ISBN: 3-540-66810-1
TITLE: Diffraction by an Immersed Elastic Wedge
AUTHOR: Croisille, Jean-Pierre; Lebeau, Gilles
TOC:
1. Introduction 1
2. Notation and results
2.1 Notation and results 3
2.2 Strategy of the study 6
2.3 Outgoing solutions 12
2.4 Translation operators 14
2.5 Main theorems 16
2.6 Integral representation of the solution 19
2.7 Asymptotics of the diffracted wave in the fluid 22
3. The spectral function
3.1 The integral system for the spectral function 27
3.2 The equations solid-fluid coupled by a plane surface 33
3.3 Some properties of the operators DM and T M 41
3.4 Decomposition of the spectral function 50
3.5 The functional equation for the spectral function 53
4. Proofs of the results
4.1 An isomophism theorem 57
4.2 Proof of Theorem 1. Existence and uniqueness of the spectral function 74
4.3 Proof of Theorem 2. Structure of the spectral function 75
5. Numerical algorithm
5.1 Introduction 79
5.2 The case of an incident wave in the fluid 80
5.3 The case of an incident Scholte-Stoneley wave 81
5.4 Approximation of the regular part of the spectral function 85
5.5 Computation of the spectral function 90
5.6 Practical issues 91
6. Numerical results
6.1 Introduction 97
6.2 Presentation of the results 100
6.3 Iterates generated by the recursive formula 103
6.4 Numerical accuracy of the direct evaluation 104
6.5 Numerical diagrams of diffraction 104
Appendix 127
Subject Index 129
References 133
END