Formal Methods for Multiscale Models Derivation

Colloque avec actes et comité de lecture. Internationale.International audienceWe are currently developing software dedicated to multiscale and multiphysics modeling of arrays of micro and nanosystems. Unlike traditional software that is based on models built once and for all, here this is the software that constructs models. It is based on the mathematical Two-Scale Transform, a technique for asymptotic methods, together with formal specification and verification techniques incomputer science, combining formal transformations and term rewriting and type theory. We aim at taking into account a wide range of geometries combining thin structures, periodic structures with the possibility of multiple nested scales and any combination of these features. In this paper we present the principle of our methods and our first results