TFETI Scalable Solvers for Transient Contact Problems

Abstract

We review our results obtained by application of the TFETI domain decomposition method to implement the time step of the Newmark scheme for the solution of transient contact problems without friction. If the ratio of the decomposition and discretization parameters is kept uniformly bounded as well as the ratio of the time and space discretization, then the cost of the time step is proved to be proportional to the number of nodal variables. The algorithm uses our MPRGP algorithm for the solution of strictly convex bound constrained quadratic programming problems with optional preconditioning by the conjugate projector to the subspace defined by the trace of the rigid body motions on the artificial subdomain interfaces. The optimality relies on our results on quadratic programming, the theory of the preconditioning by a conjugate projector for nonlinear problems, and the classical bounds on the spectrum of the mass and stiffness matrices. The results are confirmed by numerical solution of 3D transient contact problems. © Springer-Verlag Berlin Heidelberg 2013.