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Designed for accessibility to students, researchers and design and development workers, it discusses the full range of classical and modern methods for the solution of electric, magnetic, some thermal and other similar fields. It deals with 1, 2 and 3 space dimensions, with linear, non-linear and anisotropic media as well as static and ``low''-frequency time variation. Numerous examples, detailing the physical significance of the mathematics and the practical considerations involved in implementing the solutions, make this a very hands-on working reference.
For well over a decade, the numerical approach to field computation has been gaining progressively greater importance. Analytical methods offield compu tation are, at best, unable to accommodate the very wide variety of configura tions in which fields must be computed. On the other hand, numerical methods can accommodate many practical configurations that analytical methods cannot. With the advent of high-speed digital computers, numerical field computations have finally become practical. However, in order to implement numerical methods of field computation, we need algorithms, numerical methods, and mathematical tools that are largely quite different from those that have been traditionally used with analytical methods. Many of these algorithms have, in fact, been presented in the large number of papers that have been published on this subject in the last two decades. And to some of those who are already experienced in the art of numerical field computations, these papers, in addition to their own original work, are enough to give them the knowledge that they need to perform practical numerical field computations.
Analysis and Computation of Electric and Magnetic Field Problems, Second Edition is a comprehensive treatment of both analytical and numerical methods for the derivation of two-dimensional static and quasi-static electric and magnetic fields. The essence of each method of solution is emphasized and the scopes of the different methods are described, with particular regard to the influence of digital computers. This book is comprised of 12 chapters and begins with an introduction to the fundamental theory of electric and magnetic fields. The derivation of quantities of physical interest such as force, inductance, and capacitance from the field solution is explained. The next section deals with the methods of images and separation of variables and presents direct solutions of Laplace's equation and of Poisson's equation. The basic solutions are developed rigorously from considerations of surface charges and are expressed in complex variable form. Subsequent chapters discuss transformation methods as well as line and doublet sources; the transformation of regions exterior to finite boundaries; and the powerful numerical methods used to enlarge the scope of conformal transformation. The last section is devoted to finite difference methods and the Monte Carlo method, along with all classes of boundary shape and condition. This monograph is intended primarily for engineers, physicists, and mathematicians, as well as degree students towards the end of their courses.
Written by a leading expert on the electromagnetic design and engineering of superconducting accelerator magnets, this book offers the most comprehensive treatment of the subject to date. In concise and easy-to-read style, the author lays out both the mathematical basis for analytical and numerical field computation and their application to magnet design and manufacture. Of special interest is the presentation of a software-based design process that has been applied to the entire production cycle of accelerator magnets from the concept phase to field optimization, production follow-up, and hardware commissioning. Included topics: Technological challenges for the Large Hadron Collider at CERN Algebraic structures and vector fields Classical vector analysis Foundations of analytical field computation Fields and Potentials of line currents Harmonic fields The conceptual design of iron- and coil-dominated magnets Solenoids Complex analysis methods for magnet design Elementary beam optics and magnet polarities Numerical field calculation using finite- and boundary-elements Mesh generation Time transient effects in superconducting magnets, including superconductor magnetization and cable eddy-currents Quench simulation and magnet protection Mathematical optimization techniques using genetic and deterministic algorithms Practical experience from the electromagnetic design of the LHC magnets illustrates the analytical and numerical concepts, emphasizing the relevance of the presented methods to a great many applications in electrical engineering. The result is an indispensable guide for high-energy physicists, electrical engineers, materials scientists, applied mathematicians, and systems engineers.
Numerical methods for solving boundary value problems have developed rapidly. Knowledge of these methods is important both for engineers and scientists. There are many books published that deal with various approximate methods such as the finite element method, the boundary element method and so on. However, there is no textbook that includes all of these methods. This book is intended to fill this gap. The book is designed to be suitable for graduate students in engineering science, for senior undergraduate students as well as for scientists and engineers who are interested in electromagnetic fields. Objective Numerical calculation is the combination of mathematical methods and field theory. A great number of mathematical concepts, principles and techniques are discussed and many computational techniques are considered in dealing with practical problems. The purpose of this book is to provide students with a solid background in numerical analysis of the field problems. The book emphasizes the basic theories and universal principles of different numerical methods and describes why and how different methods work. Readers will then understand any methods which have not been introduced and will be able to develop their own new methods. Organization Many of the most important numerical methods are covered in this book. All of these are discussed and compared with each other so that the reader has a clear picture of their particular advantage, disadvantage and the relation between each of them. The book is divided into four parts and twelve chapters.
CD-ROM contains: Application programs with sample data files providing worked examples -- Full source code for visualisation application program.
Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. Numerical Methods in Electromagnetism will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students. Comprehensive descriptions of numerical methods In-depth introduction to finite differences, finite elements, and integral equations Illustrations and applications of linear and nonlinear solutions for multi-dimensional analysis Numerical examples to facilitate understanding of the methods Appendices for quick reference of mathematical and numerical methods employed
This book contains the edited versions of the papers presented at the Second International Workshop on Electric and Magnetic Fields held at the Katholieke Universiteit van Leuven (Belgium) in May 1994. This Workshop deals with numerical solutions of electromagnetic problems in real life applications. The topics include coupled problems (thermal, mechanical, electric circuits), CAD & CAM applications, 3D eddy current and high frequency problems, optimisation and application oriented numerical problems. This workshop was organised jointly by the AIM (Association of Engineers graduated from de Montefiore Electrical Institute) together with the Departments of Electrical Engineering of the Katholieke Universiteit van Leuven (Prof. R. Belmans), the University of Gent (Prof. J. Melkebbek) and the University of Liege (Prof. W. Legros). These laboratories are working together in the framework of the Pole d'Attraction Interuniversitaire - Inter-University Attractie-Pole 51 - on electromagnetic systems led by the University of Liege and the research work they perform covers most of the topics of the Workshop. One of the principal aims of this Workshop was to provide a bridge between the electromagnetic device designers, mainly industrialists, and the electromagnetic field computation developers. Therefore, this book contains a continuous spectrum of papers from application of electromagnetic models in industrial design to presentation of new theoretical developments.
Computer Field Models of Electromagnetic Devices, volume 34 in the book series Studies in Applied Electromagnetics and Mechanics is devoted to modeling and simulation, control systems, testing, measurements, monitoring, diagnostics and advanced software