Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations

Modélisation par sources ponctuelles multipolaires équivalentes de petites sphères pour le calcul rapide et précis de la diffraction des ondes électromagnétiques

Justine Labat (1, 2, 3) , Victor Péron (1, 2, 3) , Sébastien Tordeux (1, 2, 3)

1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
2 UPPA - Université de Pau et des Pays de l'Adour
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

In this paper, we develop reduced models to approximate the solution of the electromagnetic scattering problem in an unbounded domain which contains a small perfectly conducting sphere. Our approach is based on the method of matched asymptotic expansions. This method consists in defining an approximate solution using multi-scale expansions over outer and inner fields related in a matching area. We make explicit the asymptotics up to the second order of approximation for the inner expansion and up to the fifth order for the outer expansion. We validate the results with numerical experiments which illustrate theoretical orders of convergence for the asymptotic models requiring negligible computational cost.

Mots clés: Scattering by spheres; Reduced models; Matched asymptotic expansions; Maxwell's equations; Multipoles

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Justine Labat, Victor Péron, Sébastien Tordeux. Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations. Wave Motion, 2020, ⟨10.1016/j.wavemoti.2019.102409⟩. ⟨hal-02139201v2⟩