Ensemble Domain Decomposition Algorithm for the Fully Mixed Random Stokes–Darcy Model with the Beavers–Joseph Interface Conditions

Abstract

In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully mixed random Stokes–Darcy model with the physically realistic Beavers–Joseph interface conditions. We utilize the Monte Carlo method for the coupled model with random inputs to derive some deterministic Stokes–Darcy numerical models and use the idea of the ensemble to realize the fast computation of multiple problems. One remarkable feature of the algorithm is that multiple linear systems share a common coefficient matrix in each deterministic numerical model, which significantly reduces the computational cost and achieves comparable accuracy with the traditional methods. Moreover, by domain decomposition, we can decouple the Stokes–Darcy system into two smaller subphysics problems naturally. Both mesh-dependent and mesh-independent convergence rates of the algorithm are rigorously derived by choosing suitable Robin parameters. Optimized Robin parameters are derived and analyzed to accelerate the convergence of the proposed algorithm. Especially, for small hydraulic conductivity in practice, the almost optimal geometric convergence can be obtained by finite element discretization. Finally, two groups of numerical experiments are conducted to validate the exclusive features of the proposed algorithm.