A low-rank solver for the Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition

TL;DR

This paper introduces an efficient low-rank solver for the stochastic Stokes-Darcy model with random hydraulic conductivity, reducing computational costs while maintaining accuracy through generalized low-rank matrix approximation.

Contribution

It develops a novel low-rank approximation method for large-scale matrices in the stochastic Stokes-Darcy model with interface conditions, including Beavers-Joseph, enhancing computational efficiency.

Findings

The low-rank solver significantly reduces computational time.

The method maintains high accuracy with appropriate data compression.

Numerical experiments validate the theoretical error analysis.

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.