Unfitted Nitsche’s method for computing band structures of phononic crystals with periodic inclusions

In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with impurities general geometry. The proposed does not require background mesh fit interfaces impurities, and thus avoids expensive cost generating body-fitted meshes simplifies inclusion interface conditions in formulation. quasi-periodic boundary are handled by Floquet-Bloch transform, which converts computation into eigenvalue problem periodic conditions. More importantly, show well-posedness using a delicate argument based on trace inequality, further prove convergence Babu\v{s}ka-Osborn theory. We achieve optimal rate at presence confirm theoretical results two numerical examples, capability methods for computing without fitting impurities.