Asymptotic Modeling of the Electromagnetic Scattering by Small Spheres Perfectly Conducting

In this report, we use the method of matched asymptotic expansions to approximate the solution of the time-harmonic electromagnetic scattering problem by a small perfectly conducting sphere. This method consists in defining two local approximations using multi-scale expansions over far and near fields, related in a matching area. We make explicit the asymptotics up to the second order of approximation for the near-field expansion and up to the fifth order for the far-field expansion. We illustrate these results with numerical experiments making evident the performance of the asymptotic models.