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A computational and theoretical investigation of the accuracy of quasicontinuum methods
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Koten, Brian Van, Li, Xingjie Helen, Luskin, Mitchell Barry and Ortner, Christoph (2012) A computational and theoretical investigation of the accuracy of quasicontinuum methods. In: Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, 1972-, (eds.) Numerical analysis of multiscale problems. Lecture notes in computational science and engineering, Volume 83 . Berlin: Springer, pp. 67-96. ISBN 9783642220609
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Official URL: http://dx.doi.org/10.1007/978-3-642-22061-6_3
Abstract
We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems – the stability of a Lomer dislocation pair under shear and the stability of a lattice to plastic slip under tensile loading. We find that our theoretical analysis of the accuracy near instabilities for one-dimensional model problems can successfully explain most of the computational results for these multi-dimensional benchmark problems. However, we also observe some clear discrepancies, which suggest the need for additional theoretical analysis and benchmark problems to more thoroughly understand the accuracy of quasicontinuum methods.
Item Type: | Book Item | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Multiscale modeling, Continuum mechanics | ||||
Series Name: | Lecture notes in computational science and engineering | ||||
Publisher: | Springer | ||||
Place of Publication: | Berlin | ||||
ISBN: | 9783642220609 | ||||
ISSN: | 1439-7358 | ||||
Book Title: | Numerical analysis of multiscale problems | ||||
Editor: | Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert, 1972- | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Volume 83 | ||||
Number of Pages: | 371 | ||||
Page Range: | pp. 67-96 | ||||
DOI: | 10.1007/978-3-642-22061-6_3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 28 July 2016 | ||||
Date of first compliant Open Access: | 28 July 2016 | ||||
Funder: | National Science Foundation (U.S.) (NSF), Institute for Mathematics and Its Applications (IMA), University of Minnesota. Supercomputer Institute, United States. Department of Energy, Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | DMS-0757355 (NSF), DMS-0811039 (NSF), DE-SC0002085 (DOE), EP/H003096/1 (EPSRC) |
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