Diffraction by an obstacle located in a semi-infinite plates grating

Anne Sophie Bonnet-Bendhia; Karim Ramdani; Axel Tillequin

doi:10.1016/S0764-4442(00)01762-6

Diffraction by an obstacle located in a semi-infinite plates grating

Anne Sophie Bonnet-Bendhia, Karim Ramdani, Axel Tillequin

Unité de Mathématiques Appliquées

Research output: Contribution to journal › Article › peer-review

Abstract

A method to solve the scattering problem by a grating of semi-infinite horizontal plates locally perturbed by a bounded obstacle is proposed. This method couples a variational equation set in a bounded domain surrounding the obstacle with a pseudo-differential equation set on the vertical line located at the end of the plates. Using a variational formulation, we prove that the Fredholm alternative holds except for the resonant frequencies of the grating.

Translated title of the contribution	Diffraction par un obstacle situé dans un réseau de plaques semi-infinies
Original language	English
Pages (from-to)	977-982
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	331
Issue number	12
DOIs	https://doi.org/10.1016/S0764-4442(00)01762-6
Publication status	Published - 15 Dec 2000

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title = "Diffraction by an obstacle located in a semi-infinite plates grating",

abstract = "A method to solve the scattering problem by a grating of semi-infinite horizontal plates locally perturbed by a bounded obstacle is proposed. This method couples a variational equation set in a bounded domain surrounding the obstacle with a pseudo-differential equation set on the vertical line located at the end of the plates. Using a variational formulation, we prove that the Fredholm alternative holds except for the resonant frequencies of the grating.",

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AU - Bonnet-Bendhia, Anne Sophie

AU - Ramdani, Karim

AU - Tillequin, Axel

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Y1 - 2000/12/15

N2 - A method to solve the scattering problem by a grating of semi-infinite horizontal plates locally perturbed by a bounded obstacle is proposed. This method couples a variational equation set in a bounded domain surrounding the obstacle with a pseudo-differential equation set on the vertical line located at the end of the plates. Using a variational formulation, we prove that the Fredholm alternative holds except for the resonant frequencies of the grating.

AB - A method to solve the scattering problem by a grating of semi-infinite horizontal plates locally perturbed by a bounded obstacle is proposed. This method couples a variational equation set in a bounded domain surrounding the obstacle with a pseudo-differential equation set on the vertical line located at the end of the plates. Using a variational formulation, we prove that the Fredholm alternative holds except for the resonant frequencies of the grating.

U2 - 10.1016/S0764-4442(00)01762-6

DO - 10.1016/S0764-4442(00)01762-6

M3 - Article

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SN - 0764-4442

VL - 331

SP - 977

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JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 12

ER -

Diffraction by an obstacle located in a semi-infinite plates grating

Abstract

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