A low-rank solver for the Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916885167079424 |
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| author | Zhu, Yujun Ning, Yulan Yang, Zhipeng He, Xiaoming Ming, Ju |
| author_facet | Zhu, Yujun Ning, Yulan Yang, Zhipeng He, Xiaoming Ming, Ju |
| contents | This paper proposes, analyzes, and demonstrates an efficient low-rank solver for the stochastic Stokes-Darcy interface model with a random hydraulic conductivity both in the porous media domain and on the interface. We consider three interface conditions with randomness, including the Beavers-Joseph interface condition with the random hydraulic conductivity, on the interface between the free flow and the porous media flow. Our solver employs a novel generalized low-rank approximation of the large-scale stiffness matrices, which can significantly cut down the computational costs and memory requirements associated with matrix inversion without losing accuracy. Therefore, by adopting a suitable data compression ratio, the low-rank solver can maintain a high numerical precision with relatively low computational and space complexities. We also propose a strategy to determine the best choice of data compression ratios. Furthermore, we carry out the error analysis of the generalized low-rank matrix approximation algorithm and the low-rank solver. Finally, numerical experiments are conducted to validate the proposed algorithms and the theoretical conclusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A low-rank solver for the Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition Zhu, Yujun Ning, Yulan Yang, Zhipeng He, Xiaoming Ming, Ju Numerical Analysis This paper proposes, analyzes, and demonstrates an efficient low-rank solver for the stochastic Stokes-Darcy interface model with a random hydraulic conductivity both in the porous media domain and on the interface. We consider three interface conditions with randomness, including the Beavers-Joseph interface condition with the random hydraulic conductivity, on the interface between the free flow and the porous media flow. Our solver employs a novel generalized low-rank approximation of the large-scale stiffness matrices, which can significantly cut down the computational costs and memory requirements associated with matrix inversion without losing accuracy. Therefore, by adopting a suitable data compression ratio, the low-rank solver can maintain a high numerical precision with relatively low computational and space complexities. We also propose a strategy to determine the best choice of data compression ratios. Furthermore, we carry out the error analysis of the generalized low-rank matrix approximation algorithm and the low-rank solver. Finally, numerical experiments are conducted to validate the proposed algorithms and the theoretical conclusions. |
| title | A low-rank solver for the Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.05328 |