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

Sander Metting van Rijn, Linus Taenzer, Paolo Tiso, Bart Van Damme

Abstract

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.

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

Abstract

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.
Paper Structure (24 sections, 44 equations, 11 figures, 2 tables)

This paper contains 24 sections, 44 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Model order reduction approaches for dynamic systems with fluid structure interaction
  3. Description of the full dynamic system
  4. Unsymmetric formulation
  5. Symmetric formulation
  6. Matrix conditioning
  7. Projection-based reduced order modeling for FSI problems
  8. Modal methods
  9. Uncoupled bases
  10. Weakly Coupled Bases
  11. Strongly coupled bases
  12. Uncoupled bases extended by residual modes iteration (RMI)
  13. Iterative reduced correction algorithm (IRCA)
  14. Krylov subspace method
  15. Computational complexity due to the matrix inversion
  16. ...and 9 more sections

Figures (11)

  • Figure 1: Comparison of the eigenfrequencies of the first 20 modes using different modal methods. Only the strongly coupled basis leads to matching frequencies for all modes, the other bases skip several modes predicted by the full solution in this case of heavy fluid loading.
  • Figure 2: Left: Experimental setup of the water-filled cylinder including measurement positions of the accelerometer (A) and the hydrophone (H). Right: List of material properties of the cylinder.
  • Figure 3: The experimental setup for the water-filled cylinder on the vibration isolation table, illustrating boundary conditions, measurements devices and the type and position of the excitation.
  • Figure 4: Illustration of two FE models that are investigated in this work. Shown are the 30k (a) and 1000k (b) DOF systems, including both the fluid and solid domain.
  • Figure 5: Structural domain validation: The magnitude of the frequency response function (a) and its phase (b) are shown for the transfer path between the input force and the accelerometer at position 4 in Fig. \ref{['Fig:Experimental_setup']}.
  • ...and 6 more figures