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

Olson, Derek; Shapeev, Alexander V.; Bochev, Pavel B.; Luskin, Mitchell

doi:10.1051/m2an/2015023

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

Full Record
Other Related Research

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:

Olson, Derek ^[1]; Shapeev, Alexander V. ^[2]; Bochev, Pavel B. ^[3]; Luskin, Mitchell ^[1]

Univ. of Minnesota, Minneapolis, MN (United States)
Skolkovo Institute of Science and Technology, Skolkovo (Russia)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Mon Nov 16 00:00:00 EST 2015

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

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.

Copy to clipboard


                    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.  https://doi.org/10.1051/m2an/2015023

Copy to clipboard


                    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.  https://doi.org/10.1051/m2an/2015023.  https://www.osti.gov/servlets/purl/1313073.

Copy to clipboard


                    
@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         = {Mon Nov 16 00:00:00 EST 2015},

  month        = {Mon Nov 16 00:00:00 EST 2015}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1051/m2an/2015023

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 4 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Similar Records in DOE PAGES and OSTI.GOV collections:

An Optimization-based Atomistic-to-Continuum Coupling Method

Journal Article Olson, Derek ; Bochev, Pavel B. ; Luskin, Mitchell ; ... - SIAM Journal on Numerical Analysis

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,more »« less
Cited by 13
https://doi.org/10.1137/13091734X

Full Text Available
Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics

Journal Article Kraczek, B. ; Miller, S.T. ; Haber, R.B. ; ... - Journal of Computational Physics

We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numericalmore »« less
https://doi.org/10.1016/j.jcp.2009.11.023
A Mathematical Analysis of Atomistic-to-Continuum (AtC) Multiscale Coupling Methods

Technical Report Gunzburger, Max

We have worked on several projects aimed at improving the efficiency and understanding of multiscale methods, especially those applicable to problems involving atomistic-to-continuum coupling. Activities include blending methods for AtC coupling and efficient quasi-continuum methods for problems with long-range interactions.
https://doi.org/10.2172/1104985

Full Text Available
Coupled atomistic-continuum simulations using arbitrary overlapping domains

Journal Article Klein, P A ; Zimmerman, J A - Journal of Computational Physics

We present a formulation for coupling atomistic and continuum simulation methods for application to both quasistatic and dynamic analyses. In our formulation, a coarse-scale continuum discretization is assumed to cover all parts of the computational domain with atomistic crystals introduced only in regions of interest. The geometry of the discretization and crystal are allowed to overlap arbitrarily. Our approach uses interpolation and projection operators to link the kinematics of each region, which are then used to formulate a system potential energy from which we derive coupled expressions for the forces acting in each region. A hyperelastic constitutive formulation is usedmore »« less
https://doi.org/10.1016/j.jcp.2005.08.014
Coupled atomistic-continuum simulation using arbitrary overlapping domains.

Journal Article Zimmerman, Jonathan A ; Klein, Patrick A - Proposed for publication in Journal of Computational Physics.

We present a formulation for coupling atomistic and continuum simulation methods for application to both quasistatic and dynamic analyses. In our formulation, a coarse-scale continuum discretization is assumed to cover all parts of the computational domain with atomistic crystals introduced only in regions of interest. The geometry of the discretization and crystal are allowed to overlap arbitrarily. Our approach uses interpolation and projection operators to link the kinematics of each region, which are then used to formulate a system potential energy from which we derive coupled expressions for the forces acting in each region. A hyperelastic constitutive formulation is usedmore »« less

Similar Records