Abstract
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.
Original language | English (US) |
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Pages (from-to) | 533-547 |
Number of pages | 15 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 203 |
Issue number | 2 SPEC. ISS. |
DOIs | |
State | Published - Jun 15 2007 |
Keywords
- Active sets
- Augmented Lagrangians
- Contact problems
- Path-following
- Primal-dual methods
- Semismooth Newton methods
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics