We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element discretizations of the coupled Stokes-Darcy flow problem. We analyze the spectrum of the preconditioned matrix and we show how the new preconditioner can be efficiently applied. Numerical experiments are reported to illustrate the effectiveness of the preconditioner in conjunction with flexible GMRES for solving linear systems of equations arising from a 3D test problem.

翻译：我们提出了一种基于增广拉格朗日的预处理技术，以加速Krylov子空间方法在求解具有三乘三分块结构的线性方程组时的收敛速度，该类线性方程组源自耦合Stokes-Darcy流问题的混合有限元离散。我们分析了预处理矩阵的谱特性，并展示了如何高效应用该新型预处理技术。通过数值实验展示了该预处理技术与灵活GMRES结合求解三维测试问题线性方程组的有效性。