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Atomistic-to-continuum coupling

Published online by Cambridge University Press:  02 April 2013

Mitchell Luskin  and
Christoph Ortner
Mitchell Luskin
Affiliation:
School of Mathematics, University of Minnesota, MN 55455, USA E-mail: luskin@umn.edu
Christoph Ortner
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK E-mail: c.ortner@warwick.ac.uk
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Abstract

Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale schemes that combine the accuracy of atomistic models with the efficiency of continuum elasticity. They are increasingly being utilized in materials science to study the fundamental mechanisms of material failure such as crack propagation and plasticity, which are governed by the interaction between crystal defects and long-range elastic fields.

In the construction of a/c coupling methods, various approximation errors are committed. A rigorous numerical analysis approach that classifies and quantifies these errors can give confidence in the simulation results, as well as enable optimization of the numerical methods for accuracy and computational cost. In this article, we present such a numerical analysis framework, which is inspired by recent research activity.

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Type
Research Article
Information
Acta Numerica , Volume 22 , May 2013 , pp. 397 - 508
Copyright
Copyright © Cambridge University Press 2013

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