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

Multiphysics models of large arrays of micro- and nanosystems are too complex to be efficiently simulated by existing simulation software. Fortunately, asymptotic methods such as those based on two-scale convergence are applicable to homogenization of thin or periodic (i.e. array) structures. They generate simpler models tractable to simulation, but their application is long and requires a mathematical expertise. Our goal is to provide engineers with an implementation of this mathematical tool inside a modeling software. We follow therefore a multidisciplinary approach which combines a generalization and formalization effort of mathematical asymptotic methods, together with rewriting-based formal transformation techniques from computer science. This paper describes this approach, illustrates it with an example and presents the architecture of the software under design.