An Integral Equation And A Representation For Greens Function
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| Author | : Thomas M. Søndergaard |
| Publisher | : CRC Press |
| Total Pages | : 418 |
| Release | : 2019-01-30 |
| Genre | : Technology & Engineering |
| ISBN | : 1351260197 |
This book gives a comprehensive introduction to Green’s function integral equation methods (GFIEMs) for scattering problems in the field of nano-optics. First, a brief review is given of the most important theoretical foundations from electromagnetics, optics, and scattering theory, including theory of waveguides, Fresnel reflection, and scattering, extinction, and absorption cross sections. This is followed by a presentation of different types of GFIEMs of increasing complexity for one-, two-, and three-dimensional scattering problems. In GFIEMs, the electromagnetic field at any position is directly related to the field at either the inside or the surface of a scattering object placed in a reference structure. The properties of the reference structure, and radiating or periodic boundary conditions, are automatically taken care of via the choice of Green’s function. This book discusses in detail how to solve the integral equations using either simple or higher-order finite-element-based methods; how to calculate the relevant Green’s function for different reference structures and choices of boundary conditions; and how to calculate near-fields, optical cross sections, and the power emitted by a local source. Solution strategies for large structures are discussed based on either transfer-matrix-approaches or the conjugate gradient algorithm combined with the Fast Fourier Transform. Special attention is given to reducing the computational problem for three-dimensional structures with cylindrical symmetry by using cylindrical harmonic expansions. Each presented method is accompanied by examples from nano-optics, including: resonant metal nano-particles placed in a homogeneous medium or on a surface or waveguide; a microstructured gradient-index-lens; the Purcell effect for an emitter in a photonic crystal; the excitation of surface plasmon polaritons by second-harmonic generation in a polymer fiber placed on a thin metal film; and anti-reflective, broadband absorbing or resonant surface microstructures. Each presented method is also accompanied by guidelines for software implementation and exercises. Features Comprehensive introduction to Green’s function integral equation methods for scattering problems in the field of nano-optics Detailed explanation of how to discretize and solve integral equations using simple and higher-order finite-element approaches Solution strategies for large structures Guidelines for software implementation and exercises Broad selection of examples of scattering problems in nano-optics
| Author | : Alberto Cabada |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 180 |
| Release | : 2013-11-29 |
| Genre | : Mathematics |
| ISBN | : 1461495067 |
This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.
| Author | : Chen-to Tai |
| Publisher | : Institute of Electrical & Electronics Engineers(IEEE) |
| Total Pages | : 368 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : |
In this comprehensive, new edition, Chen-To Tai gives extensive attention to recent research surrounding the techniques of dyadic Green functions. Additional formulations are introduced, including the classifications and the different methods of finding the eigenfunction expansions. Important new features in this edition include Maxwell's equations, which has been cast in a dyadic form to make the introduction of the electric and magnetic dyadic Green functions easier to understand; the integral solutions to Maxwell's equations, now derived with the aid of the vector-dyadic Green's theorem, allowing several intermediate steps to be omitted; a detailed discussion of complementary reciprocal theorems and transient radiation in moving media; and the derivation of various dyadic Green functions for problems involving plain layered media, and a two-dimensional Fourier-integral representation of these functions. This in-depth textbook will be of particular interest to antenna and microwave engineers, research scientists, and professors.
| Author | : L. Eskola |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 203 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401123705 |
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a background in the fundamental field theories that form the basis for various geophysical methods, such as potential theory, electromagnetic theory, and elastic strain theory. A fairly extensive knowledge of mathematics, especially in vector and tensor calculus, is also assumed.
| Author | : Ernian Pan |
| Publisher | : Cambridge University Press |
| Total Pages | : 357 |
| Release | : 2015-04-30 |
| Genre | : Technology & Engineering |
| ISBN | : 131623987X |
This book presents basic theory on static Green's functions in general anisotropic magnetoelectroelastic media including detailed derivations based on the complex variable method, potential method, and integral transforms. Green's functions corresponding to the reduced cases are also presented including those in anisotropic and transversely isotropic piezoelectric and piezomagnetic media, and in purely anisotropic elastic, transversely isotropic elastic and isotropic elastic media. Problems include those in three-dimensional, (two-dimensional) infinite, half, and biomaterial spaces (planes). While the emphasis is on the Green's functions related to the line and point force, those corresponding to the important line and point dislocation are also provided and discussed. This book provides a comprehensive derivation and collection of the Green's functions in the concerned media, and as such, it is an ideal reference book for researchers and engineers, and a textbook for both students in engineering and applied mathematics.
| Author | : Abdul J. Jerri |
| Publisher | : John Wiley & Sons |
| Total Pages | : 458 |
| Release | : 1999-09-03 |
| Genre | : Mathematics |
| ISBN | : 9780471317340 |
From the reviews of the First Edition: "Extremely clear, self-contained text . . . offers to a wide class of readers the theoretical foundations and the modern numerical methods of the theory of linear integral equations."-Revue Roumaine de Mathematiques Pures et Appliquées. Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. This edition provides precise guidelines to the basic methods of solutions, details more varied numerical methods, and substantially boosts the total of practical examples and exercises. Plus, it features added emphasis on the basic theorems for the existence and uniqueness of solutions of integral equations and points out the interrelation between differentiation and integration. Other features include: * A new section on integral equations in higher dimensions. * An improved presentation of the Laplace and Fourier transforms. * A new detailed section for Fredholm integral equations of the first kind. * A new chapter covering the basic higher quadrature numerical integration rules. * A concise introduction to linear and nonlinear integral equations. * Clear examples of singular integral equations and their solutions. * A student's solutions manual available directly from the author.
| Author | : Luc T. Ikelle |
| Publisher | : SEG Books |
| Total Pages | : 1403 |
| Release | : 2018-03-26 |
| Genre | : Science |
| ISBN | : 1560803436 |
Introduction to Petroleum Seismology, second edition (SEG Investigations in Geophysics Series No. 12) provides the theoretical and practical foundation for tackling present and future challenges of petroleum seismology especially those related to seismic survey designs, seismic data acquisition, seismic and EM modeling, seismic imaging, microseismicity, and reservoir characterization and monitoring. All of the chapters from the first edition have been improved and/or expanded. In addition, twelve new chapters have been added. These new chapters expand topics which were only alluded to in the first edition: sparsity representation, sparsity and nonlinear optimization, near-simultaneous multiple-shooting acquisition and processing, nonuniform wavefield sampling, automated modeling, elastic-electromagnetic mathematical equivalences, and microseismicity in the context of hydraulic fracturing. Another major modification in this edition is that each chapter contains analytical problems as well as computational problems. These problems include MatLab codes, which may help readers improve their understanding of and intuition about these materials. The comprehensiveness of this book makes it a suitable text for undergraduate and graduate courses that target geophysicists and engineers as well as a guide and reference work for researchers and professionals in academia and in the petroleum industry.
| Author | : Andrei D. Polyanin |
| Publisher | : CRC Press |
| Total Pages | : 1143 |
| Release | : 2008-02-12 |
| Genre | : Mathematics |
| ISBN | : 0203881052 |
Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
| Author | : George C. Hsiao |
| Publisher | : Springer Nature |
| Total Pages | : 783 |
| Release | : 2021-03-26 |
| Genre | : Mathematics |
| ISBN | : 3030711277 |
This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
| Author | : National Research Council |
| Publisher | : National Academies Press |
| Total Pages | : 1018 |
| Release | : 2003-11-15 |
| Genre | : Science |
| ISBN | : 0309254701 |
This report is part of a series of reports that summarize this regular event. The report discusses research developments in ship design, construction, and operation in a forum that encouraged both formal and informal discussion of presented papers.
