Stability‐preserving model order reduction for time‐domain simulation of vibro‐acoustic FE models

• Published in: International journal for numerical methods in engineering 2017-02, Vol.109 (6), p.889-912
• Main Authors: Walle, A., Naets, F., Deckers, E., Desmet, W.
• Format: Article
• Language: English
• Subjects: Computer simulation; Finite element method; Mathematical models; model reduction; Order reduction; Preservation; Projection; Stability; Time domain; vibro‐acoustics
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.5323

Summary This work proposes novel stability‐preserving model order reduction approaches for vibro‐acoustic finite element models. As most research in the past for these systems has focused on noise attenuation in the frequency‐domain, stability‐preserving properties were of low priority. However, as the interest for time‐domain auralization and (model based) active noise control increases, stability‐preserving model order reduction techniques are becoming indispensable. The original finite element models for vibro‐acoustic simulation are already well established but require too much computational load for these applications. This work therefore proposes two new global approaches for the generation of stable reduced‐order models. Based on proven conditions for stability preservation under one‐sided projection, a reformulation of the displacement‐fluid velocity potential (u − ϕ) formulation is proposed. In contrast to the regular formulation, the proposed approach leads to a new asymmetric structure for the system matrices which is proven to preserve stability under one‐sided projection. The second approach starts from a displacement‐pressure (u − p) description where the system level projection space is decoupled for the two domains, for which we also prove the preservation of stability. Two numerical validation cases are presented which demonstrate the inadequacy of straightforward model order reduction on typical vibro‐acoustic models for time‐domain simulation and compare the performance of the proposed approaches. Both proposed approaches effectively preserve the stability of the original system. Copyright © 2016 John Wiley & Sons, Ltd.