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Publication 77

Development of 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

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 [17] 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 pro- vide numerical results to corroborate the conjecture for a 1D Lennard- Jones system with next-nearest neighbor interactiions.
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