Missing boundary data recovering for the Helmholtz problem

Riadh Ben Fatma; Mejdi Azaïez; Amel Ben Abda; Nabil Gmati

doi:10.1016/j.crme.2007.10.006

Missing boundary data recovering for the Helmholtz problem

Presented by: Michel Combarnous

Riadh Ben Fatma ¹ ; Mejdi Azaïez ²; Amel Ben Abda ¹; Nabil Gmati ¹

¹ LAMSIN, École nationale d'ingénieurs de Tunis, B.P. 37, 1002, Le Belvédère, Tunisia
² TREFLE (UMR CNRS 8508), ENSCPB, 33607 Pessac, France

Comptes Rendus. Mécanique, Volume 335 (2007) no. 12, pp. 787-792.

Abstract
Résumé

This Note is dedicated to the numerical treatment of the ill-posed Cauchy–Helmholtz problem. Resorting to the domain decomposition tools, these missing boundary data are rephrased through an ‘interfacial’ equation. This equation is solved via a preconditioned Richardson algorithm with dynamic relaxation. The efficiency of the proposed method is illustrated by some numerical experiments.

Cette Note concerne le traitement numérique du problème de Cauchy–Helmholtz. On « emprunte » les outils de type décomposition de domaines pour exprimer le problème de complétion de données en terme d'équation « d'interface ». Cette équation est résolue via un algorithme de Richardson préconditionné avec relaxation dynamique. L'efficacité de la méthode est illustrée par quelques expériences numériques.

Received: 2007-07-12
Accepted: 2007-10-10
Published online: 2007-11-26

DOI: 10.1016/j.crme.2007.10.006

Keywords: Data completion, Inverse problem, Cauchy–Helmholtz problem, Interface operator, Steklov–Poincaré operator
Mot clés : Complétion de données, Problème inverse, Problème de Cauchy–Helmholtz, Operateur d'interface, Opérateur de Steklov–Poincaré

Author's affiliations:

Riadh Ben Fatma ¹; Mejdi Azaïez ²; Amel Ben Abda ¹; Nabil Gmati ¹

¹ LAMSIN, École nationale d'ingénieurs de Tunis, B.P. 37, 1002, Le Belvédère, Tunisia
² TREFLE (UMR CNRS 8508), ENSCPB, 33607 Pessac, France

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     author = {Riadh Ben Fatma and Mejdi Aza{\"\i}ez and Amel Ben Abda and Nabil Gmati},
     title = {Missing boundary data recovering for the {Helmholtz} problem},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {787--792},
     publisher = {Elsevier},
     volume = {335},
     number = {12},
     year = {2007},
     doi = {10.1016/j.crme.2007.10.006},
     language = {en},
}

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Riadh Ben Fatma; Mejdi Azaïez; Amel Ben Abda; Nabil Gmati. Missing boundary data recovering for the Helmholtz problem. Comptes Rendus. Mécanique, Volume 335 (2007) no. 12, pp. 787-792. doi : 10.1016/j.crme.2007.10.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.006/

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