A domain decomposition method for concurrent coupling of multiscale models

Abstract

SUMMARY Motivated by atomistic‐to‐continuum coupling, we consider a fine‐scale problem defined on a small region embedded in a much larger coarse‐scale domain and propose an efficient solution technique on the basis of the domain decomposition framework. Specifically, we develop a nonoverlapping Schwarz method with two important features: (i) the use of an efficient approximation of the Dirichlet‐to‐Neumann map for the interface conditions; and (ii) the utilization of the inherent scale separation in the solution. The paper includes a detailed formulation of the proposed interface condition, along with the illustration of its effectiveness by using simple but representative numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.

Modelagem do processo de falha em materiais cimentícios reforçados com fibras de aço.

“…Another strategy widely used today consists of discretizing the regions of the problem (subdomains), in a totally independent way, according to the interest of the analyst, and then use a coupling technique to connect their non-matching interfaces. This strategy has been applied extensively to problems with adaptive mesh refinement [125,69,67], multiscale problems [121,68,116] or multiphysics analysis [35,48,8,100]. In addition, with the advent of parallel computing, this kind of approach has been extensively used to deal with the interaction effects between the subdomains, initially subdivided to be computed by different processors [72,118].…”