Numerical Analysis for Electromagnetic Integral Equations

by Warnick, Karl F.

• ISBN13: 9781596933330
• ISBN10: 159693333X
• Format: Hardcover
• Copyright: 2008-09-30
• Publisher: Artech House

Summary

"This applications-focused resource helps practitioners quickly improve EM simulation efforts. It is the first book on integral equation-based methods that combines quantitative formulas for predicting numerical simulation accuracy with rigorous error estimates and results for dozens of electromagnetics and wave propagation problems. This volume bridges the gap between abstract academic treatments and the real-world needs of engineers." "Karl F. Warnick is an associate professor in the Department of Electrical and Computer Engineering at Brigham Young University in Utah."--BOOK JACKET.

Author Biography

Karl F. Warnick is an associate professor in the Department of Electrical and Computer Engineering at Brigham Young University in Utah, where he earned his Ph.D. in electrical engineering

Table of Contents

Preface	p. xi
Introduction	p. 1
Approaches to Error Analysis	p. 2
Empirical Methods	p. 2
Sobolev Spaces and Asymptotic Error Estimates	p. 3
Sobolev Norms	p. 4
Sobolev Norms and the Scattering Amplitude	p. 5
Static Limit	p. 5
Quasioptimality and Approximation Error	p. 6
Convergence Theorems	p. 6
Limitations of Existing Error Estimates	p. 7
Spectral Convergence Theory	p. 8
Normal Operator Decomposition	p. 8
Spectral Error	p. 8
Error Contributions	p. 10
Canonical Scattering Problems	p. 11
References	p. 12
Surface Integral Equation Formulations and the Method of Moments	p. 15
Electric Field Integral Equation	p. 16
2D Scattering Problems	p. 17
Magnetic Field Integral Equation	p. 18
2D Scattering Problems	p. 19
Combined Field Integral Equation	p. 19
2D Scattering Problems	p. 20
Method of Moments	p. 20
Vector Basis Functions	p. 22
Number of Unknowns	p. 23
Scattering Amplitude, Scattering Width, and Radar Cross-section	p. 24
Error Measures	p. 26
Basic Concepts of Modal Error Analysis	p. 28
Interpolation Error	p. 28
Mesh Nyquist Frequency	p. 30
Projection Error	p. 30
References	p. 32
Error Analysis of the EFIE with W.C. Chew	p. 33
TM-EFIE with Ideal Discretizations	p. 34
Discretized Operator Spectrum	p. 36
Comparison of the Discretized and Exact Operator Spectra	p. 38
Spectral Error	p. 40
Spectral Error for Low-Order Basis Functions	p. 43
Current Solution Error	p. 46
Scattering Amplitude Error	p. 49
Variational Principles, the Moment Method, and Superconvergence	p. 51
Superconvergence	p. 54
Idealizing Assumptions	p. 55
TM-EFIE with Nonideal Discretizations	p. 56
Quadrature Error	p. 56
Reducing Quadrature Error	p. 58
Geometrical Discretization Error	p. 59
TE-EFIE	p. 62
Spectral Error	p. 62
Spectral Error for Low-Order Basis Functions	p. 63
Quadrature Error	p. 65
Geometrical Discretization Error	p. 66
Solution Error for Other Smooth Scatterers	p. 67
Summary	p. 69
References	p. 70
Error Analysis of the MFIE and CFIE with C. P. Davis	p. 73
TM-MFIE with Ideal Discretizations	p. 74
Operator Smoothing Properties	p. 74
Discretized Operator Spectrum	p. 75
Spectral Error	p. 76
Current Solution Error	p. 77
Current Error for the Point/Pulse Discretization	p. 79
Scattering Amplitude Error	p. 80
Scattering Amplitude Error for the Point/Pulse Discretization	p. 82
Nonideal Discretizations	p. 83
Quadrature Error	p. 83
Single Integration Point	p. 84
Geometrical Discretization Error	p. 85
CFIE	p. 86
Solution Error for Other Smooth Scatterers	p. 87
Superconvergence and Regularization	p. 88
Convergence Rates for EFIE and MFIE	p. 89
Nonsuperconvergent Cases	p. 93
First- and Second-Kind Operators	p. 95
Higher-Order Basis Functions	p. 96
High-Order Convergence with Low-Order Basis Functions	p. 96
Summary	p. 99
References	p. 100
Geometrical Singularities and the Flat Strip	p. 101
Flat Strip Interior Error, TM-EFIE	p. 101
Normal Operator Approximation	p. 102
Discretized Operator Spectrum	p. 104
Spectral Error	p. 107
Spectral Error for Low-Order Basis Functions	p. 108
The Magic "1/3" Discretization	p. 109
Quadrature Error	p. 110
Current Solution Error	p. 110
Scattering Amplitude Error	p. 114
Flat Strip Interior Error, TE-EFIE	p. 114
Discretized Operator Spectrum	p. 116
Spectral Error	p. 117
Current Solution Error	p. 118
Quadrature Error	p. 119
Edge Error Analysis	p. 121
Wedges	p. 124
Summary	p. 125
References	p. 127
Resonant Structures	p. 129
Resonance and the EFIE Operator Spectrum	p. 130
Quasi-Resonant Modes	p. 131
Resonance and the Method of Moments	p. 132
Internal Resonance	p. 132
Cavities	p. 134
Resonant Case	p. 137
Near-Resonant Case	p. 140
Spectral Error	p. 141
Scattering Amplitude Error	p. 143
Summary	p. 145
References	p. 145
Error Analysis for 3D Problems	p. 147
Flat Plate	p. 148
Moment Matrix Spectrum	p. 149
Rooftop Basis Functions	p. 150
RWG Basis Functions	p. 155
Nonideal Discretizations	p. 158
Summary	p. 160
References	p. 160
Higher-Order Basis Functions with A. F. Peterson	p. 161
Higher-Order Basis Functions for 2D Problems	p. 162
Interpolatory Polynomials	p. 164
Discretized Operator Spectrum	p. 164
Interpolation Transfer Function	p. 166
Spectral Error	p. 169
Current Solution Error	p. 169
Scattering Amplitude Error	p. 172
Orthogonal Polynomials	p. 174
Discretized Operator Spectrum	p. 174
Projection Transfer Function	p. 175
Spectral Error	p. 176
Current Solution Error	p. 176
Scattering Amplitude Error	p. 178
3D Problems	p. 179
Numerical Results	p. 181
Summary	p. 184
References	p. 185
Operator Spectra and Iterative Solution Methods	p. 187
Krylov Subspace Algorithms	p. 188
CG Algorithm	p. 189
CGNE and CGNR	p. 189
Residual Error	p. 190
Condition Number	p. 191
Other Krylov Subspace Methods	p. 192
Iteration Count Estimates	p. 192
Condition Number Estimates	p. 193
Circular Cylinder, TM-EFIE	p. 193
Circular Cylinder, TE-EFIE	p. 196
Flat Strip, TM-EFIE	p. 196
Flat Strip, TE-EFIE	p. 198
Parallel Strip Resonator	p. 198
Higher-Order Basis Functions	p. 201
Flat Plate-3D	p. 203
Low-Frequency Breakdown	p. 205
Helmholtz Decomposition	p. 207
Preconditioners	p. 208
Summary	p. 210
References	p. 210
About the Author	p. 213
Index	p. 215
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