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Gibson W.C. The Method of Moments in Electromagnetics

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Gibson W.C. The Method of Moments in Electromagnetics
Second Edition - CRC Press, 2015. - 448p. - ISBN-13: 978-1-4822-3580-7
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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