An Online Method for Interpolating Linear Parametric Reduced-Order Models

David Amsallem; Charbel Farhat

doi:10.1137/100813051

An Online Method for Interpolating Linear Parametric Reduced-Order Models

David Amsallem, Charbel Farhat

Research output: Contribution to journal › Article › peer-review

230 Scopus citations

Abstract

A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.

Original language	English (US)
Pages (from-to)	2169-2198
Number of pages	30
Journal	SIAM Journal on Scientific Computing
Volume	33
Issue number	5
DOIs	https://doi.org/10.1137/100813051
State	Published - Jan 2011
Externally published	Yes

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10.1137/100813051

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@article{c0580a079a1c4b1488ea183e6e6280de,

title = "An Online Method for Interpolating Linear Parametric Reduced-Order Models",

abstract = "A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. {\textcopyright} 2011 Society for Industrial and Applied Mathematics.",

author = "David Amsallem and Charbel Farhat",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Submitted to the journal's Computational Methods in Science and Engineering section October 27, 2010; accepted for publication (in revised form) June 3, 2011; published electronically September 1, 2011. This work was partially supported by a research grant from the Academic Excellence Alliance program between King Abdullah University of Science and Technology (KAUST) and Stanford University, by a research grant from King Abdulaziz City for Science and Technology (KACST), by The Boeing Company under contract 45047, and by the Air Force Office of Scientific Research under grant FA9550-10-1-0539. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2011",

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doi = "10.1137/100813051",

language = "English (US)",

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AU - Farhat, Charbel

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N2 - A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.

AB - A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.

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An Online Method for Interpolating Linear Parametric Reduced-Order Models

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