Parallel solution of contact problems

An efficient non-overlapping domain decomposition algorithm of the Neumann-Neumann type for solving both coercive and semicoercive frictionless contact problems of elasticity has been recently presented. The method reduces, by the duality theory of convex programming, the discretized problem to a quadratic programming problem with simple bounds and equality constraints on the contact interface. This dual problem is further modified by means of orthogonal projectors to the natural coarse space, and the resulting problem is solved by an augmented Lagrangian type algorithm. The projectors guarantee an optimal rate of convergence for the solution of auxiliary linear problems by the conjugate gradients method. With this approach, it is possible to deal separately with each body or subdomain, so that the algorithm can be implemented in parallel. In this paper, an efficient parallel implementation of this method is presented, together with numerical experiments that indicate the high parallel scalability of the algorithm.