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Numerical Analysis for Electromagnetic Integral Equations
Karl F. Warnick, Brigham Young University
ISBN 978-1-59693-333-0
Copyright 2008
Pages: 300
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Improve EM simulation efforts fast with this applications-focused resource. This unique volume is the first book on integral equation-based methods that combines quantitative formulas for predicting numerical simulation accuracy together with rigorous error estimates and results for dozens of actual electromagnetics and wave propagation problems. You get the latest insights on accuracy-improving methods like regularization and error-increasing effects such as edge singularities and resonance, along with full details on how to determine mesh density, choice of basis functions, and other parameters needed to optimize any numerical simulation.

Bridging the gap between abstract academic treatments and the real-world needs of engineers, this timely work introduces various surface integral equation formulations, approaches to discretizing the integral equations, and measures of solution accuracy. It gives you numerical methods for 2D radiation and scattering problems, emphasizing concrete solution error bounds with exactly given constants. Moreover, the book provides techniques for higher order basis functions and 3D problems, focusing on smooth scatterers and edge singularity effects. This informative reference also explores problems involving resonant cavities and structures, and features a comprehensive treatment of resonant scatterers. The final chapter covers the convergence of the fast multipole method with iterative linear system solvers, complete with practical methods for improving the efficiency of iterative solutions.

Introduction — Approaches to numerical analysis. Empirical methods. Previous approaches: asymptotic error estimates. Spectral convergence theory. Solution error contributions.

Surface Integral Equation Formulations and the Method of Moments — Electrical field integral equation. Magnetic field integral equation. Combined field integral equation. Method of moments. Error measures.

Numerical Analysis for 2D Radiation and Scattering Problems—Smooth scatterers. TE and TM polarizations. Quadrature error. Scattering amplitudes and RCS. Edge singularity effects.

Higher-Order Basis Functions—Error improvement as a function of basis order and polynomial type. Matrix condition number increase with basis function order.

3D Problems—Smooth scatterers. Edge singularity effects.

Resonant Structures—Resonant cavities. Internal resonances.

Iterative Solution Methods—Iteration count estimates. Matrix condition number. Fast solvers. Low-frequency breakdown.

Karl F. Warnick is an associate professor in the Department of Electrical Engineering, Brigham Young University in Utah, where he earned his Ph.D. in electrical engineering. He is also co-author of Problem Solving in Electromagnetics, Microwave Circuit, and Antenna Design for Communications Engineering (Artech House, 2006).

Weng Cho Chew is a professor in the Electrical and Computer Engineering Department at the University of Illinois at Urbana-Champaign, and serves as the dean of faculty of engineering at the University of Hong Kong. He earned his Ph.D. in electrical engineering at the Massachusetts Institute of Technology. He is the coauthor of two books, over 300 journal articles, and more than 400 conference papers.

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