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Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations |
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| Institution: | 1. Reservoir Labs, New York City, NY, United States;2. Division of Computer, Electrical and Mathematical Science and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-2900, Saudi Arabia;3. Department of Mathematics, Stanford University, United States;4. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot, France;5. Institute for Computational and Mathematical Engineering, Stanford University, United States;6. Mechanical Engineering Department, Stanford University, CA, United States |
| Abstract: | 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. |
| Keywords: | Matched asymptotic expansions Maxwell’s equations Reduced models Scattering by spheres Multipoles |
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