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

Journal Article · · SIAM Journal on Numerical Analysis
DOI:https://doi.org/10.1137/13091734X· OSTI ID:1184468
 [1];  [2];  [1];  [1]
  1. Univ. of Minnesota, Minneapolis, MN (United States). School of Mathematics
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Mathematics
+ Show Author Affiliations

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.

Research Organization:
Sandia National Laboratory (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
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 Organization:
Univ. of Minnesota, Minneapolis, MN (United States)
Grant/Contract Number:
AC04-94AL85000; SC0002085; OISE-0967140; FA9550-12-1-0187
OSTI ID:
1184468
Report Number(s):
SAND2014-18401J; 539936
Journal Information:
SIAM Journal on Numerical Analysis, Vol. 52, Issue 4; ISSN 0036-1429
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 13 works
Citation information provided by
Web of Science

References (31)

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  • Chamoin, Ludovic; Prudhomme, Serge; Ben Dhia, H.
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journal August 2010
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A decoupling algorithm for fluid-structure interaction problems based on optimization journal December 2013
Theory-based benchmarking of the blended force-based quasicontinuum method journal January 2014
Heterogeneous coupling by virtual control methods journal December 2001

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Related Subjects

97 MATHEMATICS AND COMPUTING
atomistic-to-continuum
coupling
nonlocal model
constrained optimization
virtual controls
error analysis