Numerical Analysis for Electromagnetic Integral Equations

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Artech House, 2008 - Electrical engineering - 233 pages
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Improve EM simulation efforts fast with this applications-focused resource. 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.
 

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Contents

Geometrical Singularities and the Flat Strip
511 Normal Operator Approximation
512 Discretized Operator Spectrum
513 Spectral Error
514 Spectral Error for LowOrder Basis Functions
515 Magic 13 Discretization
516 Quadrature Error
518 Scattering Amplitude Error

143 Error Contributions
144 Canonical Scattering Problems
References
Surface Integral Equation Formulations and the Method of Moments
21 Electric Field Integral Equation
211 2D Scattering Problems
22 Magnetic Field Integral Equation
221 2D Scattering Problems
231 2D Scattering Problems
241 Vector Basis Functions
25 Number of Unknowns
26 Scattering Amplitude Scattering Width and Radar CrossSection
27 Error Measures
28 Basic Concepts of Modal Error Analysis
282 Mesh Nyquist Frequency
References
Error Analysis of the EFIE
31 TMEFIE with Ideal Discretizations
311 Discretized Operator Spectrum
312 Comparison of the Discretized and Exact Operator Spectra
313 Spectral Error
314 Spectral Error for LowOrder Basis Functions
315 Current Solution Error
316 Scattering Amplitude Error
37 Variational Principles the Moment Method and Superconvergence
321 Superconvergence
322 Idealizing Assumptions
33 TMEFIE with Nonideal Discretizations
332 Reducing Quadrature Error
333 Geometrical Discretization Error
34 TEEFIE
342 Spectral Error for LowOrder Basis Functions
343 Quadrature Error
344 Geometrical Discretization Error
35 Solution Error for Other Smooth Scatterers
36 Summary
References
Error Analysis of the MFIE and CFIE
41 TMEFIE with Ideal Discretizations
412 Discretized Operator Spectrum
413 Spectral Error
414 Current Solution Error
415 Current Error for the PointPulse Discretization
416 Scattering Amplitude Error
417 Scattering Amplitude Error for the PointPulse Discretization
42 Nonideal Discretizations
422 Single Integration Point
423 Geometrical Discretization Error
43 CFIE
44 Solution Error for Other Smooth Scatterers
45 Superconvergence and Regularization
451 Convergence Rates for EFIE and MFIE
452 Nonsuperconvergent Cases
453 First and SecondKind Operators
454 HigherOrder Basis Functions
46 Summary
References
521 Discretized Operator Spectrum
522 Spectral Error
523 Current Solution Error
524 Quadrature Error
53 Edge Error Analysis
54 Wedges
55 Summary
References
Resonant Structures
61 Resonance and the EFIE Operator Spectrum
611 QuasiResonant Modes
612 Resonance and the Method of Moments
63 Cavities
631 Resonant Case
632 NearResonant Case
633 Spectral Error
634 Scattering Amplitude Error
64 Summary
Error Analysis for 3D Problems
71 Flat Plate
711 Moment Matrix Spectrum
712 Rooftop Basis Functions
72 RWG Basis Functions
721 Nonideal Discretizations
72 Summary
HigherOrder Basis Functions
81 HigherOrder Basis Functions for 2D Problems
82 Interpolatory Polynomials
822 Interpolation Transfer Function
823 Spectral Error
825 Scattering Amplitude Error
83 Orthogonal Polynomials
832 Projection Transfer Function
833 Spectral Error
835 Scattering Amplitude Error
84 3D Problems
841 Numerical Results
85 Summary
References
Operator Spectra and Iterative Solution Methods
91 Krylov Subspace Algorithms
911 CG Algorithm
913 Residual Error
914 Condition Number
915 Other Krylov Subspace Methods
93 Condition Number Estimates
932 Circular Cylinder TEEFIE
934 Flat Strip TEEFIE
936 HigherOrder Basis Functions
937 Flat Plate 3D
94 LowFrequency Breakdown
941 Helmholtz Decomposition
95 Preconditioners
96 Summary
About the Author
Index
Copyright

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About the author (2008)

Karl F. Warnick received the B.S. degree (magna cum laude) with University Honors and the Ph.D. degree from Brigham Young University (BYU), Provo, UT, in 1994 and 1997, respectively. Since 2000, he has been a faculty member in the Department of Electrical and Computer Engineering at BYU, where he is currently an Associate Professor. He was a recipient of the National Science Foundation Graduate Research Fellowship, Outstanding Faculty Member award for Electrical and Computer Engineering (2005), the BYU Young Scholar Award (2007), and an honorary Guest Professorship at Nanjing University of Science and Technology. In 2005 and 2007, he was a Visiting Professor at the Technische Universitat Munchen, Germany. Dr. Warnick has published many scientific articles and conference papers on electromagnetic theory, numerical methods, remote sensing, antenna applications, phased arrays, biomedical devices, and inverse scattering, and is the author of the books Problem Solving in Electromagnetics, Microwave Circuits, and Antenna Design for Communications Engineering (Artech House, 2006) with Peter Russer and Numerical Analysis for Electromagnetic Integral Equations (Artech House, 2008). He is a Senior Member of the Institute of Electrical and Electronics Engineers, and has served the IEEE Antennas and Propagation Society as a member of the Education Committee and as a session chair and special session organizer for the International Symposium on Antennas and Propagation.

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