Scattering and Diffraction by Wedges 2

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Vito G. Daniele. Scattering and Diffraction by Wedges 2

Table of Contents

List of Illustrations

Guide

Pages

Scattering and Diffraction by Wedges 2. The Wiener-Hopf Solution – Advanced Applications

Preface

Introduction

4. Exact Solutions for Electromagnetic Impedance Wedges. 4.1. Introduction

4.2. A list of the impedance wedge problems amenable to exact WH solutions

4.3. Cases involving classical WH equations

4.3.1. WH formulation of the diffraction by an impedance half-plane

4.3.2. Exact solutions of the diffraction by an impedance half-plane. 4.3.2.1. Exact solution in the presence of the isotropic impedances Za and Zb

4.3.2.2. Exact solution in the presence of symmetric anisotropic impedances Za = Zb

4.3.2.3. Exact solution in the presence of opposite diagonal impedances Zb = –Za at skew incidence

4.3.2.4. Exact solution in the presence of non-invertible Za (det[Za] = 0) and Zb (det[Zb] = 0) at skew incidence

4.3.2.5. Exact solution for the diffraction by a half-plane at normal incidence with diagonal impedances

4.3.2.6. Exact factorization with the scalar reflection coefficient Γ = (Za + Zb) [Za – Zb)

4.3.2.7. Exact factorization at skew incidence when Za = 0 and Zb diagonal with a null element

4.3.3. Exact solution for the full-plane junction at skew incidence

4.3.4. Exact solution of the penetrable half-plane problem (the jump)

4.3.5. Exact solution of the right-angled wedge scattering problem

4.4. Exact solutions for impedance wedge problems with the GWHE form of section 3.5 – form #1

4.4.1. The WH solution of the Malyuzhinets problem

4.4.2. Diffraction at skew incidence (α0 ≠ 0 ) by a wedge with a PEC and a PMC face

4.4.3. Diffraction at skew incidence (ao ≠ 0) by a wedge with a PEC face and the other face with diagonal Zb with one null element

4.5. Exact solutions for the impedance wedge problems with the GWHEs written in an alternative form – form #2

4.5.1. Exact factorization with diagonal polynomial matrices Pa,b (m)

4.5.2. Anisotropic symmetric impedance wedges at normal incidence

4.5.3. Non-symmetric wedges at normal incidence with commuting Pa and Pb

4.5.4. Non-symmetric wedges at skew incidence

4.5.5. Two particular wedge problems amenable to exact solutions

4.6. A general form of the GWHEs to study the arbitrary face impedance wedges – form #3

Appendix 4.A. Some important formulas of decomposition for wedge problems

5. Fredholm Factorization Solutions of GWHEs for the Electromagnetic Impedance Wedges Surrounded by an Isotropic Medium. 5.1. Introduction

5.2. Generalized Wiener-Hopf equations for the impenetrable wedge scattering problem of an electromagnetic plane wave at skew incidence

5.3. Fredholm factorization solution in the plane of GWHEs

5.4. Fredholm factorization solution in the plane of GWHEs

5.5. Approximate solution of FIEs derived from GWHEs

5.6. Analytic continuation of approximate solutions of GWHEs

5.7. Far-field computation

5.8. Criteria for the examples

5.9. Example 1: Symmetric isotropic impedance wedge at normal incidence with Ez polarization

5.10. Example 2: Non-symmetric isotropic impedance wedge at normal incidence with Hz polarization and surface wave contribution

5.11. Example 3: PEC wedge at skew incidence

5.12. Example 4: Arbitrary impedance half-plane at skew incidence

5.13. Example 5: Arbitrary impedance wedge at skew incidence

5.14. Example 6: Arbitrary impedance concave wedge at skew incidence

5.15. Discussion

Appendix 5.A. Fredholm properties of the integral equation (5.3.1)

6. Diffraction by Penetrable Wedges. 6.1. Introduction

6.2. GWHEs for the dielectric wedge at normal incidence (Ez-polarization)

6.3. Reduction of the GWHEs for the dielectric wedge at Ez-polarization to Fredholm integral equations

6.4. Analytic continuation for the solution of the dielectric wedge at Ez-polarization

6.5. Some remarks on the Fredholm integral equations (6.3.24), (6.3.26) and numerical solutions

6.6. Field evaluation in any point of the space

6.7. The dielectric wedge at skew incidence

6.8. Criteria for examples of the scattering by a dielectric wedge at normal incidence (Ez-polarization)

6.9. Example: the scattering by a dielectric wedge at normal incidence (Ez-polarization)

6.10. Discussion

Appendix 6.A. Fredholm factorization applied to (6.3.2)–(6.3.5)

Appendix 6.B. Source term

References

Index. A, B, C

D, E, F

G, H, I

J, K, L

M, N, O

P, Q, R

S, T, U

V, W

Summary of Volume 1

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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