Multi-time-step and two-scale domain decomposition method for non-linear structural dynamics

In this paper we propose a method to improve the means of taking into account the speci c time-scale and space-scale characteristics in time-dependent non-linear problems. This method enables the use of arbitrary time steps in each subdomain: these can be coupled by prescribing continuous velocities at the interfaces, which are modelled using a dual Schur formulation. For certain subdomains, in space, we adopt a two-scale resolution technique inspired by the multigrid methods in order to obtain the part of the solution related to small variation lengths on a re ned scale and the part corresponding to large variation lengths on a coarse scale. For non-linear problems, we propose an algorithm with a single iteration level to deal with both the non-linear equilibrium and the two space scales thanks to a two-grid method in which the relaxation steps are performed using a non-linear, preconditioned conjugate gradient algorithm. Finally, we present an example which demonstrates the feasibility of the method