Structure-preserved MOR method for coupled systems via orthogonal polynomials and Arnoldi algorithm
This study focuses on the topic of model order reduction (MOR) for coupled systems with inhomogeneous initial conditions and presents an MOR method by general orthogonal polynomials with Arnoldi algorithm. The main procedure is to use a series of expansion coefficients vectors in the space spanned b...
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| Veröffentlicht in: | IET circuits, devices & systems Jg. 13; H. 6; S. 879 - 887 |
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The Institution of Engineering and Technology
01.09.2019
John Wiley & Sons, Inc |
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| Abstract | This study focuses on the topic of model order reduction (MOR) for coupled systems with inhomogeneous initial conditions and presents an MOR method by general orthogonal polynomials with Arnoldi algorithm. The main procedure is to use a series of expansion coefficients vectors in the space spanned by orthogonal polynomials that satisfy a recursive formula to generate a projection based on the multiorder Arnoldi algorithm. The resulting model not only match desired number of expansion coefficients but also has the same coupled structure as the original system. Moreover, the stability is preserved as well. The error bound between the outputs is well-discussed. Finally, numerical results show that the authors’ method can deal well with those systems with inhomogeneous initial conditions in the views of accuracy and computational cost. |
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| AbstractList | This study focuses on the topic of model order reduction (MOR) for coupled systems with inhomogeneous initial conditions and presents an MOR method by general orthogonal polynomials with Arnoldi algorithm. The main procedure is to use a series of expansion coefficients vectors in the space spanned by orthogonal polynomials that satisfy a recursive formula to generate a projection based on the multiorder Arnoldi algorithm. The resulting model not only match desired number of expansion coefficients but also has the same coupled structure as the original system. Moreover, the stability is preserved as well. The error bound between the outputs is well‐discussed. Finally, numerical results show that the authors’ method can deal well with those systems with inhomogeneous initial conditions in the views of accuracy and computational cost. |
| Author | Jiang, Yao-Lin Xiao, Zhi-Hua Qi, Zhen-Zhong |
| Author_xml | – sequence: 1 givenname: Zhen-Zhong surname: Qi fullname: Qi, Zhen-Zhong email: grygera2@sina.com.cn organization: 1Department of Mathematics, Northwest University, Xi'an, Shaanxi 710127, People's Republic of China – sequence: 2 givenname: Yao-Lin surname: Jiang fullname: Jiang, Yao-Lin organization: 2Department of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, People's Republic of China – sequence: 3 givenname: Zhi-Hua surname: Xiao fullname: Xiao, Zhi-Hua organization: 3School of Information and Mathematics, Yangtze University, Jingzhou, Hubei 434023, People's Republic of China |
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| Cites_doi | 10.1007/BF02523124 10.1109/TCSI.2003.809807 10.1007/978-3-540-78841-6_14 10.1016/j.laa.2005.04.032 10.1080/13873954.2015.1065279 10.1016/j.camwa.2011.08.039 10.1109/TCPMT.2012.2204393 10.1109/TAC.1981.1102568 10.1007/s00211-010-0352-1 10.1080/00207728608926920 10.1002/oca.854 10.1016/j.jfranklin.2014.02.014 10.1049/iet-cds.2016.0430 10.1007/978-3-540-78841-6_18 10.1007/978-3-540-78841-6_7 10.1016/j.automatica.2010.12.002 10.1016/j.sysconle.2016.04.005 10.1109/43.45867 10.1016/j.sysconle.2016.11.007 10.1080/13873954.2013.867274 10.1002/rnc.3075 10.1080/00207728708967185 10.1016/S0045-7825(00)00391-1 10.1017/S0962492902000120 10.1090/coll/023 10.1007/978-3-540-78841-6_1 10.1109/TAC.2011.2161839 10.1093/oso/9780198506720.001.0001 |
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| Keywords | general orthogonal polynomials recursive formula polynomials model order reduction inhomogeneous initial conditions multiorder Arnoldi algorithm reduced order systems expansion coefficients vectors coupled structure structure-preserved MOR method coupled systems |
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| SubjectTerms | Algorithms Approximation coupled structure coupled systems expansion coefficients vectors general orthogonal polynomials inhomogeneous initial conditions Initial conditions Linear equations Methods model order reduction Model reduction multiorder Arnoldi algorithm Ordinary differential equations Partial differential equations Polynomials recursive formula reduced order systems Research Article structure-preserved MOR method |
| Title | Structure-preserved MOR method for coupled systems via orthogonal polynomials and Arnoldi algorithm |
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