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.
Recommended Citation
Y. Zhu et al., "A Low-Rank Solver for the Stokes–Darcy Model with Random Hydraulic Conductivity and Beavers–Joseph Condition," Journal of Scientific Computing, vol. 107, no. 2, article no. 40, Springer, May 2026.
The definitive version is available at https://doi.org/10.1007/s10915-026-03246-3
Department(s)
Mathematics and Statistics
Keywords and Phrases
Beavers–Joseph interface condition; Karhunen–Loève expansion; Low-rank approximation; Monte Carlo finite element method; Stochastic Stokes–Darcy interface model
International Standard Serial Number (ISSN)
1573-7691; 0885-7474
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Springer, All rights reserved.
Publication Date
01 May 2026
