The FETI family of domain decomposition methods for inequality-constrained quadratic programming: Application to contact problems with conforming and nonconforming interfaces

Two domain decomposition methods with Lagrange multipliers for solving iteratively quadratic programming problems with inequality constraints are presented. These methods are based on the FETI and FETI-DP substructuring algorithms. In the case of linear constraints, they do not perform any Newton-like iteration. Instead, they solve a constrained problem by an active set strategy and a generalized conjugate gradient based descent method equipped with controls to guarantee convergence monotonicity. Both methods possess the desirable feature of minimizing numerical oscillations during the iterative solution process. Performance results and comparisons are reported for several numerical simulations that suggest that both methods are numerically scalable with respect to both the problem size and the number of subdomains. Their parallel scalability is also illustrated on a Linux cluster for a complex 1.4 million degree of freedom multibody problem with frictionless contact and nonconforming discrete interfaces.