The Nyström method in electromagnetics. (2020)

• Record Type: Book
• Further Information: Note: Mei Song Tong, Weng Cho Chew.
• Authors: Tong, Mei Song; Chew, Weng Cho
• Contents: About the Authors xiii Preface xv Acknowledgment xxi 1 Electromagnetics, Physics, and Mathematics 1 1.1 A Brief History of Electromagnetics 1 1.2 Enduring Legacy of Electromagnetic Theory–Why? 3 1.3 The Rise of Quantum Optics and Electromagnetics 4 1.3.1 Connection of Quantum Electromagnetics to Classical Electromagnetics 5 1.4 The Early Days – Descendent from Fluid Physics 6 1.5 The Complete Development of Maxwell’s Equations 7 1.5.1 Derivation of Wave Equation 9 1.6 Circuit Physics, Wave Physics, Ray Physics, and Plasmonic Resonances 10 1.6.1 Circuit Physics 10 1.6.2 Wave Physics 14 1.6.3 Ray Physics 15 1.6.4 Plasmonic Resonance 17 1.7 The Age of Closed Form Solutions 20 1.7.1 Separable Coordinate Systems 20 1.7.2 Integral Transform Solution 21 1.8 The Age of Approximations 23 1.8.1 Asymptotic Expansions 23 1.8.2 Matched Asymptotic Expansions 24 1.8.3 Ansatz-Based Approximations 27 1.9 The Age of Computations 28 1.9.1 Computations and Mathematics 30 1.9.2 Sobolev Space and Dual Space 33 1.10 Fast Algorithms 35 1.10.1 Cruelty of Computational Complexity 36 1.10.2 Curse of Dimensionality 38 1.10.3 Multiscale Problems 38 1.10.4 Fast Algorithm for Multiscale Problems 39 1.10.5 Domain Decomposition Methods 40 1.11 High Frequency Solutions 41 1.12 Inverse Problems 41 1.12.1 Distorted Born Iterative Method 42 1.12.2 Super-Resolution Reconstruction 43 1.12.3 Super-Resolution and the Weyl-Sommerfeld Identity 43 1.13 Metamaterials 46 1.14 Small Antennas 47 1.15 Conclusions 48 Bibliography 49 2 Computational Electromagnetics 75 2.1 Introduction 75 2.2 Analytical Methods 77 2.3 Numerical Methods 82 2.3.1 The Finite-Difference Time-Domain (FDTD)Method 83 2.3.2 The Finite Element Method (FEM) 83 2.3.3 The Method of Moments (MoM) 84 2.4 Electromagnetic Integral Equations 87 2.4.1 Surface Integral Equations (SIEs) 88 2.4.2 Volume Integral Equations (VIEs) 91 2.4.3 Volume-Surface Integral Equations (VSIEs) 93 2.5 Summary 95 Bibliography 95 3 The Nyström Method 99 3.1 Introduction 99 3.2 Basic Principle 100 3.3 Singularity Treatment 101 3.4 Higher-Order Scheme 102 3.5 Comparison to the Method of Moments 103 3.6 Comparison to the Point-Matching Method 104 3.7 Summary 105 Bibliography 106 4 Numerical Quadrature Rules 107 4.1 Introduction 107 4.2 Definition and Design 108 4.3 Quadrature Rules for a Segmental Mesh 108 4.4 Quadrature Rules for a Surface Mesh 109 4.4.1 Quadrature Rules for a Triangular Patch 109 4.4.2 Quadrature Rules for a Square Patch 112 4.5 Quadrature Rules for a Volumetric Mesh 116 4.5.1 Quadrature Rules for a Tetrahedral Element 116 4.5.2 Quadrature Rules for a Cuboid Element 121 4.6 Summary 122 Bibliography 123 5 Singularity Treatment 125 5.1 Introduction 125 5.2 Singularity Subtraction 126 5.2.1 Basic Principle 126 5.2.2 Subtraction for the Kernel of Operator 127 5.2.3 Subtraction for the Kernel of Operator 130 5.2.4 Subtraction for the Kernels of VIEs 132 5.3 Singularity Cancellation 133 5.3.1 Surface Integral Equation 134 5.3.2 Evaluation of the Weakly-Singular Integrals 135 5.3.3 Numerical Examples 138 5.4 Evaluation of Hypersingular and Weakly-Singular Integrals over Triangular Patches 143 5.4.1 Hypersingular Integrals 144 5.4.2 Weakly-Singular Integrals 149 5.4.3 Non-Singular Integrals 152 5.4.4 Numerical Examples 154 5.5 Different Scheme for Evaluating Strongly-Singular and Hypersingular Integrals Over Triangular Patches 154 5.5.1 Strongly-Singular and Hypersingular Integrals 157 5.5.2 Stokes’ Theorem 159 5.5.3 Derivation of New Formulas for HSIs and SSIs 160 5.5.4 Numerical Tests 164 5.5.5 Numerical Examples 164 5.6 Evaluation of Singular Integrals Over Volume Domains 167 5.6.1 Representation of Volume Current Density 168 5.6.2 Evaluation of Singular Integrals 169 5.6.3 Numerical Examples 172 5.7 Evaluation of Near-Singular Integrals 176 5.7.1 Integral Equations and Near-Singular Integrals 177 5.7.2 Evaluation 179 5.7.3 Numerical Examples 185 5.8 Summary 187 Bibliography 188 6 Application to Conducting Media 193 6.1 Introduction 193 6.2 Solution for 2D Structures 193 6.2.1 General 2D Structures 194 6.2.2 2D Open Structures with Edge Conditions 196 6.2.3 Evaluation of Singular and Near-Singular Integrations 199 6.2.4 Numerical Examples 204 6.3 Solution for Body-of-Revolution (BOR) Structures 211 6.3.1 2D Integral Equations 212 6.3.2 Evaluation of Singular Fourier Expansion Coefficients 215 6.3.3 Numerical Examples 219 6.4 Solutions of the Electric Field Integral Equation 221 6.4.1 Higher-order Nyström method 222 6.4.2 Numerical Examples 225 6.5 Solutions of the Magnetic Field Integral Equation 228 6.5.1 Integral Equations 229 6.5.2 Singularity and Near-Singularity Treatment 230 6.5.3 Numerical Examples 233 6.6 Solutions of the Combined Field Integral Equation 238 6.6.1 Integral Equations 239 6.6.2 Quality of Triangular Patches 240 6.6.3 Nyström Discretization 241 6.6.4 Numerical Examples 242 6.7 Summary 245 Bibliography 246 7 Application to Penetrable Media 253 7.1 Introduction 253 7.2 Surface Integral Equations for Homogeneous and Isotropic Media 254 7.2.1 Surface Integral Equations 254 7.2.2 Nyström Discretization 259 7.2.3 Numerical Examples 260 7.3 Volume Integral Equations for Homogeneous and Isotropic Media 266 7.3.1 Volume Integral Equations 268 7.3.2 Nyström Discretization 268 7.3.3 Local Correction Scheme 271 7.3.4 Numerical Examples 274 7.4 Volume Integral Equations for Inhomogeneous or/and Anisotropic Media 279 7.4.1 Volume Integral Equations 280 7.4.2 Inconvenience of the Method of Moments 282 7.4.3 Nyström Discretization 283 7.4.4 Numerical Examples 284 7.5 Volume Integral Equations for Conductive Media 287 7.5.1 Volume Integral Equations 289 7.5.2 Nyström Discretization 290 7.5.3 Numerical Examples 291 7.6 Volume-Surface Integral Equations for Mixed Media 296 7.6.1 Volume-Surface Integral Equations 298 7.6.2 Nyström-Based Mixed Scheme for Solving the VSIEs 299 7.6.3 Numerical Examples 301 7.7 Summary 306 Bibliography 309 8 Incorporation with Multilevel Fast Multipole Algorithm 317 8.1 Introduction 317 8.2 Multilevel Fast Multipole Algorithm 318 8.3 Surface Integral Equations for Conducting Objects 320 8.3.1 Integral Equations 321 8.3.2 Nyström Discretization and MLFMA Acceleration 321 8.3.3 Numerical Examples 323 8.4 Surface Integral Equations for Penetrable Objects 325 8.4.1 Integral Equations 327 8.4.2 MLFMA Acceleration 329 8.4.3 Numerical Examples 331 8.5 Volume Integral Equations for Conductive Media 335</
• Edition: 1st
• Publisher Details: Hoboken : Wiley-IEEE Press
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 537.0151; Electromagnetism -- Mathematics; Integral equations -- Numerical solutions
• Languages: English
• ISBNs: 9781119284871
• Related ISBNs: 9781119284888
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
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