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Publication 78

An Optimization-Based Atomistic-to-Continuum Coupling Method


MinnesotaD. Olson
University of Minnesota, Minneapolis, USA

P. Bochev
Sandia National Laboratories, Albuquerque, USA

MinnesotaMitchell Luskin
School of Mathematics, University of Minnesota 206 Church Street SE, Minneapolis, MN 55455, U.S.A.

MinnesotaAlexander V. Shapeev
School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN 55455, USA

We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Splitting of the atomistic and continuum problems instead of blending them and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. We present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body next-nearest neighbor interactions.
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