Luskin, Mitchell Barry and Ortner, Christoph (2009) An analysis of node-based cluster summation rules in the quasicontinuum method. SIAM Journal on Numerical Analysis, Volume 47 (Number 4). pp. 3070-3086. doi:10.1137/080743391 ISSN 0036-1429.
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Abstract
We investigate two examples of node-based cluster summation rules that have been proposed for the quasicontinuum (QC) method: a force-based approach and an energy-based approach which is a generalization of the nonlocal QC method. We show that, even for the case of nearest-neighbor interaction in a one-dimensional periodic chain, both of these approaches create large errors that cannot be removed by increasing the cluster size when used with graded and, more generally, nonsmooth meshes. We offer some suggestions for how the accuracy of (cluster) summation rules may be improved.
| Item Type: | Journal Article |
|---|---|
| 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, Crystalline polymers -- Defects -- Mathematical models |
| Journal or Publication Title: | SIAM Journal on Numerical Analysis |
| Publisher: | Society for Industrial and Applied Mathematics |
| ISSN: | 0036-1429 |
| Official Date: | 4 September 2009 |
| Dates: | Date Event 4 September 2009 Published 22 June 2009 Accepted 11 December 2008 Submitted |
| Volume: | Volume 47 |
| Number: | Number 4 |
| Page Range: | pp. 3070-3086 |
| DOI: | 10.1137/080743391 |
| 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), United States. Department of Energy, Institute for Mathematics and Its Applications (IMA), University of Minnesota. Supercomputer Institute, Engineering and Physical Sciences Research Council (EPSRC) |
| Grant number: | DMS- 0757355 (NSF), DMS-0811039 (NSF), DE-FG02-05ER25706 (DOE) |
| URI: | https://wrap.warwick.ac.uk/43811/ |
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