Bloch mode synthesis for band-structure computation of unit cell with non-matching boundaries

Abstract

Bloch mode synthesis is an efficient method to calculate the band property of periodic structures, which involves the repeated solution of many eigenvalue problems on each wave vector around the Brillouin zone. It is based on projecting internal degrees of freedom (DOFs) of the unit cell to the modal domain and keeping the boundary DOFs in the physical domain. While this transformation greatly reduces the model order of the unit cell, it leaves the question of how to impose the Floquet-Bloch boundary conditions when the boundary nodes are non-matching. In this paper, an interpolation-based method is proposed to address the non-conformity problem, which consists of building a smooth function by interpolating the variables on the master boundary and determining the variables on the slave boundary by sampling that smooth function. This procedure creates an interpolation matrix to connect the master and slave variables, which can be integrated into the original Bloch mode synthesis formulation to absolve the incompatibility caused by non-matching boundaries. The accuracy of the proposed method is verified using one non-conforming unit cell example in the end.