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 (BJ) 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 sub-physics 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 and illustrate the exclusive features of the proposed algorithm.

翻译：本文提出了一种高效的集成区域分解算法，用于快速求解具有物理实际意义的Beavers-Joseph（BJ）界面条件的全混合随机Stokes-Darcy模型。我们采用蒙特卡洛方法处理带随机输入的耦合模型，推导出若干确定性Stokes-Darcy数值模型，并利用集成思想实现多问题的快速计算。该算法的一个显著特点是每个确定性数值模型中多个线性系统共享一个共同的系数矩阵，这大幅降低了计算成本，同时保持了与传统方法相当的精度。此外，通过区域分解，我们能够自然地将Stokes-Darcy系统解耦为两个更小的子物理问题。通过选取合适的Robin参数，严格推导了该算法与网格相关和网格无关的收敛速率。推导并分析了优化后的Robin参数，以加速所提算法的收敛性。特别地，在实际中水力传导率较小的情况下，通过有限元离散可获得近似最优的几何收敛。最后，通过两组数值实验验证并展示了所提算法的独特性能。