Model order reduction for unbounded second-order vibroacoustic systems using infinite elements and Dirichlet-to-Neumann map

This work addresses the efficient numerical simulation of time-harmonic vibroacoustic problems in unbounded domains, with a focus on fluid-structure interaction. The underlying mathematical model is a second-order dynamical system arising from the coupling of structural and acoustic domains, incorporating material damping effects, relevant in structural acoustics and noise control applications. A central novelty of the proposed method is its unified computational framework that supports two distinct strategies for treating unbounded fluid domains: (1) non-local absorbing boundary conditions based on Dirichlet-to-Neumann map, and (2) infinite elements, which extend the computational domain rather than truncate it. Both approaches are integrated into a consistent formulation that enables flexible and accurate modeling of exterior wave propagation. To efficiently evaluate frequency-domain transfer functions, the method employs model order reduction using the Padé-via-Lanczos technique. While this algorithm typically targets first-order systems, the present approach uses a Schur complement strategy to reduce the second-order system in a way that maintains computational efficiency and storage requirements comparable to first-order formulations. Importantly, the framework seamlessly embeds both interior structural damping and the additional dissipation introduced by the acoustic-domain truncation into the model-order reduction process. The exterior acoustic field is represented via spherical harmonic expansions, with expansion coefficients computed from the reduced system. Numerical results demonstrate the method’s accuracy, efficiency, and scalability, making it well-suited for high-fidelity vibroacoustic analysis in unbounded domains.