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

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:
OSTI Identifier:
1313073
Report Number(s):
SAND--2014-18401J
Journal ID: ISSN 0764-583X; PII: m2an141103
Grant/Contract Number:
AC04-94AL85000
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
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS atomistic-to-continuum coupling; atomic lattice; constrained optimization; point defect