Department of Mathematics

Speaker: Xingjie Helen Li
Title: Blended Atomistic-to-Continuum Hybrid Methods for Modeling Crystalline Materials
Affiliation: Brown University
Date: Monday, January 26, 2015
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. The development of consistent and stable atomistic-to-continuum coupling models for multi-dimensional crystalline solids remains a challenge. In this talk, we consider two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods, with a comprehensive error analysis that is valid in two and three dimensions, for finite many-body interactions (e.g., Embedded-Atom Method potential type), and in the presence of lattice defects (point defects and dislocations). Based on a precise choice of blending mechanism, the error estimates are considered in terms of degrees of freedom. The numerical experiments confirm the theoretical predictions, and demonstrate a superior accuracy of the force-based blending over energy-based blending schemes.