Advanced Studies in the Mathematical Theory of Scattering, Volume 3

Auteur

Jean-Michel L. Bernard is a former Research Director at the CEA, France, and an associate researcher at the CMLA-ENS, Paris-Saclay, France. Currently, he is a senior member of the IEEE engineering association. His research interests include the evaluation of electromagnetic fields scattered by complex objects, especially by analytical and semi-analytical technics.

Texte du rabat

This book presents a collection of independent mathematical studies, describing the analytical reduction of complex generic problems in the theory of scattering and propagation of electromagnetic waves in the presence of imperfectly conducting objects. Their subjects include: a global method for scattering by a multimode plane; diffraction by an impedance curved wedge; scattering by impedance polygons; advanced properties of spectral functions in frequency and time domains; bianisotropic media and related coupling expressions; and exact and asymptotic reductions of surface radiation integrals. The methods developed here can be qualified as analytical when they lead to exact explicit expressions, or semi-analytical when they drastically reduce the mathematical complexity of studied problems. Therefore, they can be used in mathematical physics and engineering to analyse and model, but also in applied mathematics to calculate the scattered fields in electromagnetism for a low computational cost.

Contenu

Introduction xv

Chapter 1 A Global Method for the Scattering by a Multimode Plane with Arbitrary Primary Sources and Complete Series with Error Functions 1

Chapter 2 Diffraction by an Impedance Curved Wedge with Arbitrary Angle and Uniform Higher Order Asymptotics 39

Chapter 3 Spectral Equations for Scattering by Impedance Polygons: Properties and Solutions 81

Chapter 4. Advanced Properties of Spectral Functions in Frequency and Time Domains for Diffraction by a Wedge-shaped Region 137

Chapter 5 General Integral Identities for Bianisotropic Media and Related Equations, Properties and Coupling Expressions 201

Chapter 6. Exact and Asymptotic Reductions of Surface Radiation Integrals with Complex Exponential Arguments to Efficient Contour Integrals 251

Index 337