## Diffraction by an Immersed Elastic Wedge, Issue 1723This monograph presents the mathematical description and numerical computation of the high-frequency diffracted wave by an immersed elastic wave with normal incidence. The mathematical analysis is based on the explicit description of the principal symbol of the pseudo-differential operator connected with the coupled linear problem elasticity/fluid by the wedge interface. This description is subsequently used to derive an accurate numerical computation of diffraction diagrams for different incoming waves in the fluid, and for different wedge angles. The method can be applied to any problem of coupled waves by a wedge interface. This work is of interest for any researcher concerned with high frequency wave scattering, especially mathematicians, acousticians, engineers. |

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### Contents

1 Introduction | 1 |

2 Notation and Results | 3 |

22 Strategy of the Study | 6 |

23 Outgoing Solutions | 12 |

24 Translation Operators | 14 |

25 Main Theorems | 16 |

26 Integral Representation of the Solution | 19 |

27 Asymptotics of the Diffracted Wave in the Fluid | 22 |

43 Proof of Theorem 2 Structure of the Spectral Function | 75 |

5 Numerical Algorithm | 79 |

52 The Case of an Incident Plane Wave in the Fluid | 80 |

53 The Case of an Incident ScholteStoneley Wave | 81 |

54 Approximation of the Regular Part of the Spectral Function | 85 |

55 Computation of the Spectral Function | 90 |

56 Practical Issues | 91 |

6 Numerical Results | 97 |

3 The Spectral Function | 27 |

32 The Equations SolidFluid Coupled by a Plane Surface | 33 |

33 Some Properties of the Operators DM TM | 41 |

34 Decomposition of the Spectral Function | 50 |

35 The Functional Equation for the Spectral Function | 53 |

4 Proofs of the Results | 57 |

42 Proof of Theorem 1 Existence and Uniqueness of the Spectral Function | 74 |

62 Presentation of the Results | 100 |

63 Iterates Generated by the Recursive Formula | 103 |

64 Numerical Accuracy of the Direct Evaluation | 104 |

Appendix | 124 |

130 | |

### Other editions - View all

Diffraction by an Immersed Elastic Wedge Jean-Pierre Croisille,Gilles LeBeau No preview available - 2014 |

### Common terms and phrases

200 observation angle A+(u Algebraic analytic angle ip approximation asymptotics Cetraro collocation points complex computation contour corresponding critical angles decomposition deduce defined Diagram of diffraction diffracted wave Dirichlet displayed on Fig domain dural wedge Editor Elliptic existence and uniqueness face fluid Fourier transform functional equation Galerkin basis geometric given half-plane Hardy inequality holomorphic holomorphic function immersed in water Incident Scholte-Stoneley wave Incident volume wave incident wave interface-wave kernel Lebeau Lemma lNClDENCE lNClDENT SCHOLTE-STONELEY WAVE meromorphic Montecatini Terme neighborhood Neumann observation angle Fig outgoing solution path pictured pictured on Fig plane wave poles of reflection Probability Theory problem prove Quantum Groups real axis real part Fig resp semi-axis Seminaire de Probabilites sequel singularities space spectral function Stoneley tempered distribution vector velocity Vlll Wedge of Angle wedge of ip