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Title: An Optimization-based Atomistic-to-Continuum Coupling Method

Abstract

In this paper, we present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the latter 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. Separation, rather then blending of the atomistic and continuum problems, and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. Finally, we present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body potential with next-nearest neighbor interactions.

Authors:
 [1];  [2];  [1];  [1]
+ Show Author Affiliations
  1. Univ. of Minnesota, Minneapolis, MN (United States). School of Mathematics
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Mathematics
Publication Date:
Research Org.:
Sandia National Laboratory (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); Department of Defense (DoD); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR)
Contributing Org.:
Univ. of Minnesota, Minneapolis, MN (United States)
OSTI Identifier:
1184468
Report Number(s):
SAND2014-18401J
Journal ID: ISSN 0036-1429; 539936
Grant/Contract Number:  
AC04-94AL85000; SC0002085; OISE-0967140; FA9550-12-1-0187
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Numerical Analysis
Additional Journal Information:
Journal Volume: 52; Journal Issue: 4; Journal ID: ISSN 0036-1429
Publisher:
Society for Industrial and Applied Mathematics (SIAM)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; atomistic-to-continuum; coupling; nonlocal model; constrained optimization; virtual controls; error analysis

Citation Formats

Olson, Derek, Bochev, Pavel B., Luskin, Mitchell, and Shapeev, Alexander V. An Optimization-based Atomistic-to-Continuum Coupling Method. United States: N. p., 2014. Web. doi:10.1137/13091734X.
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Olson, Derek, Bochev, Pavel B., Luskin, Mitchell, & Shapeev, Alexander V. An Optimization-based Atomistic-to-Continuum Coupling Method. United States. https://doi.org/10.1137/13091734X
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Olson, Derek, Bochev, Pavel B., Luskin, Mitchell, and Shapeev, Alexander V. Thu . "An Optimization-based Atomistic-to-Continuum Coupling Method". United States. https://doi.org/10.1137/13091734X. https://www.osti.gov/servlets/purl/1184468.
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@article{osti_1184468,
title = {An Optimization-based Atomistic-to-Continuum Coupling Method},
author = {Olson, Derek and Bochev, Pavel B. and Luskin, Mitchell and Shapeev, Alexander V.},
abstractNote = {In this paper, we present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the latter 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. Separation, rather then blending of the atomistic and continuum problems, and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. Finally, we present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body potential with next-nearest neighbor interactions.},
doi = {10.1137/13091734X},
journal = {SIAM Journal on Numerical Analysis},
number = 4,
volume = 52,
place = {United States},
year = {Thu Aug 21 00:00:00 EDT 2014},
month = {Thu Aug 21 00:00:00 EDT 2014}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1137/13091734X
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Cited by: 13 works
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