A computational and theoretical investigation of the accuracy of quasicontinuum methods
Koten, Brian, Li, Xingjie Helen, Luskin, Mitchell and Ortner, Christoph (2011) 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, (eds.) Numerical Analysis of Multiscale Problems. Lecture Notes in Computational Science and Engineering, Vol.83 . Berlin : Heidelberg: Springer, pp. 67-96. ISBN 9783642220609Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/978-3-642-22061-6_3
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|
|Divisions:||Faculty of Science > Mathematics|
|Series Name:||Lecture Notes in Computational Science and Engineering|
|Place of Publication:||Berlin : Heidelberg|
|Book Title:||Numerical Analysis of Multiscale Problems|
|Editor:||Graham, Ivan G. and Hou, Thomas Y. and Lakkis, Omar and Scheichl, Robert|
|Number of Pages:||371|
|Page Range:||pp. 67-96|
|Access rights to Published version:||Restricted or Subscription Access|
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