École Nationale Supérieure de
Techniques Avancées

Abstract

The Wiener-Hopf technique is an elegant method to solve some partial differential equations. We applied it to the diffraction of an acoustic plane wave on an infinite grating. This project is based on the new asymptotic factorisation proposed by Mishuris and Rogosin (2014 [3]). We first compute a rational approximation of the general functions studied, which in our case of application are hyperbolic, using the Matlab library Chebfun. Thus, the problem becomes algebraic rather than analytic, and the factorisations are implemented in Matlab for these rational matrix functions. We then investigate the accuracy of this approach and its convergence, in order to precise which kind of functions will give satisfying results.