Solution of contact problems by FETI domain decomposition with natural coarse space projections

Abstract

An efficient non-overlapping domain decomposition algorithm of the Neumann–Neumann type for solving both coercive and semicoercive contact problems is presented. The discretized problem is first turned by the duality theory of convex programming to the quadratic programming problem with bound and equality constraints and the latter is further modified by means of orthogonal projectors to the natural coarse space introduced by Farhat and Roux in the framework of their FETI method. The resulting problem is then solved by an augmented Lagrangian type algorithm with an outer loop for the Lagrange multipliers for the equality constraints and an inner loop for the solution of the bound constrained quadratic programming problems. The projectors are shown to guarantee fast convergence of iterative solution of auxiliary linear problems and to comply with efficient quadratic programming algorithms proposed earlier. Reported theoretical results and numerical experiments indicate high numerical scalability of the algorithm which preserves the parallelism of the FETI methods.