Rewriting Strategies for a Two-Scale Method: Application to Combined Thin and Periodic Structures

B. Yang 1 W. Belkhir 1, 2 R.N. Dhara 1 A. Giorgetti 1, 2 M. 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 : Multiphysics models of large arrays of micro- and nanosystems are too complex to be efficiently simulated by existing simulation software. Fortunately, asymptotic methods such as those based on two-scale convergence are applicable to homogenization of thin or periodic (i.e. array) structures. They generate simpler models tractable to simulation, but their application is long and requires a mathematical expertise. Our goal is to provide engineers with an implementation of this mathematical tool inside a modeling software.We follow therefore a multidisciplinary approach which combines a generalization and formalization effort of mathematical asymptotic methods, together with rewriting-based formal transformation techniques from computer science. This paper describes this approach, illustrates it with an example and presents the architecture of the software under design.
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https://hal.inria.fr/hal-00753003
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Submitted on : Friday, November 16, 2012 - 6:17:08 PM
Last modification on : Tuesday, December 18, 2018 - 4:38:25 PM

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B. Yang, W. Belkhir, R.N. Dhara, A. Giorgetti, M. Lenczner. Rewriting Strategies for a Two-Scale Method: Application to Combined Thin and Periodic Structures. d Software Implementation for Distributed MEMS - dMEMS 2012, Apr 2012, Besançon, France. pp.82-89, ⟨10.1109/dMEMS.2012.14⟩. ⟨hal-00753003⟩

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