在每个区域内是网格共形和几何共形的，但可以是两个相邻区域之间的网格非共形和几何非共形。为了解决这一问题，提出了一种混合方法，该方法采用有限元撕裂和互连(FETI)方法来处理网格-非共形和/或几何-非共形界面，其中应用二阶传输条件和交叉点校正技术来改善界面系统的迭代收敛，并确保子域界面之间的正确互连。对于每个区域内的网格-共形和几何-共形界面，混合方法采用双原始有限元撕裂和互连(FETI-DP)方法来构造有效的粗网格校正。对于非共形界面和共形界面的界面未知量，最终建立了统一的整体方程组。通过对宽带天线、复盖天线罩和近场焦透镜的相控阵天线的波传播和辐射仿真，验证了该方法的有效性。
This paper presents a unified framework for solving large-scale multi-region electromagnetic problems using a hybrid conformal/nonconformal domain decomposition method. In this method, an original electrically large problem is first divided into several regions based on its geometry. Each region is then meshed and further decomposed into smaller subdomains. As such, the decomposed problem is mesh-conformal and geometry-conformal within each region but could be mesh-nonconformal and geometry-nonconformal between two neighboring regions. To solve such a problem, a hybrid method is proposed that employs the finite-element tearing and interconnecting (FETI) method to deal with mesh-nonconformal and/or geometry-nonconformal interfaces, where a second-order transmission condition and a crosspoint correction technique are applied to improve the iterative convergence of the interface system and ensure a correct interconnection across subdomain interfaces. For mesh-conformal and geometry-conformal interfaces inside each region, the hybrid method employs the dual-primal finite element tearing and interconnecting (FETI-DP) method to construct an effective coarse grid correction for the interface problem. A unified global system of equations is finally formulated for the interface unknowns from both nonconformal and conformal interfaces. The proposed method is validated with simulation of wave propagation and radiation by broadband antennas and phased-array antennas covered with a radome and a near-field focal lens.