Computer-Aided Derivation of Multi-scale Models: A Rewriting Framework

Bin Yang 1 Walid Belkhir 2 Michel Lenczner 1
2 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : We introduce a framework for computer-aided derivation of multi-scale 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 multi-scale 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, and second order rewriting principles dedicated to transformations of model derivations. We apply the method to generate a family of homogenized models for second order elliptic equations with periodic coefficients that could be posed in multi-dimensional domains, with possibly multi-domains and/or thin domains.
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https://hal.inria.fr/hal-00916568
Contributor : Walid Belkhir <>
Submitted on : Tuesday, December 10, 2013 - 2:21:51 PM
Last modification on : Tuesday, December 18, 2018 - 4:38:25 PM

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  • HAL Id : hal-00916568, version 1
  • ARXIV : 1302.2224

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Bin Yang, Walid Belkhir, Michel Lenczner. Computer-Aided Derivation of Multi-scale Models: A Rewriting Framework. International Journal for Multiscale Computational Engineering, Begell House, 2014, 12 (2), pp.91--114. ⟨hal-00916568⟩

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