A symbolic transformation language and its application to a multiscale method

Abstract

The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro-and nanosystems. In this domain a model is a partial differential equation. Multiscale methods 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 geometries combining thin and periodic structures with the possibility of multiple nested scales.In this paper we present a transformation language that will make the development of MEMSALab more feasible. It is proposed as a Maple TM package for rule-based programming, rewriting strategies and their combination with standard Maple TM code. We illustrate the practical interest of this language by using it to encode two examples of multiscale derivations, namely the two-scale limit of the derivative operator and the two-scale model of the stationary heat equation.

A Strategic Graph Rewriting Model of Rational Negligence in Financial Markets

“…Tom [3] is an extension of Java with algebraic terms, rule definitions and a strategy language, thus allowing programmers to combine imperative object-oriented programming and strategic term rewriting. The symbolic transformation language symbtrans designed in the context of MEM-SALab [4] (where models are defined using partial differential equations) extends Maple TM with conditional rewriting, strategies and pattern-matching modulo associativity and commutativity.…”

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

“…Both are separately wellstudied but there are only few works about the combination of algebraic computation and term rewriting [7], [17], [18], [19]. We have implemented a Maple package, named symbtrans, extending Maple with rule-based programming, where rules, strategies and usual Maple functions can be freely combined [19]. The transformation language provided by the symbtrans package is deliberately an adaptation for Maple of popular strategy languages such as ρ-log [8] or TOM [20].…”

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

“…In [2] we presented a transformation language implemented as a Maple package. It relies on the paradigm of rulebased programming and rewriting strategies as well as their combination with standard Maple code.…”