Spectral approximation of a boundary condition for an eigenvalue problem

Anne-Sophie Bonnet-Ben Dhia 1 Nabil Gmati
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : To compute the guided modes of an optical fiber, the authors use a scalar approximation of Maxwell's equations. This formulation leads to a bidimensional eigenvalue problem set in an unbounded domain. An equivalent formulation set in a bounded domain is derived. The boundary condition involves a Fourier series expansion. For the numerical treatment, only a finite number N of terms of the series is retained. The authors prove that the error on the eigenvalues and the eigenfunctions decreases faster than any power of ${1 / N}$. Copyright © 1995 Society for Industrial and Applied Mathematics
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Anne-Sophie Bonnet-Ben Dhia, Nabil Gmati. Spectral approximation of a boundary condition for an eigenvalue problem. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 1995, 32 (4), pp.1263-1279. ⟨10.1137/0732058⟩. ⟨hal-01010193⟩

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