A posteriori error estimation for model order reduction of parametric systems
Abstract This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most relate...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-03-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s40323-024-00260-8 |
| _version_ | 1797259165741088768 |
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| author | Lihong Feng Sridhar Chellappa Peter Benner |
| author_facet | Lihong Feng Sridhar Chellappa Peter Benner |
| author_sort | Lihong Feng |
| collection | DOAJ |
| description | Abstract This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the vector space $${\mathbb {C}}^n$$ C n and provide the corresponding proofs in $$\mathbb C^n$$ C n . Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for three examples show the robustness of the new error estimator. |
| first_indexed | 2024-04-24T23:05:06Z |
| format | Article |
| id | doaj.art-a0224ff6d8684e3c8b562ecd3046629f |
| institution | Directory Open Access Journal |
| issn | 2213-7467 |
| language | English |
| last_indexed | 2024-04-24T23:05:06Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advanced Modeling and Simulation in Engineering Sciences |
| spelling | doaj.art-a0224ff6d8684e3c8b562ecd3046629f2024-03-17T12:33:03ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672024-03-0111113410.1186/s40323-024-00260-8A posteriori error estimation for model order reduction of parametric systemsLihong Feng0Sridhar Chellappa1Peter Benner2Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical SystemsComputational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical SystemsComputational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical SystemsAbstract This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the vector space $${\mathbb {C}}^n$$ C n and provide the corresponding proofs in $$\mathbb C^n$$ C n . Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for three examples show the robustness of the new error estimator.https://doi.org/10.1186/s40323-024-00260-8A posteriori error estimationParametric systemsModel order reduction |
| spellingShingle | Lihong Feng Sridhar Chellappa Peter Benner A posteriori error estimation for model order reduction of parametric systems Advanced Modeling and Simulation in Engineering Sciences A posteriori error estimation Parametric systems Model order reduction |
| title | A posteriori error estimation for model order reduction of parametric systems |
| title_full | A posteriori error estimation for model order reduction of parametric systems |
| title_fullStr | A posteriori error estimation for model order reduction of parametric systems |
| title_full_unstemmed | A posteriori error estimation for model order reduction of parametric systems |
| title_short | A posteriori error estimation for model order reduction of parametric systems |
| title_sort | posteriori error estimation for model order reduction of parametric systems |
| topic | A posteriori error estimation Parametric systems Model order reduction |
| url | https://doi.org/10.1186/s40323-024-00260-8 |
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