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

TL;DR

This paper introduces an unfitted Nitsche's method for accurately computing wave modes in complex topological materials with heterogeneous structures, validated through theoretical convergence proofs and numerical experiments.

Contribution

It develops a novel unfitted Nitsche's method tailored for topological materials, enabling efficient and accurate eigenvalue computations on complex geometries.

Findings

Method converges optimally as proven theoretically.

Numerical examples validate the method's accuracy.

Capable of simulating wave modes in heterogeneous 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.