A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems

Kevin Carlberg; Charbel Farhat

doi:10.1002/nme.3074

A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems

Kevin Carlberg, Charbel Farhat

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

88 Scopus citations

Abstract

A novel model reduction technique for static systems is presented. The method is developed using a goal-oriented framework, and it extends the concept of snapshots for proper orthogonal decomposition (POD) to include (sensitivity) derivatives of the state with respect to system input parameters. The resulting reduced-order model generates accurate approximations due to its goal-oriented construction and the explicit 'training' of the model for parameter changes. The model is less computationally expensive to construct than typical POD approaches, since efficient multiple right-hand side solvers can be used to compute the sensitivity derivatives. The effectiveness of the method is demonstrated on a parameterized aerospace structure problem. © 2010 John Wiley & Sons, Ltd.

Original language	English (US)
Pages (from-to)	381-402
Number of pages	22
Journal	International Journal for Numerical Methods in Engineering
Volume	86
Issue number	3
DOIs	https://doi.org/10.1002/nme.3074
State	Published - Dec 10 2010
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The first author acknowledges the partial support by a National Science Foundation Graduate Fellowship, and the partial support by a National Defense Science and Engineering Graduate Fellowship. The second author acknowledges the partial support by a research grant from the Academic Excellence Alliance program between King Abdullah University of Science and Technology (KAUST) and Stanford University. Both authors also acknowledge the partial support by the Motor Sports Division of the Toyota Motor Corporation under Agreement Number 48737. They thank Prof. Kurt Maute and his research group at the University of Colorado for providing the SDESIGN tool for managing shape parameters in their research, and Julien Cortial and David Amsallem at Stanford University for assisting in this research effort. This work received support from National Science Foundation (0540419).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1002/nme.3074

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title = "A low-cost, goal-oriented {\textquoteleft}compact proper orthogonal decomposition{\textquoteright} basis for model reduction of static systems",

abstract = "A novel model reduction technique for static systems is presented. The method is developed using a goal-oriented framework, and it extends the concept of snapshots for proper orthogonal decomposition (POD) to include (sensitivity) derivatives of the state with respect to system input parameters. The resulting reduced-order model generates accurate approximations due to its goal-oriented construction and the explicit 'training' of the model for parameter changes. The model is less computationally expensive to construct than typical POD approaches, since efficient multiple right-hand side solvers can be used to compute the sensitivity derivatives. The effectiveness of the method is demonstrated on a parameterized aerospace structure problem. {\textcopyright} 2010 John Wiley & Sons, Ltd.",

author = "Kevin Carlberg and Charbel Farhat",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The first author acknowledges the partial support by a National Science Foundation Graduate Fellowship, and the partial support by a National Defense Science and Engineering Graduate Fellowship. The second author acknowledges the partial support by a research grant from the Academic Excellence Alliance program between King Abdullah University of Science and Technology (KAUST) and Stanford University. Both authors also acknowledge the partial support by the Motor Sports Division of the Toyota Motor Corporation under Agreement Number 48737. They thank Prof. Kurt Maute and his research group at the University of Colorado for providing the SDESIGN tool for managing shape parameters in their research, and Julien Cortial and David Amsallem at Stanford University for assisting in this research effort. This work received support from National Science Foundation (0540419). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2010",

month = dec,

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doi = "10.1002/nme.3074",

language = "English (US)",

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journal = "International Journal for Numerical Methods in Engineering",

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N2 - A novel model reduction technique for static systems is presented. The method is developed using a goal-oriented framework, and it extends the concept of snapshots for proper orthogonal decomposition (POD) to include (sensitivity) derivatives of the state with respect to system input parameters. The resulting reduced-order model generates accurate approximations due to its goal-oriented construction and the explicit 'training' of the model for parameter changes. The model is less computationally expensive to construct than typical POD approaches, since efficient multiple right-hand side solvers can be used to compute the sensitivity derivatives. The effectiveness of the method is demonstrated on a parameterized aerospace structure problem. © 2010 John Wiley & Sons, Ltd.

AB - A novel model reduction technique for static systems is presented. The method is developed using a goal-oriented framework, and it extends the concept of snapshots for proper orthogonal decomposition (POD) to include (sensitivity) derivatives of the state with respect to system input parameters. The resulting reduced-order model generates accurate approximations due to its goal-oriented construction and the explicit 'training' of the model for parameter changes. The model is less computationally expensive to construct than typical POD approaches, since efficient multiple right-hand side solvers can be used to compute the sensitivity derivatives. The effectiveness of the method is demonstrated on a parameterized aerospace structure problem. © 2010 John Wiley & Sons, Ltd.

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A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems

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