Improving the generalized Bloch mode synthesis method using algebraic condensation

Abstract

The generalized Bloch mode synthesis (GBMS) is an efficient model-order reduction technique to reduce the computational cost for band-structure calculations of periodic media. In this article, an attempt is made to improve the computational performance of the GBMS method by employing algebraic condensation (AC). The interior component of the unit cell is firstly partitioned into a set of small substructures automatically in the algebraic domain, and these substructures are then absorbed into boundary sets by using the improved reduced system (IRS) method. The boundary degrees of freedom (DOFs) are subsequently reduced via the enhanced Craig–Bampton (ECB) method and the local-level characteristic constraint mode reduction, respectively. The coupling residual modes of IRS and ECB processes are then compensated after imposing the Bloch boundary conditions. Through several numerical examples, the performance of the proposed method is demonstrated in terms of accuracy and computational cost. The influence of partitioned numbers on the computational efficiency of the proposed method is finally discussed. The numerical results show that the computational efficiency of the GBMS method can be greatly enhanced by using AC for the unit cells with relatively large DOFs or with dense meshes of the exterior boundary, which hence extends the application scope of the GBMS method.