Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations
Proper orthogonal decomposition is a popular approach for determining the principal spatial structures from the measured data. Generally, model reduction using empirical eigenfunctions (EEFs) can generate a relatively low-dimensional model among all linear expansions. However, the neglectful modes r...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/347248 |
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| author | Jun Shuai Xuli Han |
| author_facet | Jun Shuai Xuli Han |
| author_sort | Jun Shuai |
| collection | DOAJ |
| description | Proper orthogonal decomposition is a popular approach for determining the principal spatial structures from the measured data. Generally, model reduction using empirical eigenfunctions (EEFs) can generate a relatively low-dimensional model among all linear expansions. However, the neglectful modes representing only a tiny amount of energy will be crucial in the modeling for certain type of nonlinear partial differential equations (PDEs). In this paper, an optimal combination of EEFs is proposed for model reduction of nonlinear partial differential equations (PDEs), obtained by the basis function transformation from the initial EEFs. The transformation matrix is derived from straightforward optimization techniques. The present new EEFs can keep the dynamical information of neglectful modes and generate a lower-dimensional and more precise dynamical system for the PDEs. The numerical example shows its effectiveness and feasibility for model reduction of the nonlinear PDEs. |
| format | Article |
| id | doaj-art-a663f733a3624717a1a6ddf3d2a149c5 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a663f733a3624717a1a6ddf3d2a149c52025-02-03T01:09:49ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/347248347248Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential EquationsJun Shuai0Xuli Han1School of Mathematics and Statistics, Central South University, Changsha 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha 410083, ChinaProper orthogonal decomposition is a popular approach for determining the principal spatial structures from the measured data. Generally, model reduction using empirical eigenfunctions (EEFs) can generate a relatively low-dimensional model among all linear expansions. However, the neglectful modes representing only a tiny amount of energy will be crucial in the modeling for certain type of nonlinear partial differential equations (PDEs). In this paper, an optimal combination of EEFs is proposed for model reduction of nonlinear partial differential equations (PDEs), obtained by the basis function transformation from the initial EEFs. The transformation matrix is derived from straightforward optimization techniques. The present new EEFs can keep the dynamical information of neglectful modes and generate a lower-dimensional and more precise dynamical system for the PDEs. The numerical example shows its effectiveness and feasibility for model reduction of the nonlinear PDEs.http://dx.doi.org/10.1155/2013/347248 |
| spellingShingle | Jun Shuai Xuli Han Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations Journal of Applied Mathematics |
| title | Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations |
| title_full | Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations |
| title_fullStr | Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations |
| title_full_unstemmed | Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations |
| title_short | Optimal Combination of EEFs for the Model Reduction of Nonlinear Partial Differential Equations |
| title_sort | optimal combination of eefs for the model reduction of nonlinear partial differential equations |
| url | http://dx.doi.org/10.1155/2013/347248 |
| work_keys_str_mv | AT junshuai optimalcombinationofeefsforthemodelreductionofnonlinearpartialdifferentialequations AT xulihan optimalcombinationofeefsforthemodelreductionofnonlinearpartialdifferentialequations |