The book has a dual purpose. The first is to expose a general methodology to solve problems of electromagnetism in geometries constituted of angular regions. The second is to bring the solutions of some canonical problems of fundamental importance in modern electromagnetic engineering with the use of the Wiener-Hopf technique. In particular, the general mathematical methodology is very ingenious and original. It is based on sophisticated and attractive procedures exploiting simple and advanced properties of analytical functions. Once the reader has acquired the methodology, they can easily…mehr
The book has a dual purpose. The first is to expose a general methodology to solve problems of electromagnetism in geometries constituted of angular regions. The second is to bring the solutions of some canonical problems of fundamental importance in modern electromagnetic engineering with the use of the Wiener-Hopf technique. In particular, the general mathematical methodology is very ingenious and original. It is based on sophisticated and attractive procedures exploiting simple and advanced properties of analytical functions. Once the reader has acquired the methodology, they can easily obtain the solution of the canonical problems reported in the book. The book can be appealing also to readers who are not directly interested in the detailed mathematical methodology and/ or in electromagnetics. In fact the same methodology can be extended to acoustics and elasticity problems. Moreover, the proposed practical problems with their solutions constitute a list of reference solutions and can be of interest in engineering production in the field of radio propagations, electromagnetic compatibility and radar technologies.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Vito G. Daniele, Ecole Polytechnique of Turin, Italia. Lombardi Guido, Ecole Polytechnique of Turin, Italia.
Inhaltsangabe
Preface ix Introduction xiii Chapter 1. Introduction to the Wiener-Hopf Method 1 1.1. A brief history of the Wiener-Hopf method 1 1.2. Fundamental definitions and assumptions to develop the Wiener-Hopf technique in the spectral domain 1 1.3. WH equations from the physical domain to the spectral domain 4 1.4. WH equations in wave scattering problems 5 1.5. Classical solution of WH equations 8 1.6. The decomposition (Cauchy) equations 11 1.7. General formula for factorization of scalar kernels 13 1.8. Some explicit factorization of matrix kernels useful in wedge scattering 15 1.9. The Fredholm factorization technique: a general technique to solve WH equations 19 1.10. Spectral properties of the unknowns 22 1.11. Semi-analytical solution of the Fredholm integral equation 25 1.12. Analytic continuation outside the integration line in the -plane 28 1.13. The complex plane w 30 1.14. The WH unknowns in the w plane 34 1.15. The Fredholm factorization technique in the w plane 36 1.16. Analytic continuation in the w plane 40 1.17. The Fredholm factorization technique to factorize the kernel 42 1.18. Some examples of the Fredholm factorization method 45 Appendix 1.A: effect of using j and i as imaginary units in Fourier transforms 52 Appendix 1.B: compactness of the matrix kernel G-1( )G(u)-1/u- Chapter 2. A Basic Example: Scattering by a Half-plane 59 2.1. The fundamental problem of diffraction in wave motion 59 2.2. Unified theory of transverse equations in arbitrary stratified regions 62 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 67 2.4. Non-standard contributions of WH unknowns in the PEC half-plane illuminated by an Ez-polarized plane wave at normal incidence 69 2.5. Solution of the WH equation of the PEC half-plane using classical closed-form factorization 71 2.6. Solution of the WH equation of the PEC half-plane using the Fredholm factorization method 72 2.7. Field estimation 73 2.8. Numerical validation of the Fredholm factorization method 85 2.9. Generality of the wave motion in a homogeneous isotropic elastic solid 91 2.10. Plane waves in a homogeneous elastic solid and simplifications 103 2.11. Diffraction by a half-infinite crack in a homogeneous elastic solid planar problem 110 2.12. Diffraction by a half-infinite crack in a homogeneous isotropic two-dimensional elastic solid problem 113 Chapter 3. The Wiener-Hopf Theory for Angular Region Problems 123 3.1. A brief history of the classical methods for studying angular regions 123 3.2. Introduction to the generalized Wiener-Hopf technique 125 3.3. WH functional equations in the angular region filled by a homogeneous isotropic medium in Electromagnetics 127 3.4. Reduction of the generalized functional equations of an angular region to functional equations defined in the same complex plane 141 3.5. Generalized Wiener-Hopf equations for the impenetrable wedge scattering problem 151 3.6. Solution of generalized Wiener-Hopf equations for the impenetrable wedge scattering problem 153 3.7. Non-standard parts of the plus and minus functions in GWHEs for the impenetrable wedge scattering problem 154 3.8. Closed-form solution of the PEC wedge scattering problem at normal incidence 158 3.9. Alternative solution of the PEC wedge scattering problem at normal incidence via difference equations 160 3.10. Generalized WH functional equations for angular regions in the w plane 164 3.11. Rotating wave method 167 3.12. Properties of rotating waves 172 3.13. Spectral field component in w for an arbitrary direction using rotating waves 178 3.14. Rotating waves in areas different from electromagnetism 180 3.15. Closed-form solution of the diffraction of an elastic SH wave by wedge with classical factorization 182 3.16. Rotating waves with the MF transform for wedge problems 185 3.17. Alternative solution of PEC wedge scattering problems via difference equations and the MF transform in terms of rotating waves 187 Appendix 3.A: the Malyuzhinets-Fourier (MF) transform 188 References 193 Index 197 Summary of Volume 2 201
Preface ix Introduction xiii Chapter 1. Introduction to the Wiener-Hopf Method 1 1.1. A brief history of the Wiener-Hopf method 1 1.2. Fundamental definitions and assumptions to develop the Wiener-Hopf technique in the spectral domain 1 1.3. WH equations from the physical domain to the spectral domain 4 1.4. WH equations in wave scattering problems 5 1.5. Classical solution of WH equations 8 1.6. The decomposition (Cauchy) equations 11 1.7. General formula for factorization of scalar kernels 13 1.8. Some explicit factorization of matrix kernels useful in wedge scattering 15 1.9. The Fredholm factorization technique: a general technique to solve WH equations 19 1.10. Spectral properties of the unknowns 22 1.11. Semi-analytical solution of the Fredholm integral equation 25 1.12. Analytic continuation outside the integration line in the -plane 28 1.13. The complex plane w 30 1.14. The WH unknowns in the w plane 34 1.15. The Fredholm factorization technique in the w plane 36 1.16. Analytic continuation in the w plane 40 1.17. The Fredholm factorization technique to factorize the kernel 42 1.18. Some examples of the Fredholm factorization method 45 Appendix 1.A: effect of using j and i as imaginary units in Fourier transforms 52 Appendix 1.B: compactness of the matrix kernel G-1( )G(u)-1/u- Chapter 2. A Basic Example: Scattering by a Half-plane 59 2.1. The fundamental problem of diffraction in wave motion 59 2.2. Unified theory of transverse equations in arbitrary stratified regions 62 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 67 2.4. Non-standard contributions of WH unknowns in the PEC half-plane illuminated by an Ez-polarized plane wave at normal incidence 69 2.5. Solution of the WH equation of the PEC half-plane using classical closed-form factorization 71 2.6. Solution of the WH equation of the PEC half-plane using the Fredholm factorization method 72 2.7. Field estimation 73 2.8. Numerical validation of the Fredholm factorization method 85 2.9. Generality of the wave motion in a homogeneous isotropic elastic solid 91 2.10. Plane waves in a homogeneous elastic solid and simplifications 103 2.11. Diffraction by a half-infinite crack in a homogeneous elastic solid planar problem 110 2.12. Diffraction by a half-infinite crack in a homogeneous isotropic two-dimensional elastic solid problem 113 Chapter 3. The Wiener-Hopf Theory for Angular Region Problems 123 3.1. A brief history of the classical methods for studying angular regions 123 3.2. Introduction to the generalized Wiener-Hopf technique 125 3.3. WH functional equations in the angular region filled by a homogeneous isotropic medium in Electromagnetics 127 3.4. Reduction of the generalized functional equations of an angular region to functional equations defined in the same complex plane 141 3.5. Generalized Wiener-Hopf equations for the impenetrable wedge scattering problem 151 3.6. Solution of generalized Wiener-Hopf equations for the impenetrable wedge scattering problem 153 3.7. Non-standard parts of the plus and minus functions in GWHEs for the impenetrable wedge scattering problem 154 3.8. Closed-form solution of the PEC wedge scattering problem at normal incidence 158 3.9. Alternative solution of the PEC wedge scattering problem at normal incidence via difference equations 160 3.10. Generalized WH functional equations for angular regions in the w plane 164 3.11. Rotating wave method 167 3.12. Properties of rotating waves 172 3.13. Spectral field component in w for an arbitrary direction using rotating waves 178 3.14. Rotating waves in areas different from electromagnetism 180 3.15. Closed-form solution of the diffraction of an elastic SH wave by wedge with classical factorization 182 3.16. Rotating waves with the MF transform for wedge problems 185 3.17. Alternative solution of PEC wedge scattering problems via difference equations and the MF transform in terms of rotating waves 187 Appendix 3.A: the Malyuzhinets-Fourier (MF) transform 188 References 193 Index 197 Summary of Volume 2 201
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