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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 1995

Spectral approximation of a boundary condition for an eigenvalue problem

Nabil Gmati

Résumé

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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Dates et versions

hal-01010193 , version 1 (19-06-2014)

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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, 1995, 32 (4), pp.1263-1279. ⟨10.1137/0732058⟩. ⟨hal-01010193⟩
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