Scattering and Diffraction by Wedges 1

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Vito G. Daniele. Scattering and Diffraction by Wedges 1

Table of Contents

List of Illustrations

Guide

Pages

Scattering and Diffraction by Wedges 1. The Wiener-Hopf Solution – Theory

Preface

Introduction

1. Introduction to the Wiener-Hopf Method. 1.1 A brief history of the Wiener-Hopf method

1.2 Fundamental definitions and assumptions to develop the Wiener-Hopf technique in the spectral domain

1.3 WH equations from the physical domain to the spectral domain

1.4 WH equations in wave scattering problems

1.5 Classical solution of WH equations

1.6 The decomposition (Cauchy) equations

1.7 General formula for factorization of scalar kernels

1.8 Some explicit factorization of matrix kernels useful in wedge scattering

1.9 The Fredholm factorization technique: a general technique to solve WH equations

1.10 Spectral properties of the unknowns

1.11 Semi-analytical solution of the Fredholm integral equation

1.12 Analytic continuation outside the integration line in the η -plane

1.13 The complex plane w

1.14 The WH unknowns in the w plane

1.15 The Fredholm factorization technique in the w plane

1.16 Analytic continuation in the w plane

1.17 The Fredholm factorization technique to factorize the kernel

1.18 Some examples of the Fredholm factorization method

Appendix 1.A: effect of using j and i as imaginary units in Fourier transforms

Appendix 1.B: compactness of the matrix kernel

Note

2. A Basic Example: Scattering by a Half-plane. 2.1. The fundamental problem of diffraction in wave motion

2.2. Unified theory of transverse equations in arbitrary stratified regions

2.3. WH equation for electromagnetic diffraction by a perfectly electrically conducting (PEC) half-plane illuminated by an Ez-polarized plane wave at normal incidence

2.4. Non-standard contributions of WH unknowns in the PEC half-plane illuminated by an Ez-polarized plane wave at normal incidence

2.5. Solution of the WH equation of the PEC half-plane using classical closed-form factorization

2.6. Solution of the WH equation of the PEC half-plane using the Fredholm factorization method

2.7. Field estimation

2.8. Numerical validation of the Fredholm factorization method

2.9. Generality of the wave motion in a homogeneous isotropic elastic solid

2.10. Plane waves in a homogeneous elastic solid and simplifications

2.11. Diffraction by a half-infinite crack in a homogeneous elastic solid planar problem

2.12. Diffraction by a half-infinite crack in a homogeneous isotropic two-dimensional elastic solid problem

Note

3. The Wiener-Hopf Theory for Angular Region Problems. 3.1. A brief history of the classical methods for studying angular regions

3.2. Introduction to the generalized Wiener-Hopf technique

3.3. WH functional equations in the angular region filled by a homogeneous isotropic medium in Electromagnetics

3.4. Reduction of the generalized functional equations of an angular region to functional equations defined in the same complex plane

3.5. Generalized Wiener-Hopf equations for the impenetrable wedge scattering problem

3.6. Solution of generalized Wiener-Hopf equations for the impenetrable wedge scattering problem

3.7. Non-standard parts of the plus and minus functions in GWHEs for the impenetrable wedge scattering problem

3.8. Closed-form solution of the PEC wedge scattering problem at normal incidence

3.9. Alternative solution of the PEC wedge scattering problem at normal incidence via difference equations

3.10. Generalized WH functional equations for angular regions in the w plane

3.11. Rotating wave method

3.12. Properties of rotating waves

3.13. Spectral field component in w for an arbitrary direction ϕ using rotating waves

3.14. Rotating waves in areas different from electromagnetism

3.15. Closed-form solution of the diffraction of an elastic SH wave by wedge with classical factorization

3.16. Rotating waves with the MF transform for wedge problems

3.17. Alternative solution of PEC wedge scattering problems via difference equations and the MF transform in terms of rotating waves

Appendix 3.A: the Malyuzhinets–Fourier (MF) transform

Note

References

Index. A,B,C

D,E,F

G,H,I

K,L,M

N,O,P

R,S,T

U,V,W

Summary of Volume 2

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WILEY END USER LICENSE AGREEMENT

Отрывок из книги

To my beloved grandchildren Marianna and Roberto V.G.D.

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Furthermore, even though formal solutions can be obtained in particular cases, a long and difficult elaboration may be required to make them effective from the physical and engineering points of view. For this purpose, tools such as the saddle point method are necessary for the asymptotic evaluation of integrals.

In this book, we aim to solve these problems systematically by helping the reader to implement solutions using the WH method with precise, simple steps and reducing the restrictions on generalization.

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