Error Estimation and Stopping Criteria for Krylov-Based Model Order Reduction in Acoustics
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912156068347904 |
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| author | Hu, Siyang Wulbusch, Nick Chernov, Alexey Bechtold, Tamara |
| author_facet | Hu, Siyang Wulbusch, Nick Chernov, Alexey Bechtold, Tamara |
| contents | Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second order linear dynamical system with sparse matrices, mathematical model order reduction provides an interesting possibility to speed up the simulation process. In this work, we tackle the question of finding an optimal order for the reduced system, given a desired accuracy. To do so, we revisit a heuristic error estimator based on the difference of two reduced models from two consecutive Krylov iterations. We perform a mathematical analysis of the estimator and show that the difference of two consecutive reduced models does provide a sufficiently accurate estimation for the true model reduction error. This claim is supported by numerical experiments on two acoustic models. We briefly discuss its feasibility as a stopping criterion for Krylov-based model order reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error Estimation and Stopping Criteria for Krylov-Based Model Order Reduction in Acoustics Hu, Siyang Wulbusch, Nick Chernov, Alexey Bechtold, Tamara Numerical Analysis Systems and Control Dynamical Systems 37M05, 65P99, 33J05 Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second order linear dynamical system with sparse matrices, mathematical model order reduction provides an interesting possibility to speed up the simulation process. In this work, we tackle the question of finding an optimal order for the reduced system, given a desired accuracy. To do so, we revisit a heuristic error estimator based on the difference of two reduced models from two consecutive Krylov iterations. We perform a mathematical analysis of the estimator and show that the difference of two consecutive reduced models does provide a sufficiently accurate estimation for the true model reduction error. This claim is supported by numerical experiments on two acoustic models. We briefly discuss its feasibility as a stopping criterion for Krylov-based model order reduction. |
| title | Error Estimation and Stopping Criteria for Krylov-Based Model Order Reduction in Acoustics |
| topic | Numerical Analysis Systems and Control Dynamical Systems 37M05, 65P99, 33J05 |
| url | https://arxiv.org/abs/2412.10559 |