A Reduced Order Modeling Method with Variable-Separation-Based Domain Decomposition for Parametric Dynamical Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918328376754176 |
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| author | Ba, Yuming Chen, Liang Chen, Yaru Li, Qiuqi |
| author_facet | Ba, Yuming Chen, Liang Chen, Yaru Li, Qiuqi |
| contents | This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing frequency variables and parameters inherited from the original model. To reduce the computational cost of the frequency-variable elliptic equations, we extend the variable-separation-based domain decomposition method to the complex-valued context, resulting in an offline-online procedure for solving the parametric dynamical systems. At the offline stage, separate representations of the solutions for the interface problem and the subproblems are constructed. At the online stage, the solutions of the parametric dynamical systems for new parameter values can be directly derived by utilizing the separate representations and implementing the inverse Fourier transform. The proposed approach is capable of being highly efficient because the online stage is independent of the spatial discretization. Finally, we present three specific instances of parametric dynamical systems to demonstrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Reduced Order Modeling Method with Variable-Separation-Based Domain Decomposition for Parametric Dynamical Systems Ba, Yuming Chen, Liang Chen, Yaru Li, Qiuqi Numerical Analysis 35R60, 37M99, 65P99 This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing frequency variables and parameters inherited from the original model. To reduce the computational cost of the frequency-variable elliptic equations, we extend the variable-separation-based domain decomposition method to the complex-valued context, resulting in an offline-online procedure for solving the parametric dynamical systems. At the offline stage, separate representations of the solutions for the interface problem and the subproblems are constructed. At the online stage, the solutions of the parametric dynamical systems for new parameter values can be directly derived by utilizing the separate representations and implementing the inverse Fourier transform. The proposed approach is capable of being highly efficient because the online stage is independent of the spatial discretization. Finally, we present three specific instances of parametric dynamical systems to demonstrate the effectiveness of the proposed method. |
| title | A Reduced Order Modeling Method with Variable-Separation-Based Domain Decomposition for Parametric Dynamical Systems |
| topic | Numerical Analysis 35R60, 37M99, 65P99 |
| url | https://arxiv.org/abs/2508.17276 |