Stabilization of projection‐based reduced‐order models |
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| Authors: | David Amsallem Charbel Farhat |
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| Affiliation: | 1. Department of Aeronautics and Astronautics, Stanford University, , Stanford, CA 94305, U.S.A.;2. Department of Mechanical Engineering, Stanford University, , Stanford, CA 94305, U.S.A.;3. Institute for Computational and Mathematical Engineering, Stanford University, , Stanford, CA 94305, U.S.A. |
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| Abstract: | 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. |
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| Keywords: | convex optimization linear time‐invariant systems model reduction projection methods |
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