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International Journal for Multiscale Computational Engineering

Publicou 6 edições por ano

ISSN Imprimir: 1543-1649

ISSN On-line: 1940-4352

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Indexed in

COMPUTER-AIDED DERIVATION OF MULTISCALE MODELS: A REWRITING FRAMEWORK

Volume 12, Edição 2, 2014, pp. 91-114
DOI: 10.1615/IntJMultCompEng.2014006595
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RESUMO

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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CITADO POR
  1. Duy Duc Nguyen , Belkhir Walid, Ratier Nicolas, Yang Bin, Lenczner Michel, Zamkotsian Frederic, Cirstea Horatiu, A multi-scale model of a Micro-Mirror Array and an automatic model derivation tool, 2015 16th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, 2015. Crossref

  2. Belkhir Walid, Ratier Nicolas, Nguyen Duy Duc, Yang Bin, Lenczner Michel, Zamkotsian Frederic, Cirstea Horatiu, Towards an Automatic Tool for Multi-scale Model Derivation Illustrated with a Micro-mirror Array, 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2015. Crossref

  3. Belkhir Walid, Ratier Nicolas, Nguyen Duy Duc, Nguyen Nhat Binh Trinh, Lenczner Michel, Zamkotsian Frederic, A tool for aided multi-scale model derivation and its application to the simulation of a micro mirror array, 2017 18th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 2017. Crossref

  4. Trinh Nguyen Nhat Binh, Lenczner Michel, Zamkotsian Frederic, Ratier Nicolas, A multiscale model of a two-dimensional micro-mirror array, 2018 19th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 2018. Crossref

  5. Lenczner M., Belkhir W., Ratier N., Trinh N.B., Cavallier B., Automatic assembly of multiscale models and its application to a family of homogenized models of wave propagation through interfaces having a periodic structure, 2019 20th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), 2019. Crossref

  6. Belkhir Walid, Ratier Nicolas, Nguyen Duy Duc, Lenczner Michel, Unification and combination of a class of traversal strategies made with pattern matching and fixed-points, Journal of Logical and Algebraic Methods in Programming, 125, 2022. Crossref

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