An improvement of generalized Bloch mode synthesis method-based model order reduction technique for band-structure computation of periodic structures

Abstract

In this paper, an improvement of generalized Bloch mode synthesis (GBMS) method-based model order reduction technique is presented for accelerating the band-structure computation of periodic structures. The improvement is implemented through employing firstly the algebraic substructuring, which enables the mass and stiffness matrices of a single unit cell partitioned into a set of small substructures automatically in the algebraic perspective without considering the physical domain. Then these substructures are reduced via the enhanced Craig-Bampton (ECB) method. The boundary sets are divided into interior boundary and exterior boundary components. The reduced interior modes and interior boundary sets are regarded as the new interior sets relative to the exterior boundary component, and its size can be further reduced via the second level ECB method. Local-level characteristic constraint (L-CC) mode reduction technique is employed for exterior boundary reduction for further reducing the computational cost. The coupling residual modes of the two-level ECB processes are compensated after imposing the Bloch boundary conditions. Two numerical examples are presented to demonstrate the potential benefits of the proposed GBMS-based model-order reduction technique in accelerating band-structure computation of periodic structures. The results show that the proposed method can effectively improve the computational efficiency and have good computational convergence compared with the generalized Bloch mode synthesis with algebraic condensation method.