In this talk, I will present information-passing and concurrent discrete-to-continuum scale bridging approaches. In the concurrent approach both, the discrete and continuum scales are simultaneously resolved, whereas in the information-passing schemes, the discrete scale is modeled and its gross response is infused into the continuum scale. For the information-passing multiscale methods to be valid both the temporal and spatial scales should be separable. Among the information-passing bridging techniques, I will present the Generalized Mathematical Homogenization (GMH) theory [
] and the Multiscale Enrichment based on the Partition of Unity (MEPU) method [
]. The GMH constructs an equivalent continuum description directly from molecular dynamics (MD) equations. The MEPU approach gives rise to the enriched quasicontinuum formulation, capable of dealing with heterogeneous inter-atomic potentials, nonperiodic fields and high velocity impact applications.
The second part of the talk will focus on multiscale systems, whose response depend inherently on physics at multiple scales, such as turbulence, crack propagation, friction, and problems involving nano-like devices. For these types of problems, multiple scales have to be simultaneously resolved in different portions of the problem domain. Among the concurrent bridging techniques, attention will be restricted to multilevel-like methods [
]. A space-time multilevel method for bridging discrete scales with either coarse grained discrete or continuum scales will be presented. The method consists of the wave-form relaxation scheme aimed at capturing the high frequency response of the atomistic vibrations and the coarse scale solution (explicit or implicit) intended to resolve the coarse scale features (in both space and time domains) of the discrete medium