Advances in Computational Mathematics

, Volume 16, Issue 2–3, pp 113–138 | Cite as

Diffraction by an Acoustic Grating Perturbed by a Bounded Obstacle

  • Anne-Sophie Bonnet-Bendhia
  • Karim Ramdani
Article

Abstract

An original approach to solve 2D time harmonic diffraction problems involving locally perturbed gratings is proposed. The propagation medium is composed of a periodically stratified half-space and a homogeneous half-space containing a bounded obstacle. Using Fourier and Floquet transforms and integral representations, the diffraction problem is formulated as a coupled problem of Fredholm type with two unknowns: the trace of the diffracted field on the interface separating the two half-spaces on one hand, and the restriction of the diffracted field to a bounded domain surrounding the obstacle, on the other hand.

acoustic diffraction perturbed gratings Floquet transform 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Anne-Sophie Bonnet-Bendhia
    • 1
  • Karim Ramdani
    • 2
  1. 1.Laboratoire UMAENSTAParis Cedex 15France
  2. 2.IECN, Département de MathématiquesUniversité de Nancy IVandœuvre les Nancy CedexFrance

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