Error estimates for model order reduction of Burgers' equation

M.H. Abbasi; L. Iapichino; B. Besselink; W. Schilders; N. van de Wouw

doi:10.1016/j.ifacol.2020.12.1575

Error estimates for model order reduction of Burgers' equation

M.H. Abbasi (Corresponding author), L. Iapichino, B. Besselink, W. Schilders, N. van de Wouw

Onderzoeksoutput: Bijdrage aan tijdschrift › Congresartikel › peer review

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Burgers' equation is a nonlinear scalar partial differential equation, commonly used as a testbed for model order reduction techniques and error estimates. Model order reduction of the parameterized Burgers' equation is commonly done by using the reduced basis method. In this method, an error estimate plays a crucial rule in both accelerating the offline phase and quantifying the error induced after reduction in the online phase. In this study, we introduce two new estimates for this reduction error. The first error estimate is based on a Lur'e-type model formulation of the system obtained after the full-discretization of Burgers' equation. The second error estimate is built upon snapshots generated in the offline phase of the reduced basis method. The second error estimate is applicable to a wider range of systems compared to the first error estimate. Results reveal that when conditions for the error estimates are satisfied, the error estimates are accurate and work efficiently in terms of computational effort.

Originele taal-2	Engels
Pagina's (van-tot)	5609-5616
Aantal pagina's	8
Tijdschrift	IFAC-PapersOnLine
Volume	53
Nummer van het tijdschrift	2
DOI's	https://doi.org/10.1016/j.ifacol.2020.12.1575
Status	Gepubliceerd - 2020
Evenement	21st World Congress of the International Federation of Aufomatic Control (IFAC 2020 World Congress) - Berlin, Duitsland Duur: 12 jul. 2020 → 17 jul. 2020 Congresnummer: 21 https://www.ifac2020.org/

Bibliografische nota

Publisher Copyright:
Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

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has received funding from the European Union’s Horizon 2020 r★esTeahrischreasnedaricnhnohvaastbioenenprcoagrrraiemd uountdeinr gtrhaenHt aYgDreRemAepnrtoNjeoct6,7w5h73ic1h. has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 675731.

Financiers	Financiernummer
European Union’s Horizon Europe research and innovation programme
European Union’s Horizon Europe research and innovation programme	675731

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abstract = "Burgers' equation is a nonlinear scalar partial differential equation, commonly used as a testbed for model order reduction techniques and error estimates. Model order reduction of the parameterized Burgers' equation is commonly done by using the reduced basis method. In this method, an error estimate plays a crucial rule in both accelerating the offline phase and quantifying the error induced after reduction in the online phase. In this study, we introduce two new estimates for this reduction error. The first error estimate is based on a Lur'e-type model formulation of the system obtained after the full-discretization of Burgers' equation. The second error estimate is built upon snapshots generated in the offline phase of the reduced basis method. The second error estimate is applicable to a wider range of systems compared to the first error estimate. Results reveal that when conditions for the error estimates are satisfied, the error estimates are accurate and work efficiently in terms of computational effort.",

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AU - Besselink, B.

AU - Schilders, W.

AU - van de Wouw, N.

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N2 - Burgers' equation is a nonlinear scalar partial differential equation, commonly used as a testbed for model order reduction techniques and error estimates. Model order reduction of the parameterized Burgers' equation is commonly done by using the reduced basis method. In this method, an error estimate plays a crucial rule in both accelerating the offline phase and quantifying the error induced after reduction in the online phase. In this study, we introduce two new estimates for this reduction error. The first error estimate is based on a Lur'e-type model formulation of the system obtained after the full-discretization of Burgers' equation. The second error estimate is built upon snapshots generated in the offline phase of the reduced basis method. The second error estimate is applicable to a wider range of systems compared to the first error estimate. Results reveal that when conditions for the error estimates are satisfied, the error estimates are accurate and work efficiently in terms of computational effort.

AB - Burgers' equation is a nonlinear scalar partial differential equation, commonly used as a testbed for model order reduction techniques and error estimates. Model order reduction of the parameterized Burgers' equation is commonly done by using the reduced basis method. In this method, an error estimate plays a crucial rule in both accelerating the offline phase and quantifying the error induced after reduction in the online phase. In this study, we introduce two new estimates for this reduction error. The first error estimate is based on a Lur'e-type model formulation of the system obtained after the full-discretization of Burgers' equation. The second error estimate is built upon snapshots generated in the offline phase of the reduced basis method. The second error estimate is applicable to a wider range of systems compared to the first error estimate. Results reveal that when conditions for the error estimates are satisfied, the error estimates are accurate and work efficiently in terms of computational effort.

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KW - Reduced basis method

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Error estimates for model order reduction of Burgers' equation

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