Topology Optimization of Defect State Phononic Crystal with Craig-Bampton Method
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The topology optimization of phononic crystal (PnC) defects requires repeated dispersion analyses of large-scale supercells, creating a severe computational bottleneck that limits practical design applications. To address this challenge, this work introduces the Craig-Bampton (CB) model order reduction method to significantly accelerate supercell eigenvalue analysis within the optimization loop. The primary efficiency gain is achieved through a localized sub-structuring strategy: the reduced-order model of the pristine base cell, which serves as the background, is computed only once at the beginning of the optimization. During subsequent iterations, only the localized defect cell undergoes CB decomposition. The resulting reduced matrices are then assembled with the pre-computed background matrices for global modal analysis. This mechanism ensures that only the modified portions of the supercell require re-computation, drastically reducing the numerical overhead of each iteration. Numerical examples demonstrate that the CB-based framework achieves a 7-fold speedup while maintaining high fidelity. Both the optimized topologies and their corresponding dispersion curves are nearly identical to full-order results. These results indicate that the CB-based reduction enables the practical optimization of larger supercells, such as 5×5 or beyond, for efficient and advanced defect mode engineering.
