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Analysis of boundary conditions for crystal defect atomistic simulations
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Ehrlacher, V., Ortner, Christoph and Shapeev, A. V. (2016) Analysis of boundary conditions for crystal defect atomistic simulations. Archive for Rational Mechanics and Analysis, 222 (3). pp. 1217-1268. doi:10.1007/s00205-016-1019-6 ISSN 0003-9527.
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Official URL: http://dx.doi.org/10.1007/s00205-016-1019-6
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.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Library of Congress Subject Headings (LCSH): | Boundary value problems, Dirichlet series, Crystallography, Mathematical | ||||||||||
Journal or Publication Title: | Archive for Rational Mechanics and Analysis | ||||||||||
Publisher: | Springer | ||||||||||
ISSN: | 0003-9527 | ||||||||||
Official Date: | December 2016 | ||||||||||
Dates: |
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Volume: | 222 | ||||||||||
Number: | 3 | ||||||||||
Page Range: | pp. 1217-1268 | ||||||||||
DOI: | 10.1007/s00205-016-1019-6 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||
Date of first compliant deposit: | 1 February 2017 | ||||||||||
Date of first compliant Open Access: | 1 February 2017 | ||||||||||
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