Rewriting and Symbolic Transformations for Multiscale Methods
Résumé
This work is motivated by a challenging problem of computer-aided 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. The challenge is to formalize these approximating methods within a computer algebra system, e.g. Maple. Since most of the transformation steps correspond to equational reasoning (i.e. symbolic transformations based on equalities) we address the question of extending Maple with rewriting and strategies. Our contribution consists in transferring most of the term rewriting concepts and techniques to the symbolic computation community. We provide a Maple package for rule-based programming and its combination with standard Maple code. We illustrate its practical interest by applying the package functions to provide a formal proof of a convergence property of a two-scale operator