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:
-
- Univ. of Minnesota, Minneapolis, MN (United States). School of Mathematics
- 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.
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
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.
@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}
}
Web of Science
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