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Title: Analysis of an optimization-based atomistic-to-continuum coupling method for point defects

Abstract

Here, we formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Application of a potential-based atomistic model near the defect core enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.

Authors:
 [1];  [2];  [3];  [1]
  1. Univ. of Minnesota, Minneapolis, MN (United States)
  2. Skolkovo Institute of Science and Technology, Skolkovo (Russia)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1313073
Report Number(s):
SAND-2014-18401J
Journal ID: ISSN 0764-583X; PII: m2an141103
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Mathematical Modelling and Numerical Analysis
Additional Journal Information:
Journal Volume: 50; Journal Issue: 1; Journal ID: ISSN 0764-583X
Publisher:
EDP Sciences
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; atomistic-to-continuum coupling; atomic lattice; constrained optimization; point defect

Citation Formats

Olson, Derek, Shapeev, Alexander V., Bochev, Pavel B., and Luskin, Mitchell. Analysis of an optimization-based atomistic-to-continuum coupling method for point defects. United States: N. p., 2015. Web. doi:10.1051/m2an/2015023.
Olson, Derek, Shapeev, Alexander V., Bochev, Pavel B., & Luskin, Mitchell. Analysis of an optimization-based atomistic-to-continuum coupling method for point defects. United States. doi:10.1051/m2an/2015023.
Olson, Derek, Shapeev, Alexander V., Bochev, Pavel B., and Luskin, Mitchell. Mon . "Analysis of an optimization-based atomistic-to-continuum coupling method for point defects". United States. doi:10.1051/m2an/2015023. https://www.osti.gov/servlets/purl/1313073.
@article{osti_1313073,
title = {Analysis of an optimization-based atomistic-to-continuum coupling method for point defects},
author = {Olson, Derek and Shapeev, Alexander V. and Bochev, Pavel B. and Luskin, Mitchell},
abstractNote = {Here, we formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Application of a potential-based atomistic model near the defect core enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.},
doi = {10.1051/m2an/2015023},
journal = {Mathematical Modelling and Numerical Analysis},
number = 1,
volume = 50,
place = {United States},
year = {2015},
month = {11}
}

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