论文标题
块预先调节器，用于stokes-darcy方程的标记和细胞离散化
Block Preconditioners for the Marker-and-Cell Discretization of the Stokes-Darcy Equations
论文作者
论文摘要
我们考虑迭代解决大型稀疏的双鞍点系统，该系统由固定的stokes-darcy方程在二维中，由标记和细胞（MAC）有限差方法离散。我们分析了一些理想的块预处理的特征值分布。然后，我们得出基于在双鞍点矩阵的块分解中产生的Schur补充的近似值的实用预调节器。我们表明，包括预处理中的接口条件是追求可伸缩性的关键。数值结果显示了我们预处理的GMRE求解器的良好收敛行为，并证明了针对问题的物理参数的提出的预处理的鲁棒性。
We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes-Darcy equations in two dimensions, discretized by the Marker-and-Cell (MAC) finite difference method. We analyze the eigenvalue distribution of a few ideal block preconditioners. We then derive practical preconditioners that are based on approximations of Schur complements that arise in a block decomposition of the double saddle-point matrix. We show that including the interface conditions in the preconditioners is key in the pursuit of scalability. Numerical results show good convergence behavior of our preconditioned GMRES solver and demonstrate robustness of the proposed preconditioner with respect to the physical parameters of the problem.
