Towards an automatic tool for multi-scale model derivation

Walid Belkhir (1, 2) , Nicolas Ratier (2) , Duy Duc Nguyen (2) , Bin Yang (2) , Michel Lenczner (2) , Frédéric Zamkotsian (3) , Horatiu Cirstea (4)

1 CASSIS - Combination of approaches to the security of infinite states systems
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
3 LAM - Laboratoire d'Astrophysique de Marseille
4 PAREO - Formal islands: foundations and applications

This paper reports recent advances in the development of a symbolic asymptotic mod-eling software package, called MEMSALab, which will be used for automatic generation of asymptotic models for arrays of micro and nanosystems. More precisely, a model is a partial differential equation and an asymptotic method approximate it by another partial differential equation which can be numerically simulated in a reasonable time. The challenge consists in taking into account a wide range of different physical features and geometries e.g. thin structures, periodic structures, multiple nested scales etc. The main purpose of this software is to construct models incrementally so that model features can be included step by step. This idea, conceptualized under the name "by-extension-combination", is presented in detail for the first time.

Domaines: Logiciel mathématique [cs.MS]

Walid Belkhir, Nicolas Ratier, Duy Duc Nguyen, Bin Yang, Michel Lenczner, et al.. Towards an automatic tool for multi-scale model derivation. 2015. ⟨hal-01223141⟩