标题： 最优且可扩展的虚域问题增广拉格朗日预条件器 显示英文标题

标题： Optimal and Scalable Augmented Lagrangian preconditioners for Fictitious Domain problems

摘要： 我们提出最优且可扩展的预处理技术，以解决来自虚构域问题和浸入边界方法的有限元离散化所产生的一类具有块二乘二和三乘三结构的线性方程组。 特别是，我们提出了两种基于增广拉格朗日的预处理器，以加速这两种类型线性问题的迭代求解器的收敛。 我们考虑两个相关的例子，以说明在与灵活GMRES结合使用时这些预处理器的性能：泊松和斯托克斯虚构域问题。 为这些预处理器的精确和不精确版本建立了谱分析。 我们通过在二维和三维中的大量数值测试，展示了所提出方法的有效性和预处理策略的鲁棒性。 显示英文摘要

摘要： We present optimal and scalable preconditioning techniques to solve linear systems of equations with a block two-by-two and three-by-three structure arising from fictitious domain problems and from finite element discretizations of immersed boundary methods. In particular, we propose two augmented Lagrangian-based preconditioners to accelerate the convergence of iterative solvers for these two classes of linear. We consider two relevant examples to illustrate the performance of these preconditioners when used in conjunction with flexible GMRES: the Poisson and the Stokes fictitious domain problems. A spectral analysis is established for both exact and inexact versions of these preconditioners. We show the effectiveness of the proposed approach and the robustness of our preconditioning strategy through extensive numerical tests in both two and three dimensions.