Stable Model Reduction for Time‐Domain Room Acoustics: A Structure‐Preserving Formulation for Complex Boundaries

ABSTRACT This work presents novel structure‐preserving formulations for stable model order reduction in the context of time‐domain room acoustics simulations. A solution to address the instability in conventional model order reduction formulations based on the Linearized Euler Equations is derived and validated through numerical experiments. For the scenarios presented, the proposed formulation demonstrates 3.5 times speedup in calculating the full‐order model compared to the unstable formulation. A critical stability analysis is performed to identify the eigenvalues of the reduced operator matrices falling on the right half of complex plane along with their out of phase eigen angles as the source of instabilities in the reduced system. The performance of the proposed MOR formulation is tested for perfectly rigid, frequency‐independent, and locally reacting frequency‐dependent boundary conditions in two‐dimensional cases. The study shows that MOR using the stable formulation results in a 100‐fold speedup. The proposed formulation is further evaluated to assess its impact on accuracy, computational speedup, and overall reduction potential of the system.