1 research outputs found
Unfitted Nitsche's method for computing band structures in phononic crystals with impurities
In this paper, we propose an unfitted Nitsche's method to compute the band
structures of phononic crystal with impurities of general geometry. The
proposed method does not require the background mesh to fit the interfaces of
impurities, 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 trace inequality,
and further prove the convergence by the Babu\v{s}ka-Osborn theory. We achieve
the optimal convergence rate at the presence of the impurities of general
geometry. We confirm the theoretical results by two numerical examples, and
show the capability of the proposed methods for computing the band structures
without fitting the interfaces of impurities.Comment: 20 page