Bridging Methods for Coupling Atomistic and Continuum Models

Abstract. We review some recent developments in the coupling of atomistic and continuum models based on the blending of the two models in a bridge region connecting the other two regions in which the models are separately applied. We define four such models and subject them to patch and consistency tests. We also discuss important implementation issues such as: the enforcement of displacement continuity constraints in the bridge region; and how one defines, in two and three dimensions, the blending function that is a basic ingredient in the methods. Key words: atomistic to continuum coupling; blended coupling; molecular statics 1 Coupling atomistic and continuum models For us, continuum models are PDE models that are derived by invoking a (physical) continuum hypothesis. In most situations, these models are local in nature, e.g., forces at any point and time depend only on the state at that point. Atomistic models are discrete models. In particular, we consider molecular statics mode...

• Type: Conference
• Year: 2007
• Where: LSSC
• Authors: Santiago Badia, Pavel B. Bochev, Max Gunzburger, Richard B. Lehoucq, Michael L. Parks
• Keywords: Applied Computing, Atomistic Model, Continuum Model, Coupling, LSSC 2007