Unfitted Nitsche's method for computing band structures of phononic crystals with periodic inclusions
Hailong Guo, Xu Yang, Yi Zhu
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | ELSEVIER SCIENCE SA | Published : 2021
In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with periodic inclusions of general geometry. The proposed method does not require the background mesh to fit the interfaces of periodic inclusions, and thus avoids the expensive cost of generating body-fitted meshes and simplifies the inclusion of interface conditions in the formulation. The quasi-periodic boundary conditions are handled by the Floquet–Bloch transform, which converts the computation of band structures into an eigenvalue problem with periodic boundary conditions. More importantly, we show the well-posedness of the proposed method using a delicate argument based on the tr..View full abstract
Awarded by National Science Foundation, USA
Awarded by National Natural Science Foundation of China
H.G. was partially supported by Andrew Sisson Fund of the University of Melbourne, Australia, X.Y. was partially supported by the National Science Foundation, USA under grant DMS-1818592, and Y.Z. was partially supported by National Natural Science Foundation of China under grant 11871299.