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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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 |
|---|---|
| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
| 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: | Date Event 2012 Published |
| 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) |
| URI: | https://wrap.warwick.ac.uk/43782/ |
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