Path-following and augmented Lagrangian methods for contact problems in linear elasticity
- 作者：Georg Stadler
- 关键词：Contact problems ; Path-following ; Semismooth Newton methods ; Active sets ; Augmented Lagrangians ; Primal– ; dual methods
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2007
- 期刊代码：72_03770427
- 类别：cp
- 出版时间：15 June 2007
- 卷：203
- 期：2
- 页码：533-547
- 文件大小：753 K
摘要
A certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite-dimensional semismooth Newton methods, or in this case equivalently, primal–dual active set strategies. We present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem: first-order augmented Lagrangian, and path-following methods. The first strategy is based on a multiplier-update, while path-following with respect to the regularization parameter uses theoretical results about the path-value function to increase the regularization parameter appropriately. Comprehensive numerical tests investigate the performance of the proposed strategies for both a 2D as well as a 3D contact problem.