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Stabilization of projection‐based reduced‐order models
Author(s) -
Amsallem David,
Farhat Charbel
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4274
Subject(s) - reduction (mathematics) , transonic , computational fluid dynamics , model order reduction , aeroelasticity , projection (relational algebra) , truncation (statistics) , computer science , supersonic speed , mathematics , mathematical optimization , algorithm , computational complexity theory , control theory (sociology) , aerodynamics , engineering , geometry , control (management) , machine learning , artificial intelligence , aerospace engineering
SUMMARY A rigorous method for stabilizing projection‐based linear reduced‐order models without significantly affecting their accuracy is proposed. Unlike alternative approaches, this method is computationally efficient. It requires primarily the solution of a small‐scale convex optimization problem. Furthermore, it is nonintrusive in the sense that it operates directly on readily available reduced‐order operators. These can be precomputed using any data compression technique including balanced truncation, balanced proper orthogonal decomposition, proper orthogonal decomposition, or moment matching. The proposed method is illustrated with three applications: the stabilization of the reduction of the Computational Fluid Dynamics‐based model of a linearized unsteady supersonic flow, the reduction of a Computational Structural Dynamics system, and the stabilization of the reduction of a coupled Computational Fluid Dynamics–Computational Structural Dynamics model of a linearized aeroelastic system in the transonic flow regime. Copyright © 2012 John Wiley & Sons, Ltd.