Path-following and augmented Lagrangian methods for contact problems in linear elasticity |
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Authors: | Georg Stadler |
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Institution: | Center of Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal |
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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. |
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Keywords: | 49M15 74M15 49M37 65K05 |
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