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Title: Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations
Authors: Ma, Lina
Yang, Zhiguo
Wang, Li-Lian
Keywords: Helmholtz Equations
Maxwell Equations
Issue Date: 2017
Source: Ma, L., Wang, L.-L., & Yang, Z. (2017). Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations. IMA Journal of Numerical Analysis, drx014-.
Series/Report no.: IMA Journal Of Numerical Analysis
Abstract: This article is devoted to wavenumber explicit analysis of the electric field satisfying the second-order time-harmonic Maxwell equations in a spherical shell and, hence, for variant scatterers with ϵ-perturbation of the inner ball radius. The spherical shell model is obtained by assuming that the forcing function is zero outside a circumscribing ball and replacing the radiation condition with a transparent boundary condition involving the capacity operator. Using the divergence-free vector spherical harmonic expansions for two components of the electric field, the Maxwell system is reduced to two sequences of decoupled one-dimensional boundary value problems in the radial direction. The reduced problems naturally allow for truncated vector spherical harmonic spectral approximation of the electric field and one-dimensional global polynomial approximation of the boundary value problems. We analyse the error in the resulting spectral approximation for the spherical shell model. Using a perturbation transformation, we generalize the approach for ϵ-perturbed nonspherical scatterers by representing the resulting field in ϵ-power series expansion with coefficients being spherical shell electric fields.
ISSN: 0272-4979
DOI: 10.1093/imanum/drx014
Rights: © 2017 The Author(s) (published by Oxford University Press on behalf of the Institute of Mathematics and its Applications).
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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