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arXiv · 1309.5988

Development of an Optimization-Based Atomistic-to-Continuum Coupling Method

Derek Olson·Pavel Bochev·Mitchell Luskin·Alexander V. Shapeev
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Abstract

Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in arXiv:1304.4976 for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions.

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Derek Olson, Pavel Bochev, Mitchell Luskin, Alexander V. Shapeev. 2013-09-23. Development of an Optimization-Based Atomistic-to-Continuum Coupling Method. https://arxiv.org/abs/1309.5988

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