A nonlinear domain decomposition formulation with application to granular dynamics

Simulation of granular media undergoing dynamic evolution involves nonsmooth problems when grains are modeled as rigid bodies. With dense samples, this nonsmoothness occurs everywhere in the studied domain, and large sized systems lead to computationally intensive simulations. In this article, we combine domain decomposition approaches and nonsmooth contact dynamics. Unlike the smooth continuum media case, a coarse space problem does not trivially increase the convergence rate, as it is exemplified in this article, with semi-analytical examples and real size numerical simulations. Nevertheless, the description of an underlying force network in the samples may guide the analysis for new approximation schemes or algorithms.