标题： 基于增广拉格朗日的块三阶线性系统预处理技术 显示英文标题

标题： An augmented Lagrangian-based preconditioning technique for a class of block three-by-three linear systems

摘要： 我们提出了一种基于增广拉格朗日的预条件器，以加速应用于具有块三对三结构的线性方程组的Krylov子空间方法的收敛，如从耦合Stokes-Darcy流问题的混合有限元离散化中产生的方程组。 我们分析了预条件矩阵的谱，并展示了新预条件器如何被高效应用。 报告了数值实验，以说明该预条件器与灵活GMRES结合在求解来自三维测试问题的线性方程组中的有效性。 显示英文摘要

摘要： 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.