COMPUTER-AIDED DERIVATION OF MULTISCALE MODELS: A REWRITING FRAMEWORK

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.