Numerical simulation is essential to electrical engineers working in antenna design, wireless communications, optical systems, and a host of other areas. This new applications-focused book provides engineers with state-of-the-art methods for predicting simulation accuracy, worked-out results for dozens of real-world problems, the latest accuracy-improving techniques, and detailed guidance for all parameters required to optimize numerical simulations. Bridging the gap between abstract academic treatments and practical engineering needs, this timely work introduces various surface integral equation formulations, approaches to discretizing the integral equations, and measures of solution accuracy. All told, this definitive resource is indispensable for all engineers and software developers working with computational simulation tools in electromagnetics and wave propagation. Electromagnetic Analysis Numerical Analysis for Electromagnetic Integral Equations 2 Contents 6 Preface 12 Chapter 1 Introduction 16 1.1 Approaches to Error Analysis 17 1.2 Empirical Methods 17 1.3 Sobolev Spaces and Asymptotic Error Estimates 18 1.3.1 Sobolev Norms 19 1.3.2 Sobolev Norms and the Scattering Amplitude 20 1.3.3 Static Limit 20 1.3.4 Quasioptimality and Approximation Error 21 1.3.5 Convergence ¿eorems 21 1.3.6 Limitations of Existing Error Estimates 22 1.4 Spectral Convergence Theory 23 1.4.1 Normal Operator Decomposition 23 1.4.2 Spectral Error 23 1.4.3 Error Contributions 25 1.4.4 Canonical Scattering Problems 26 References 27 Chapter 2 Surface Integral Equation Formulations and the Method of Moments 30 2.1 Electric Field Integral Equation 31 2.1.1 2D Scattering Problems 32 2.2 Magnetic Field Integral Equation 33 2.2.1 2D Scattering Problems 34 2.3 Combined Field Integral Equation 34 2.3.1 2D Scattering Problems 35 2.4 Method of Moments 35 2.4.1 Vector Basis Functions 37 2.5 Number of Unknowns 38 2.6 Scattering Amplitude, ScatteringWidth, and Radar Cross-section 39 2.7 Error Measures 41 2.8 Basic Concepts of Modal Error Analysis 42 2.8.1 Interpolation Error 43 2.8.2 Mesh Nyquist Frequency 45 2.8.3 Projection Error 45 References 47 Chapter 3 Error Analysis of the EFIE 48 3.1 TM-EFIE with Ideal Discretizations 49 3.1.1 Discretized Operator Spectrum 51 3.1.2 Comparison of the Discretized and Exact Operator Spectra 53 3.1.3 Spectral Error 55 3.1.4 Spectral Error for Low-Order Basis Functions 58 3.1.5 Current Solution Error 61 3.1.6 Scattering Amplitude Error 64 3.2 Variational Principles, the MomentMethod, and Superconvergence 66 3.2.1 Superconvergence 69 3.2.2 Idealizing Assumptions 70 3.3 TM-EFIE with Nonideal Discretizations 71 3.3.1 Quadrature Error 71 3.3.2 Reducing Quadrature Error 73 3.3.3 Geometrical Discretization Error 74 3.4 TE-EFIE 77 3.4.1 Spectral Error 77 3.4.2 Spectral Error for Low-Order Basis Functions 78 3.4.3 Quadrature Error 80 3.4.4 Geometrical Discretization Error 81 3.5 Solution Error for Other SmoothScatterers 82 3.6 Summary 84 References 85 Chapter 4 Error Analysis of the MFIE and CFIE 88 4.1 TM-MFIE with Ideal Discretizations 89 4.1.1 Operator Smoothing Properties 89 4.1.2 Discretized Operator Spectrum 90 4.1.3 Spectral Error 91 4.1.4 Current Solution Error 92 4.1.5 Current Error for the Point/Pulse Discretization 94 4.1.6 Scattering Amplitude Error 95 4.1.7 Scattering Amplitude Error for the Point/Pulse Discretization 97 4.2 Nonideal Discretizations 98 4.2.1 Quadrature Error 98 4.2.2 Single Integration Point 99 4.2.3 Geometrical Discretization Error 100 4.3 CFIE 101 4.4 Solution Error for Other SmoothScatterers 102 4.5 Superconvergence and Regularization 103 4.5.1 Convergence Rates for EFIE and MFIE 104 4.5.2 Nonsuperconvergent Cases 108 4.5.3 First- and Second-Kind Operators 110 4.5.4 Higher-Order Basis Functions 111 4.5.5 High-Order Convergence with Low-Order Basis Functions 111 4.6 Summary 114 References 115 Chapter 5 Geometrical Singularities and the Flat Strip 116 5.1 Flat Strip Interior Error, TM-EFIE 116 5.1.1 Normal Operator Approximation 117 5.1.2 Discretized Operator Spectrum 119 5.1.3 Spectral Error 122 5.1.4 Spectral Error for Low-Order Basis Functions 123 5.1.5 The Magic “1/3” Discretization 124 5.1.6 Quadrature Error 125 5.1.7 Current Solution Error 125 5.1.8 Scattering Amplitude Error 129 5.2 Flat Strip Interior Error, TE-EFIE 129 5.2.1 Discretized Operator Spectrum 131 5.2.2 Spectral Error 132 5.2.3 Current Solution Error 133 5.2.4 Quadrature Error 134 5.3 Edge Error Analysis 136 5.4 Wedges 139 5.5 Summary 140 References 142 Chapter 6 Resonant Structures 144 6.1 Resonance and the EFIE OperatorSpectrum 145 6.1.1 Quasi-Resonant Modes 146 6.1.2 Resonance and the Method of Moments 147 6.2 Internal Resonance 147 6.3 Cavities 149 6.3.1 Resonant Case 152 6.3.2 Near-Resonant Case 155 6.3.3 Spectral Error 156 6.3.4 Scattering Amplitude Error 158 6.4 Summary 160 References 160 Chapter 7 Error Analysis for 3D Problems 162 7.1 Flat Plate 163 7.1.1 MomentMatrix Spectrum 164 7.1.2 Rooftop Basis Functions 165 7.2 RWG Basis Functions 170 7.2.1 Nonideal Discretizations 173 7.3 Summary 175 References 175 Chapter 8 Higher-Order Basis Functions 176 8.1 Higher-Order Basis Functions for 2D Problems 177 8.2 Interpolatory Polynomials 179 8.2.1 Discretized Operator Spectrum 179 8.2.1 Discretized Operator Spectrum 179 8.2.2 Interpolation Transfer Function 181 8.2.3 Spectral Error 184 8.2.4 Current Solution Error 184 8.2.5 Scattering Amplitude Error 187 8.3 Orthogonal Polynomials 189 8.3.1 Discretized Operator Spectrum 189 8.3.2 Projection Transfer Function 190 8.3.3 Spectral Error 191 8.3.4 Current Solution Error 191 8.3.5 Scattering Amplitude Error 193 8.4 3D Problems 194 8.4.1 Numerical Results 196 8.5 Summary 199 References 200 Chapter 9 Operator Spectra and Iterative Solution Methods 202 9.1 Krylov Subspace Algorithms 203 9.1.1 CG Algorithm 204 9.1.2 CGNE and CGNR 204 9.1.3 Residual Error 205 9.1.4 Condition Number 206 9.1.5 Other Krylov Subspace Methods 207 9.2 Iteration Count Estimates 207 9.3 Condition Number Estimates 208 9.3.1 Circular Cylinder, TM-EFIE 208 9.3.2 Circular Cylinder, TE-EFIE 211 9.3.3 Flat Strip, TM-EFIE 211 9.3.4 Flat Strip, TE-EFIE 213 9.3.5 Parallel Strip Resonator 213 9.3.6 Higher-Order Basis Functions 216 9.3.7 Flat Plate—3D 218 9.4 Low-Frequency Breakdown 220 9.4.1 Helmholtz Decomposition 222 9.5 Preconditioners 223 9.6 Summary 225 References 225 About the Author 228 Index 230 electromagnetic analysis,artech house,integral equations,numerical analysis,9781596933330
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.
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 Surface integral equation formulations and the method of moments Error analysis of the EFIE / with W.C. Chew Error analysis of the MFIE and CFIE / with C.P. Davis Geometrical singularities and the flat strip Resonant structures Error analysis for 3D problems Higher-order basis functions / with A.F. Peterson Operator spectra and iterative solution methods.
