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ebook for download The J & P Transformer Book, The Method of Moments in Electromagnetics

The J & P Transformer Book, Twelfth Edition
Primarily the objective has been to provide a description of the principles of transformer design and construction, testing operation and maintenance, as well as specification and procurement, in sufficient depth to enable those engineers who have involvement with transformers in a system design, installation or maintenance capacity to become ‘informed users,’ and it is hoped that, in addition, all of that valuable operational guidance contained in earlier editions has been retained and made more relevant by being brought fully into line with current thinking. Above all, the hope is that the successful formula which has led to the enormous popularity of earlier editions has not been lost and it is hoped that the information contained in this edition will prove even more useful to today’s engineers than those editions which have gone before.
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The Method of Moments in Electromagnetics
This book is for a one- or two-semester course in computational electromagnetics and a reference for the practicing engineer. It is expected that the reader will be familiar with time-harmonic electromagnetic fields and vector calculus, as well as differential equations and linear algebra. The reader should also have some basic experience with computer programming in a language such as C or FORTRAN or a mathematical environment such as MATLAB. Because some of the expressions in this book require the calculation of special functions, the reader at least should be aware of what they are and be able to calculate them. This book comprises nine chapters:

Chapter 1 presents a very brief overview of computational electromagnetics and some commonly used numerical techniques in this field.
Chapter 2 begins by reviewing some necessary background material on timeharmonic electromagnetic fields. We next develop expressions for radiation and scattering, vector potentials, and the two- and three-dimensional Green’s functions. We then discuss surface equivalents and derive the electric and magnetic field integral equations for conducting surfaces.
Chapter 3 introduces the solution of integral equations by converting the problem into a linear system. The method of moments is formalized, and commonly used two-dimensional basis functions are covered. We then discuss the solution of matrix equations, Gaussian elimination, LU decomposition, condition numbers, iterative solvers, and preconditioning.
Chapter 4 is dedicated to scattering and radiation by thin wires. We derive the thin wire kernel and the Hall´en and Pocklington thin wire integral equations, and show how to solve them. We then apply the MOM to thin wires of arbitrary shape, and consider several practical thin wire problems.
Chapter 5 applies the moment method to two-dimensional problems. The
electric and magnetic field integral equations are applied to problems of TM and
TE polarization, and expressions are summarized that can be applied to general twodimensional
boundaries.
Chapter 6 considers three-dimensional objects that can described as bodies of
revolution. The application of the MOM to this problem follows the treatment of
Harrington and Mautz, with additional derivations and discussion. We then look at
the radar cross section predictions of rotationally symmetric objects and compare
them to measurements.
Chapter 7 covers three-dimensional surfaces of arbitrary shape. We discuss
modeling of surfaces by triangular facets, and devote significant effort to summarizing
the expressions used to evaluate singular potential integrals over triangular
elements. We then consider several radar cross section problems and the input
impedance calculations of some three-dimensional antennas.
Chatper 8 introduces the fast multipole method and its use with iterative
solvers and the moment method. We cover the addition theorem, wave translation,
and single- and multi-level fast multipole algorithms. The treatment is concise and
contains all the information required to succesfully implement the FMM in a new or
existing moment method code.
Chapter 9 discusses some commonly used methods of numerical integration
including the trapezoidal and Simpson’s rule, area coordinates, and Gaussian quadrature
in one dimension and over planar triangular elements.
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