Closed combination of context-embedding iterative strategies

This work is motivated by the challenging problem of the computer-aided generation of approximations (viewed as a series of transformations) of partial derivative equations. In this framework, the approximations posed over complex settings are incrementally constructed by extending an approximation posed on a simple setting and combining these extensions. In order to formalize these extensions and their combination, we introduce a class of rewriting strategies, called context-embedding iterative strategies (CE-strategies, for short). Roughly speaking, the class of CE-strategies is constructed by means of adding contexts and an iteration operator allowing the definition of recursive strategies. We show that the class of CE-strategies is closed under combination with respect to a correctness-completeness criterion. It turns out that the class CE-strategies enjoy nice algebraic properties, namely, the combination is associative, has a neutral element, and all the elements are idempotents

Towards an automatic tool for multi-scale model derivation illustrated with a micro-mirror array

International audienceThis paper reports recent advances in the development of a symbolic asymptotic modeling 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 for the first time. A user friendly language recently introduced is also shortly discussed. We illustrate the mathematical operations that need to be implemented in MEMSALab by an example of an asymptotic model for the stationary heat equation in a Micro-Mirror Array developed for astrophysics