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.

在本文中，我们提出了一种未拟合的 Nitsche 方法来计算拓扑材料中的波模式。所提出的方法是基于 Nitsche 的技术来研究具有强异质结构（例如，折射率是具有高对比度的分段常数）的性能增强拓扑材料。对于周期性散装材料，我们使用 Floquet-Bloch 理论并解决具有未拟合网格的环面上的特征值问题。对于具有线缺陷的材料，使用具有零边界条件的足够大的域来计算对应于边缘模式的局部特征函数。接口由 Nitsche 方法在未拟合的均匀网格上处理。我们证明了所提出的方法最优收敛。