Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes

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• 作者：David Amsallem^a ; ^{amsallem@stanford.edu" class="auth_mail" title="E-mail the corresponding author} ; Radek Tezaur^a ; ^{rtezaur@stanford.edu" class="auth_mail" title="E-mail the corresponding author} ; Charbel Farhat^b ; ^{cfarhat@stanford.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Acoustic scattering ; Aeroelasticity ; Database of ROMs ; Interpolation ; Matrix manifold ; Mobile computing ; Parametric model order reduction ; Real-time computing ; Reduced-order model
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：326
• 期：Complete
• 页码：373-397
• 全文大小：5008 K

文摘

A comprehensive approach for real-time computations using a database of parametric, linear, projection-based reduced-order models (ROMs) based on arbitrary underlying meshes is proposed. In the offline phase of this approach, the parameter space is sampled and linear ROMs defined by linear reduced operators are pre-computed at the sampled parameter points and stored. Then, these operators and associated ROMs are transformed into counterparts that satisfy a certain notion of consistency. In the online phase of this approach, a linear ROM is constructed in real-time at a queried but unsampled parameter point by interpolating the pre-computed linear reduced operators on matrix manifolds and therefore computing an interpolated linear ROM. The proposed overall model reduction framework is illustrated with two applications: a parametric inverse acoustic scattering problem associated with a mockup submarine, and a parametric flutter prediction problem associated with a wing-tank system. The second application is implemented on a mobile device, illustrating the capability of the proposed computational framework to operate in real-time.