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A comprehensive, step-by-step reference to the Nyström Method for solving Electromagnetic problems using integral equations Computational electromagnetics studies the numerical methods or techniques that solve electromagnetic problems by computer programming. Currently, there are mainly three numerical methods for electromagnetic problems: the finite-difference time-domain (FDTD), finite element method (FEM), and integral equation methods (IEMs). In the IEMs, the method of moments (MoM) is the most widely used method, but much attention is being paid to the Nyström method as another IEM, because it possesses some unique merits which the MoM lacks. This book focuses on that method—providing information on everything that students and professionals working in the field need to know. Written by the top researchers in electromagnetics, this complete reference book is a consolidation of advances made in the use of the Nyström method for solving electromagnetic integral equations. It begins by introducing the fundamentals of the electromagnetic theory and computational electromagnetics, before proceeding to illustrate the advantages unique to the Nyström method through rigorous worked out examples and equations. Key topics include quadrature rules, singularity treatment techniques, applications to conducting and penetrable media, multiphysics electromagnetic problems, time-domain integral equations, inverse scattering problems and incorporation with multilevel fast multiple algorithm. Systematically introduces the fundamental principles, equations, and advantages of the Nyström method for solving electromagnetic problems Features the unique benefits of using the Nyström method through numerical comparisons with other numerical and analytical methods Covers a broad range of application examples that will point the way for future research The Nystrom Method in Electromagnetics is ideal for graduate students, senior undergraduates, and researchers studying engineering electromagnetics, computational methods, and applied mathematics. Practicing engineers and other industry professionals working in engineering electromagnetics and engineering mathematics will also find it to be incredibly helpful.
New method for the characterization of electromagnetic wave dynamics Modern Characterization of Electromagnetic Systems introduces a new method of characterizing electromagnetic wave dynamics and measurements based on modern computational and digital signal processing techniques. The techniques are described in terms of both principle and practice, so readers understand what they can achieve by utilizing them. Additionally, modern signal processing algorithms are introduced in order to enhance the resolution and extract information from electromagnetic systems, including where it is not currently possible. For example, the author addresses the generation of non-minimum phase or transient response when given amplitude-only data. Presents modern computational concepts in electromagnetic system characterization Describes a solution to the generation of non-minimum phase from amplitude-only data Covers model-based parameter estimation and planar near-field to far-field transformation as well as spherical near-field to far-field transformation Modern Characterization of Electromagnetic Systems is ideal for graduate students, researchers, and professionals working in the area of antenna measurement and design. It introduces and explains a new process related to their work efforts and studies.
This lecture provides a tutorial introduction to the Nyström and locally-corrected Nyström methods when used for the numerical solutions of the common integral equations of two-dimensional electromagnetic fields. These equations exhibit kernel singularities that complicate their numerical solution. Classical and generalized Gaussian quadrature rules are reviewed. The traditional Nyström method is summarized, and applied to the magnetic field equation for illustration. To obtain high order accuracy in the numerical results, the locally-corrected Nyström method is developed and applied to both the electric field and magnetic field equations. In the presence of target edges, where current or charge density singularities occur, the method must be extended through the use of appropriate singular basis functions and special quadrature rules. This extension is also described. Table of Contents: Introduction / Classical Quadrature Rules / The Classical Nyström Method / The Locally-Corrected Nyström Method / Generalized Gaussian Quadrature / LCN Treatment of Edge Singularities
The seismic applications of the reciprocity theorem developed in this book are partly based on lecture notes and publications from Professor de Hoop. Every student Professor de Hoop has taught knows the egg-shaped figure (affectionately known as "de Hoop's egg") that plays such an important role in his theoretical description of acoustic, electromagnetic and elastodynamic wave phenomena.On the one hand this figure represents the domain for the application of a reciprocity theorem in the analysis of a wavefield and on the other hand it symbolizes the power of a consistent wavefield description of this theorem.The roots of the reciprocity theorem lie in Green's theorem for Laplace's equation and Helmholtz's extension to the wave equation. In 1894, J.W. Strutt, who later became Lord Rayleigh, introduced in his book The Theory of Sound this extension under the name of Helmholtz's theorem. Nowadays it is known as Rayleigh's reciprocity theorem.Progress in seismic data processing requires the knowledge of all the theoretical aspects of the acoustic wave theory. The reciprocity theorem was chosen as the central theme of this book as it constitutes the fundaments of the seismic wave theory. In essence, two states are distinguished in this theorem. These can be completely different, although sharing the same time-invariant domain of application, and they are related via an interaction quantity. The particular choice of the two states determines the acoustic application, in turn making it possible to formulate the seismic experiment in terms of a geological system response to a known source function.In linear system theory, it is well known that the response to a known input function can be written as an integral representation where the impulse response acts as a kernel and operates on the input function. Due to the temporal invariance of the system, this integral representation is of the convolution type. In seismics, the temporal behaviour of the system is dealt with in a similar fashion; however the spatial interaction needs a different approach. The reciprocity theorem handles this interaction by identifying one state with the spatial impulse function, also known as the Green's function, while the other state is connected with the actual source distribution. In general, the resulting integral representation is not a spatial convolution. Moreover, the systematic use of the reciprocity theorem leads to a hierarchical description of the seismic experiment in terms of increasing complexity. Also from an educational point of view this approach provides a hierarchy and the student learns to break down the seismic problem into constituent partial solutions.This book should contribute to the understanding that the reciprocity theorem is a powerful tool in the analysis of the seismic experiment.
This exceptional book introduces the reader to the principles, theory and applications of physical layer wireless/mobile communications, applicators and millimetric antennas.
Written by leading experts in the field, this book is a research monograph on Fresnel zone antennas. Readers will find a wealth of novel antenna configurations, first-hand experimental results, and a large number of equations.