A mathematical framework of the bridging scale method
Identifieur interne : 000274 ( Main/Exploration ); précédent : 000273; suivant : 000275A mathematical framework of the bridging scale method
Auteurs : Shaoqiang Tang [République populaire de Chine, États-Unis] ; Thomas Y. Hou [États-Unis] ; Wing Kam Liu [États-Unis]Source :
- International Journal for Numerical Methods in Engineering [ 0029-5981 ] ; 2006-03-05.
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Abstract
In this paper, we present a mathematical framework of the bridging scale method (BSM), recently proposed by Liu et al. Under certain conditions, it had been designed for accurately and efficiently simulating complex dynamics with different spatial scales. From a clear and consistent derivation, we identify two error sources in this method. First, we use a linear finite element interpolation, and derive the coarse grid equations directly from Newton's second law. Numerical error in this length scale exists mainly due to inadequate approximation for the effects of the fine scale fluctuations. An modified linear element (MLE) scheme is developed to improve the accuracy. Secondly, we derive an exact multiscale interfacial condition to treat the interfaces between the molecular dynamics region ΩD and the complementary domain ΩC, using a time history kernel technique. The interfacial condition proposed in the original BSM may be regarded as a leading order approximation to the exact one (with respect to the coarsening ratio). This approximation is responsible for minor reflections across the interfaces, with a dependency on the choice of ΩD. We further illustrate the framework and analysis with linear and non‐linear lattices in one‐dimensional space. Copyright © 2005 John Wiley & Sons, Ltd.
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DOI: 10.1002/nme.1514
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Engng.</title><idno type="ISSN">0029-5981</idno><idno type="eISSN">1097-0207</idno><imprint><publisher>John Wiley & Sons, Ltd.</publisher><pubPlace>Chichester, UK</pubPlace><date type="published" when="2006-03-05">2006-03-05</date><biblScope unit="volume">65</biblScope><biblScope unit="issue">10</biblScope><biblScope unit="page" from="1688">1688</biblScope><biblScope unit="page" to="1713">1713</biblScope></imprint><idno type="ISSN">0029-5981</idno></series><idno type="istex">FFE8D2FCF3E0FE3E5089F79E60DFEC9C1735E325</idno><idno type="DOI">10.1002/nme.1514</idno><idno type="ArticleID">NME1514</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0029-5981</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>bridging scale method</term><term>coarse–fine decomposition</term><term>molecular dynamics coupled with finite elements</term><term>multiscale computation</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="fr">In this paper, we present a mathematical framework of the bridging scale method (BSM), recently proposed by Liu et al. Under certain conditions, it had been designed for accurately and efficiently simulating complex dynamics with different spatial scales. From a clear and consistent derivation, we identify two error sources in this method. First, we use a linear finite element interpolation, and derive the coarse grid equations directly from Newton's second law. Numerical error in this length scale exists mainly due to inadequate approximation for the effects of the fine scale fluctuations. An modified linear element (MLE) scheme is developed to improve the accuracy. Secondly, we derive an exact multiscale interfacial condition to treat the interfaces between the molecular dynamics region ΩD and the complementary domain ΩC, using a time history kernel technique. The interfacial condition proposed in the original BSM may be regarded as a leading order approximation to the exact one (with respect to the coarsening ratio). This approximation is responsible for minor reflections across the interfaces, with a dependency on the choice of ΩD. We further illustrate the framework and analysis with linear and non‐linear lattices in one‐dimensional space. Copyright © 2005 John Wiley & Sons, Ltd.</div></front></TEI><affiliations><list><country><li>République populaire de Chine</li><li>États-Unis</li></country><region><li>Pékin</li></region><settlement><li>Pékin</li></settlement><orgName><li>Université de Pékin</li></orgName></list><tree><country name="République populaire de Chine"><noRegion><name sortKey="Tang, Shaoqiang" sort="Tang, Shaoqiang" uniqKey="Tang S" first="Shaoqiang" last="Tang">Shaoqiang Tang</name></noRegion></country><country name="États-Unis"><noRegion><name sortKey="Tang, Shaoqiang" sort="Tang, Shaoqiang" uniqKey="Tang S" first="Shaoqiang" last="Tang">Shaoqiang Tang</name></noRegion><name sortKey="Hou, Thomas Y" sort="Hou, Thomas Y" uniqKey="Hou T" first="Thomas Y." last="Hou">Thomas Y. Hou</name><name sortKey="Hou, Thomas Y" sort="Hou, Thomas Y" uniqKey="Hou T" first="Thomas Y." last="Hou">Thomas Y. Hou</name><name sortKey="Liu, Wing Kam" sort="Liu, Wing Kam" uniqKey="Liu W" first="Wing Kam" last="Liu">Wing Kam Liu</name><name sortKey="Liu, Wing Kam" sort="Liu, Wing Kam" uniqKey="Liu W" first="Wing Kam" last="Liu">Wing Kam Liu</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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