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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 233-237 (février 2008)
Doi : 10.1016/j.crma.2007.12.003
Received : 23 November 2007 ;  accepted : 4 December 2007
Étude de l’erreur de troncature du domaine pour un problème aux valeurs propres
Study of domain truncation error for an eigenvalue problem
 

Abdelaziz Choutri
Département de mathématiques, École normale supérieure, B.P. 92, Vieux Kouba, 16050 Alger, Algérie 

Résumé

Le calcul des modes guidés dans une fibre optique à gaine homogène, dans le cas scalaire, est un problème aux valeurs propres posé dans tout le plan  . La principale difficulté dans la résolution numérique de ce problème est liée au caractère non borné du domaine. Dans cette Note, nous donnons une estimation de l’erreur lorsqu’on tronque le domaine et on impose une condition de Robin sur la frontière du domaine ainsi obtenu. C’est ce qu’on a appelé l’erreur dûe à la troncature du domaine. Pour citer cet article : A. Choutri, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Abstract

The computation of guided modes in an optical fiber is an eigenvalue problem posed in the whole of  . To compute the eigenvalues and the associated eigenfunctions, we truncate the domain and we impose a Robin condition on the boundary of the truncated domain. In this Note, we give an error estimate between the solutions of the physical problem and the truncated one. To cite this article: A. Choutri, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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