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Analysis of a Prototypical Multiscale Method Coupling Atomistic and Continuum Mechanics:the Convex Case

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Acta Mathematicae Applicatae Sinica 2007年第2期23卷 209-216页

作者： Xavier Blanc claude le bris Frédériclegoll Laboratoire J.L.-Lions Université Pierre et Marie CurieBoite courrier 187F-75252 ParisFrance CERMICS Ecole Nationale des Ponts et Chaussées 6 et 8 avenue Blaise PascalCité DescartesF-77455 Marne-la-Vallée and MICMACInria RocquencourtF-78153 Le ChesnayFrance CERMICS Ecole Nationale des Ponts et Chaussées 6 et 8 avenue Blaise PascalCité DescartesF-77455 Marne-la-Vallée and MICMACInria RocquencourtF-78153 Le ChesnayFrance EDF R & D1 avenue du Général de GaulleF-92140 ClamartFrance

In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model （discrete mechanics） with a macroscopic model （continuum mechanics）. We provide here a theoretical basis for such a coupling in a one-dimensional setting, in the case of convex energy.

关键词： Multiscale methods variational problems continuum mechanics discrete mechanics

MsFEM à la Crouzeix-Raviart for Highly Oscillatory Elliptic Problems

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Chinese Annals of Mathematics,Series B 2013年第1期34卷 113-138页

作者： claude le bris Frédéric leGOLL Alexei LOZINSKI cole Nationale des Ponts et Chaussées 6 et 8 avenue Blaise Pascal INRIA Rocquencourt MICMAC project-team Institut de Mathématiques de Toulouse Université Paul Sabatier Laboratoire de Mathématiques CNRS UMR 6623 Université de Franche-Comté

We introduce and analyze a multiscale finite element type method (MsFEM) in the vein of the classical Crouzeix-Raviart finite element method that is specifically adapted for highly oscillatory elliptic problems. We il... 详细信息

关键词： Homogenization Finite elements Galerkin methods Highly oscillatoryPDE

Micro-macro models for viscoelastic fluids： modelling, mathematics and numerics Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

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Science China Mathematics 2012年第2期55卷 353-384页

作者： le bris claude leLIVRE Tony CERMICS Ecole des Ponts ParisTech INRIA Rocquencourt MICMAC team

This paper is an introduction to the modelling of viscoelastic fluids, with an emphasis on micromacro （or multiscale） models. Some elements of mathematical and numerical analysis are provided. These notes closely follow the lectures delivered by the second author at the Chinese Academy of Science during the Workshop ＂Stress Tensor Effects on Fluid Mechanics＂ in January 2010.

关键词： viscoelastic fluids micro-macro models entropy methods Monte Carlo methods