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Archive for Rational Mechanics and Analysis

, Volume 222, Issue 3, pp 1217–1268 | Cite as

Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations

  • V. Ehrlacher
  • C. OrtnerEmail author
  • A. V. Shapeev
Open Access
Article

Abstract

Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.

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Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.CERMICS, ENPCMarne la Valle Cedex 2France
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK
  3. 3.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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