Advances in Mathematical Methods for Electromagnetics

by Kazuya Kobayashi (Editor), Paul Denis Smith (Editor)

Overview

This book covers recent achievements in the area of advanced analytical and associated numerical methods as applied to various problems arising in all branches of electromagnetics. The unifying theme is the application of advanced or novel mathematical techniques to produce analytical solutions or effective analytical-numerical methods for computational electromagnetics addressing more general problems.

Each chapter contains an outline of its topic, discusses its scientific context and importance, describes approaches to date, gives an exposition of the author's approach to the problem tackled in the chapter, describes the results, and concludes with a discussion of the range or class of problems where the techniques described work most appropriately and effectively.

Intended primarily for researchers in the fields of electrical engineering, mathematics, physics and related disciplines, the book offers systematic and thorough coverage of this complex topic. It is hoped that the book will help to stimulate further investigation and discussion of the important problems in electromagnetics within this research community.

Product Details

ISBN-13:	9781785613845
Publisher:	The Institution of Engineering and Technology
Publication date:	02/04/2021
Series:	Electromagnetic Waves
Pages:	748
Product dimensions:	6.14(w) x 9.21(h) x (d)

About the Author

Kazuya Kobayashi is a professor in the Department of Electrical, Electronic, and Communication Engineering at Chuo University, Japan. He has received a number of awards including The President's Award (2020) from URSI (International Union of Radio Science) and the M.A. Khizhnyak Award (2016) at the 16th International Conference on Mathematical Methods in Electromagnetic Theory. He is a Fellow of The Electromagnetics Academy and a Fellow of URSI. He has held various positions in the international radio science, electromagnetics, and optics communities including URSI Assistant Secretary-General for AP-RASC (since 2015); Chair of URSI Commission B (since 2017); Chair of the AP-RASC Standing Committee (since 2015); President of the Japan National Committee of URSI (2008-2018); Chair of the PIERS Young Scientists Award Committee, The Electromagnetics Academy (since 2018); Editor of Radio Science (since 2019); and Series Editor of Springer Series in Optical Sciences (since 2020). His research areas include developments of rigorous mathematical techniques as applied to electromagnetic wave problems; radar cross section; and scattering and diffraction.

Paul Denis Smith is a professor of mathematics at the Macquarie University, Australia. His awards include the best paper award at the 1987 International Symposium on Electromagnetic Compatibility. He served as associate editor of J. IEEE Antennas and Propagation from 2004 to 2011 and is currently an associate editor of Radio Science and a Board Member for Proceedings of the Royal Society(A). He is president of the Australian URSI Committee and is a member of the Australian Academy of Science National Committee for Space and Radio Science. His research areas include analytical and semi-analytical techniques for wave scattering and diffraction.

Table of Contents

• Introduction
• Chapter 1: New insights in integral representation theory for the solution of complex canonical diffraction problems
• Chapter 2: Scattering of electromagnetic surface waves on imperfectly conducting canonical bodies
• Chapter 3: Dielectric-wedge Fourier series
• Chapter 4: Green's theorem, Green's functions and Huygens' principle in discrete electromagnetics
• Chapter 5: The concept of generalized functions and universal properties of the Green's functions associated with the wave equation in bounded piece-wise homogeneous domains
• Chapter 6: Elliptic cylinder with a strongly elongated cross-section: high frequency techniques and function theoretic methods
• Chapter 7: High-frequency hybrid ray-mode techniques
• Chapter 8: Scattering and diffraction of scalar and electromagnetic waves using spherical-multipole analysis and uniform complex-source beams
• Chapter 9: Changes in the far-field pattern induced by rounding the corners of a scatterer: dependence upon curvature
• Chapter 10: Radiation from a line source at the vertex of a right-angled dielectric wedge
• Chapter 11: Wiener-Hopf analysis of the diffraction by a thin material strip
• Chapter 12: The Wiener-Hopf Fredholm factorization technique to solve scattering problems in coupled planar and angular regions
• Chapter 13: On the analytical regularization method in scattering and diffraction
• Chapter 14: Resonance scattering of E-polarized plane waves by two-dimensional arbitrary open cavities: spectrum of complex eigenvalues
• Chapter 15: Numerical solutions of integral equations for electromagnetics
• Chapter 16: Electromagnetic modelling at arbitrarily low frequency via the quasi-Helmholtz projectors
• Chapter 17: Resistive and thin dielectric disk antennas with axially symmetric excitation analyzed using the method of analytical regularization
• Chapter 18: Scattering and guiding problems of electromagnetic waves in inhomogeneous media by improved Fourier series expansion method
• Chapter 19: Methods and fast algorithms for the solution of volume singular integral equations
• Chapter 20: Herglotz functions and applications in electromagnetics
• Chapter 21: Scattering and guidance by layered cylindrically periodic arrays of circular cylinders
• Chapter 22: Analytical and numerical solution techniques for forward and inverse scattering problems in waveguides
• Chapter 23: Beam-based local diffraction tomography
• Chapter 24: Modal expansions in dispersive material systems with application to quantum optics and topological photonics
• Chapter 25: Multiple scattering by a collection of randomly located obstacles distributed in a dielectric slab
• Chapter 26: Electromagnetics of complex environments applied to geophysical and biological media
• Chapter 27: Innovative tools for SI units in solving various problems of electrodynamics