Wavenumber explicit analysis for time-harmonic Maxwell equations in a spherical shell and spectral approximations. (22nd May 2017)

• Record Type: Journal Article
• Authors: Ma, Lina; Shen, Jie; Wang, Li-Lian; Yang, Zhiguo
• Is Part Of: IMA journal of numerical analysis. Volume 38:Number 2(2018)
• Page Start: 810
• Page End: 851
• Publication Date: 2017-05-22
• Subjects: Maxwell equations -- Helmholtz equation -- wavenumber explicit analysis -- Dirichlet-to-Neumann boundary conditions -- divergence-free vector spherical harmonic expansions; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drx014
• Languages: English
• ISSNs: 0272-4979

Abstract

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 $\epsilon$ -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 $\epsilon$ -perturbed nonspherical scatterers by representing the resulting field in $\epsilon$ -power series expansion with coefficients being spherical shell electric fields.