Towards an Automatic Tool for Multi-scale Model Derivation Illustrated with a Micro-mirror Array

Abstract

This 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.