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International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2014006595
pages 91-114

COMPUTER-AIDED DERIVATION OF MULTISCALE MODELS: A REWRITING FRAMEWORK

Bin YANG
Department of Applied Mathematics, Northwestern Polytechnical University, 710129 Xi'an Shaanxi, China, and University of Franche-Comte, 26 Chemin de l'Epitaphe, 25030 Besancon Cedex, France
Walid Belkhir
LIFC, University of Franche-Comte, 16 route de Gray, 25030, Besancon Cedex, France, and INRIA Nancy - Grand Est, CASSIS project, 54600 Villers-les-Nancy, France
Michel Lenczner
FEMTO-ST, Departement Temps-Frequence, University of Franche-Comte, 26 Chemin de l'Epitaphe, 25030 Besancon Cedex, France

Краткое описание

We introduce the first part of a framework for computer-aided derivation of multiscale models. It relies on a combination of an asymptotic method used in the field of partial differential equations with term-rewriting techniques coming from computer science. In our approach, a multiscale model derivation is characterized by the features taken into account in the asymptotic analysis. Its formulation consists in a derivation of a reference model associated to an elementary nominal model, and in a set of transformations to apply to this proof until it takes into account the wanted features. In addition to the reference model proof, the framework includes first-order rewriting principles designed for asymptotic model derivations, second-order rewriting principles dedicated to elementary extensions of model derivations, and their combinations. The latter point is only briefly sketched and will be detailed in another work. We report implementation results regarding three simple extensions of the reference proof.

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