Scattering and diffraction by wedges 1 the Wiener-Hopf solution - theory - Daniele, Vito 1942-; Lombardi, Guido (ISTE, 2020)
Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Introduction -- Chapter 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 -- Chapter 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-po... -- 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 -- Chapter 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... -- 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... -- Appendix 3.A: the Malyuzhinets-Fourier (MF) transform -- References -- Index -- Summary of Volume 2 -- Preface -- Introduction -- Chapter 4. Exact Solutions for Electromagnetic Impedance Wedges -- Chapter 5. Fredholm Factorization Solutions of GWHEs for the Electromagnetic Impedance Wedges Surrounded by an Isotropic Medium -- Chapter 6. Diffraction by Penetrable Wedges -- References -- Other titles from ISTE in Waves -- EULA.