Asynchronous space–time domain decomposition method with localized uncertainty quantification

Abstract

The computational cost associated with uncertainty quantification of engineering problems featuring localized phenomenon can be reduced by confining the random variability of the model parameters within a region of interest. Here in this case, a localized treatment of mesh and time resolutions is required to capture the effect of the confined material uncertainty on the global response. We present a computational approach for localized uncertainty quantification with the capability of asynchronous treatment of mesh and time resolutions. In particular, we allow each subdomain to have its local uncertainty representation and the corresponding mesh and time resolutions. As a result, computing resources can be directed toward a small region of interest where a model with high spatial and temporal resolutions is required. To verify the numerical implementation, we consider elastic wave propagation in an axially loaded beam. Moreover, we perform convergence studies with respect to the spatial and temporal discretizations as well as the size of an uncertain subdomain. A projectile impacting a composite sandwich plate is considered as an engineering application for the proposed method.