A Newton-Krylov-FETI-DP Method with an Adaptive Coarse Space Applied to Elastoplasticity

We consider a Newton-Krylov-FETI-DP algorithm to solve problems in elastoplasticity. First, the material model and its discretization will be described. The model contains a Prandtl-Reuss flow rule and a von Mises flow function. We restrict ourselves to the case of perfect elastoplasticity; thus, there is no hardening. For more information on elastoplasticity; see, e.g., Carstensen and Klose [2002], Han and Reddy [2013], Simo and Hughes [1998]. In this material model we will have local nonlinearities introduced by plastic material behavior in activated zones of the domain. For the finite element discretization we follow the framework given in Carstensen and Klose [2002]. Second, we will briefly present the linearization and the FETI-DP method which is used to solve the linearized problems. For more details on the FETIDP algorithm, see, e.g., Klawonn et al. [2002, 2008], Farhat et al. [2001], Toselli and Widlund [2005]. The convergence of the Newton-Krylov-FETIDP method using a standard coarse space with vertices and edge averages can deteriorate when the plastically activated zone intersects the interface introduced by the domain decomposition. In this case, we use an adaptive coarse space which successfully decreases the number of cg iterations and the condition numbers of the preconditioned linearized systems. Only a small amount of adaptive constraints is needed if the plastically activated zone is