DC9 Model Order Reduction of coupled vibro-acoustic systems:

The vibro-acoustic field is a prime example where geometry-enhanced methods can have a strong influence on current applications. At mid- and high-frequency problems, where the acoustic wavelength is typically smaller or of the same order than the geometrical details within the object considered, the accuracy of the geometric representation is the driving factor for the analysis. To suppress the high computational burden, DC9 will work towards efficient model order reduction (MOR) schemes for one-way coupled and fully coupled vibro-acoustic analysis where the acoustic domain is described using an isogeometric boundary discretisation

Model order reduction of isogeometric BEM systems

In the first part of the PhD, DC9 worked on model order reduction strategies for the acoustic boundary element method within the IGA-framework (IGABEM) to speed-up the computational time and alleviate the memory costs. Specifically, an automatic MOR scheme based on Krylov subspaces recycling [1] is applied in conjunction with IGABEM to solve acoustic problems. The automatic MOR method automates the selection of Krylov subspaces to be recycled and creates a projection basis which sufficiently approximates the solution of the full-order model (FOM). The projection basis is used in combination with a Chebyshev polynomial approximation of the IGABEM system to create a reduced-order model (ROM), thus alleviating the computational burden.

In the following the presented method is investigated and verified by an analytical solution, the sphere. A plane wave with an unit amplitude is propagating through an unbounded air volume and is impinging from the left on a rigid sphere (particle velocity = 0 m/s for the entire boundary surface). The acoustic pressure is studied in a frequency range from 1 to 1000 Hz with a step size of 1 Hz. The sphere consists of 6 identical conforming patches and is modeled with NURBS polynomial of degree four. The sphere consists of 726 degrees of freedom (DoFs).

The following Figure shows that the sound pressure level (SPL) of the ROM matches that of the FOM, implying that the set threshold for the MOR method is sufficient. By inspecting the normalized residual for the defined frequency range, the residual is below the predefined tolerance. To generate the projection basis, the AKR algorithm only requires 3 full assemblies and 2 partial solutions, producing a basis spanning a subspace of 62 dimensions.

Figure 1: (a) Sound pressure level at an evaluated point; (b) Normalized residual error of the double layer potential of ROM; (c) Configuration for AKR with x(ω), ω ∈ Ω

References

[1] . Panagiotopoulos, W. Desmet, and E. Deckers, “An automatic krylov subspaces recycling technique for the construction of a global solution basis of non-affine parametric linear systems,” Computer Methods in Applied Mechanics and Engineering, vol. 373, p. 113510, 2021.