论文标题
与海狸约瑟夫界面条件完全混合的随机stokes-darcy模型的集合域分解算法
Ensemble Domain Decomposition Algorithm for the Fully-mixed Random Stokes-Darcy Model with the Beavers-Joseph Interface Conditions
论文作者
论文摘要
在本文中，提出了一种有效的集合域分解算法，用于快速求解完全混合的随机stokes-darcy模型，该模型具有物理逼真的海狸 - 约瑟夫（BJ）界面条件。我们利用带有随机输入的耦合模型的蒙特卡洛方法来得出一些确定性的stokes-darcy数值模型，并使用集合的概念来实现多个问题的快速计算。该算法的一个显着特征是，多个线性系统在每个确定性数值模型中共享一个常见的系数矩阵，该模型可显着降低计算成本，并与传统方法达到可比的准确性。此外，通过域的分解，我们可以自然地将Stokes-Darcy系统分解为两个较小的子物理问题。通过选择合适的罗宾参数，严格得出了算法的网格依赖性和与网格独立的收敛速率。得出优化的罗宾参数并分析以加速所提出算法的收敛性。特别是，对于实践中小的水力电导率，几乎最佳的几何收敛可以通过有限元离散化获得。最后，进行了两组数值实验，以验证和说明所提出的算法的专有特征。
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.
