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Nouvelles formulations intégrales pour les problèmesde diffraction d'ondes

Published online by Cambridge University Press:  15 February 2004

David P. Levadoux  and
Bastiaan L. Michielsen
David P. Levadoux
Affiliation:
ONERA, centre de Palaiseau, Chemin de la Hunière, 91761 Palaiseau, France. [email protected].
Bastiaan L. Michielsen
Affiliation:
ONERA, centre de Palaiseau, Chemin de la Hunière, 91761 Palaiseau, France. [email protected].
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Abstract

We present an integral equation method for solving boundary valueproblems of the Helmholtz equation in unbounded domains. Themethod relies on the factorisation of one of the Calderón projectors by an operator approximating the exterioradmittance (Dirichlet to Neumann) operator of the scatteringobstacle. We show how the pseudo-differential calculus allows usto construct such approximations and that this yields integralequations without internal resonances and being well-conditionedat all frequencies. An implementation technique is elaborated,where again reasonings from pseudo-differential calculus play animportant rôle. Some numerical examples are presented which appearto confirm that the new integral equation leads to linear systemswhich are much better conditioned than the classical ("direct")integral equations and hence have much better behaviour whensolved with iterative techniques and matrix sparsification.

Keywords

Équations intégralesopérateurs pseudo-différentielséquation de Helmholtz.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 1 , January 2004 , pp. 157 - 175
Copyright
© EDP Sciences, SMAI, 2004

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