A low-rank solver for the Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition
Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Zhu, Yujun, Ning, Yulan, Yang, Zhipeng, He, Xiaoming, Ming, Ju
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979298510
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