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

Abstract

In this paper, we propose an unfitted Nitsche's method for computing wave modes in topological materials. The proposed method is based on 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 Nitsche's method on an unfitted uniform mesh. We prove the proposed methods converge optimally, and present numerical examples to validate the theoretical results and demonstrate the capability of simulating topological materials.