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|Title:||Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations||Authors:||Ma, Lina
|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.||URI:||https://hdl.handle.net/10356/85563
|ISSN:||0272-4979||DOI:||http://dx.doi.org/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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