Unfitted Nitsche’s Method for Computing Wave Modes in Topological Materials
Unfitted Nitsche’s Method for Computing Wave Modes in Topological Materials
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DOI：
10.1007/s10915-021-01540-w
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发表时间：
2019-08
影响因子：
2.5
通讯作者：
Hailong Guo;Xu Yang;Yi Zhu
中科院分区：
文献类型：
--
作者：
Hailong Guo;Xu Yang;Yi Zhu
本文提出了一种计算拓扑材料中波模的非拟合Nitsche方法。所提出的方法是基于Nitsche的技术来研究具有强异质结构的性能增强拓扑材料（例如，折射率是分段恒定的，具有高对比度）。对于周期性块体材料，我们使用Floquet-Bloch理论，并解决了一个特征值问题的环面与非拟合网格。对于具有线缺陷的材料，使用一个足够大的零边界条件的区域来计算对应于边缘模式的局域本征函数。在不拟合的均匀网格上，用Nitsche方法处理界面。我们证明了所提出的方法最优收敛。数值算例验证了理论结果，并展示了该方法模拟拓扑材料的能力。
In this paper, we propose an unfitted Nitsche’s method for computing wave modes in topological materials. The proposed method is based on the Nitsche’s technique to study the performance-enhanced topological materials which have strongly heterogeneous structures (e.g., the refractive index is piecewise constant with high contrasts). For periodic bulk materials, we use Floquet-Bloch theory and solve an eigenvalue problem on a torus with unfitted meshes. For the materials with a line defect, a sufficiently large domain with zero boundary conditions is used to compute the localized eigenfunctions corresponding to the edge modes. The interfaces are handled by the Nitsche’s method on an unfitted uniform mesh. We prove the proposed methods converge optimally. Several numerical examples are presented to validate the theoretical results and demonstrate the capability of simulating topological materials.