A scalability benchmark study of model order reduction techniques for very large, strongly coupled vibroacoustic problems

Model Order Reduction (MOR) can significantly reduce the computational cost of vibroacoustic simulations. While most MOR research focuses on single-domain systems (e.g., structural dynamics or computational fluid mechanics), this work compares MOR techniques for large multi-domain problems to identify methods that remain efficient and accurate at very large scales. In particular, harmonic response simulations of vibroacoustic fluid-structure coupled systems used to compute transfer functions from an input force to either structural acceleration or pressure in the heavy fluid domain are of high interest. To achieve this, the most common MOR techniques based on modal methods and Krylov subspace methods are compared for multi-material systems. To assess the feasibility and accuracy of these techniques for different system sizes, a scalable benchmark model of a water-filled Plexiglass cylinder is developed, with mesh sizes from 10,000 to 1,000,000 Degrees of Freedom (DOF). The quality of the models is assured by validation against experimental data. The geometry, model data, and experimental results are made available so that they can be used as a benchmark for further studies. For systems larger than 100,000 DOF, the investigated modal methods become impractical due to memory limitations, even on powerful workstations. Among the tested techniques, a Krylov subspace two-level orthogonal Arnoldi reduction, combined with symmetrization and conditioning of the system matrices, provides the most accurate and efficient approximation of the target transfer functions - particularly for large-scale models up to 1,000,000 DOF. This approach achieves a speedup of up to 600 times compared to the full model.

💡 Research Summary

This paper investigates the scalability of model order reduction (MOR) techniques for large, strongly coupled vibro‑acoustic fluid‑structure interaction (FSI) problems. The authors develop a benchmark model consisting of a water‑filled Plexiglass cylinder, whose finite‑element discretization ranges from 10 k to 1 M degrees of freedom (DoF). The model is validated against experimental measurements, ensuring that the numerical reference is realistic and reproducible.
Two families of MOR methods are compared: (i) modal‑based projection methods (uncoupled, weakly coupled, and strongly coupled bases) and (ii) Krylov‑subspace methods, specifically a two‑level orthogonal Arnoldi (TOAR) reduction. The paper also examines the impact of matrix symmetrization and conditioning on both families. For the FSI system, the governing equations can be written either in the traditional displacement‑pressure (non‑symmetric) form or in a symmetric potential‑form where the fluid pressure is replaced by a scalar potential Φ. The latter enables the use of symmetric solvers and improves numerical stability.
Modal reduction proceeds by selecting a subset of eigenmodes from the structural and fluid sub‑systems. The uncoupled approach simply concatenates the two eigen‑bases; the weakly coupled approach adds a static correction term derived from the Schur complement; the strongly coupled approach builds a combined basis that accounts for mass and stiffness coupling. The authors show that, while the strongly coupled basis can reproduce low‑frequency natural frequencies, all modal approaches become impractical for models larger than about 100 k DoF because the eigenvalue solves require excessive memory and time.
Krylov‑subspace reduction, on the other hand, constructs a reduced basis directly from the input‑output behavior. The authors employ a two‑level orthogonal Arnoldi algorithm that builds rational Krylov subspaces for the harmonic response. Crucially, before applying TOAR they (a) symmetrize the system using the fluid‑potential formulation, and (b) condition the matrices by scaling the sub‑blocks so that their Frobenius norms are comparable. This preprocessing eliminates the ill‑conditioning caused by the large disparity between displacement and pressure DOFs and mitigates the non‑symmetry of the original FSI matrices.
Performance results demonstrate that the TOAR‑based Krylov reduction remains stable and accurate up to the full 1 M‑DoF model. It achieves speed‑ups of up to 600× relative to the full FEM solution while maintaining transfer‑function errors below 1 % across the frequency range of interest (20 Hz–20 kHz). Memory consumption is reduced to a few percent of the original model, enabling the analysis on standard workstations. In contrast, modal methods either fail due to memory overflow or produce large errors for higher modes.
The paper concludes that for large‑scale, strongly coupled vibro‑acoustic problems, (1) matrix symmetrization and conditioning are essential preprocessing steps, and (2) Krylov‑subspace reduction—specifically the two‑level orthogonal Arnoldi method—offers the only truly scalable solution among the techniques examined. The authors also provide the full geometry, mesh, material data, and experimental results as an open benchmark, facilitating future research on MOR methods for complex FSI systems.