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In this paper, we propose an unfitted Nitsche's method for computing wavemodes in topological materials. The proposed method is based on Nitsche'stechnique to study the performance-enhanced topological materials which havestrongly heterogeneous structures (e.g., the refractive index is piecewiseconstant with high contrasts). For periodic bulk materials, we useFloquet-Bloch theory and solve an eigenvalue problem on a torus with unfittedmeshes. For the materials with a line defect, a sufficiently large domain withzero boundary conditions is used to compute the localized eigenfunctionscorresponding to the edge modes. The interfaces are handled by Nitsche's methodon an unfitted uniform mesh. We prove the proposed methods converge optimally,and present numerical examples to validate the theoretical results anddemonstrate the capability of simulating topological materials.

Unfitted Nitsche's method for computing wave modes in topological materials