Two-scale Dirichlet–Neumann preconditioners for elastic problems with boundary refinements
Two-scale Dirichlet–Neumann preconditioners for elastic problems with boundary refinements
复制标题
用于边界细化弹性问题的两尺度 Dirichlet-Neumann 预条件子
DOI：
10.1016/j.cma.2006.03.021
复制
发表时间：
2007
影响因子：
7.2
通讯作者：
P. Tallec
中科院分区：
文献类型：
--
作者：
P. Hauret;P. Tallec
目前的工作涉及边界细化域上的弹性静力学问题的有效解决。所提出的方法通过砂浆法将边界细化与域内部分开，并使用狄利克雷-诺伊曼预处理器来求解相应的代数系统。我们证明最简单的狄利克雷-诺依曼算法实现了预处理系统的条件数与小细节的数量和大小的独立性。然而，当细化边界被钳制时，这种情况就不再存在。然后通过引入粗糙空间来设计增强的预处理器以减轻上述敏感性。进行了一些数值试验来证实分析，并且通过在非线性弹性情况下提出拟牛顿法来扩展工具。本文是 DD16 会议上提出的一项工作的扩展版本，包含证明和完整的数值结果。
The present work deals with the efficient resolution of elastostatics problems on domains with boundary refinements. The proposed approach separates the boundary refinements from the interior of the domain by the mortar method, and uses Dirichlet–Neumann preconditioners to solve the corresponding algebraic system. We prove that the simplest Dirichlet–Neumann algorithm achieves independence of the condition number of the preconditioned system with respect to the number and the size of the small details. Nevertheless, the situation no longer prevails when the refined boundary is clamped. An enhanced preconditioner is then designed by the introduction of a coarse space to mitigate the aforementioned sensitivity. Some numerical tests are performed to confirm the analysis, and the tools are extended by the proposition of a quasi-Newton method in the case of nonlinear elasticity. This paper is an extended version of a work presented at the DD16 conference with proofs and complete numerical results.