Abstract
The dual Schur complement domain decomposition method introduced recently by Farhat and Roux [4] turned out to be an efficient algorithm for parallel solution of self-adjoint elliptic partial differential equations. In this paper, we combine this approach with the Polyak type algorithms in order to solve quadratic programming problems arising in the solution of unilateral contact problems of linear elasticity. The main feature of our new algorithm for the solution of coercive problems is that it accepts approximate solutions of auxiliary minimization problems and that it is able to drop and add many constraints whenever the active set is changed. The algorithm for the solution of semi-coercive problems is also presented. The performance of the algorithms is demonstrated on the solution of model problems.
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