Essentials of Computational Electromagnetics

Sheng and Song provide an overview of the three main full-wave numerical methods in computational electromagnetics (CEM); namely, the method of moment (MoM), the finite element method (FEM), and the finite-difference time-domain (FDTD) method. Numerous monographs can be found addressing one of the above three methods. However, few give a broad general overview of essentials embodied in these methods, or were published too early to include recent advances. Furthermore, many existing monographs only present the final numerical results without specifying practical issues, such as how to convert discretized formulations into computer programs, and the numerical characteristics of the computer programs. In this book, the authors elaborate the above three methods in CEM using practical methods, explaining their own research experiences along with a review of current literature. A full analysis is provided for typical cases, including characteristics of numerical methods, helping beginners a quick and deep understanding of the essentials of CEM.

Xin-Qing Sheng, Beijing Institute of Technology, China
Xin-Qing Sheng is a Chang-Jiang Professor at the School of Information and Electronics at the Beijing Institute of Technology. His research interests include computational electromagnetics, scattering and antenna analysis, electromagnetic compatibility, and microwave imaging. He has authored and coauthored over 70 papers in refereed journals, as well as two books. He has written SINOCOM, the simulation software for scattering by complex targets. Sheng is a recipient of the 1995 President Awards of the Chinese Academy of Sciences, the 2001 One Hundred Talents Program awarded by the Chinese Academy of Sciences, the 2004 Cheung Kong Scholar Program awarded by the Ministry of Education, China. Sheng has taught the course "Modern Computational Electromagnetics" for graduate-level students using the book "A Brief Treatise on Computational Electromagnetics"(in Chinese ) for 5 years. He holds a B.S., M.S., and PhD in Electronic Engineering and Information Science from The University of Science and Technology of China.

Wei Song, Beijing Institute of Technology, China
Wei Song is an Assistant Professor of the School of Information and Electronics at the Beijing Institute of Technology. Her research interests include computational electromagnetics, scattering, antennas, and metamaterial analysis. She has published several papers on the topic of numerical methods and metamaterials. She also has contributed a chapter to FDTD Modeling of Metamaterials: Theory and Applications (Artech House Publishers, 2008). She holds a PhD in Electronic Engineering, specializing in Electromagnetics, awarded by the Antennas and Radio Propagation Research Group at University of London.

Preface	p. ix
Mathematical Formulations for Electromagnetic Fields	p. 1
Deterministic Vector Partial Differential System of the Electromagnetic Fields	p. 1
Maxwell's Equations	p. 1
Constitutive Relations	p. 3
Boundary Conditions	p. 3
Maxwell's Equations in the Frequency Domain	p. 5
Uniqueness Theorem	p. 6
Vector Wave Equation of the Electromagnetic Fields	p. 8
Vector Integral Equation of the Electromagnetic Fields	p. 8
Equivalence Principle	p. 9
Solution of Maxwell's Equation in Free Space	p. 11
Integral Equations of Metallic Scattering Problems	p. 14
Integral Equation of Homogeneous Dielectric Scattering Problems	p. 16
Integral Equation of Inhomogeneous Dielectric Scattering Problems	p. 19
Integral Equations of Scattering in Layered Medium	p. 20
References	p. 28
Method of Moments	p. 29
Scattering from 3D PEC Objects	p. 29
Formulation of the Problem	p. 30
Discretization in MoM	p. 30
Choice of Basis and Testing Functions	p. 31
Discretized Integral Equation (DIE) and the Numerical Behavior Analysis	p. 34
Handling of Singularity	p. 36
Comparison of EFffi and MFIE	p. 71
Interior Resonance Problem	p. 73
Fast Multipole Method	p. 74
Calculation of Scattered Fields	p. 86
Writing Computer Program	p. 89
Numerical Examples	p. 94
Parallel Technology	p. 100
Strong Scalability	p. 106
Weak Scalability	p. 107
Scattering from Three-Dimensional Homogeneous Dielectric Objects	p. 109
Mathematic Formulation of the Problem	p. 111
Discretized Forms and Their Numerical Performance	p. 112
Numerical Examples	p. 118
Implementation of Single Integral Equation and the Numerical Characteristics	p. 122
Scattering from Three-Dimensional Inhomogeneous Dielectric Objects	p. 128
Mathematic Formulation of the Problem	p. 129
Rooftop Basis Functions	p. 130
Discretization of the VIE	p. 131
Singularity Processing	p. 134
Fast Solution of the Discretized VIE	p. 135
Numerical Examples	p. 136
Essential Points in MoM for Solving Other Problems	p. 136
Scattering from Two-Dimensional Objects	p. 138
Scattering from Periodic Structures	p. 141
Scattering from Two-and-Half-Dimensional Objects	p. 144
Radiation Problems	p. 146
References	p. 150
Finite-Element Method	p. 153
Eigenmodes Problems of Dielectric-Loaded Waveguides	p. 153
Functional Formulation	p. 154
Choice of Basis Functions	p. 159
Discretization of the Functional	p. 161
Imposition of the Boundary Condition	p. 164
Solution of the Generalized Eigenvalue Equation	p. 165
Computer Programming	p. 166
Numerical Examples	p. 170
Discontinuity Problem in Waveguides	p. 170
Functional Formulation	p. 171
Choice of the Basis Functions	p. 174
Discretization of the Functional	p. 176
Solution of the Linear Equations	p. 178
Extraction of the Scattering Parameters	p. 180
Numerical Examples	p. 182
Scattering from Three-Dimensional Objects	p. 184
Mathematic Formulation of the Problem	p. 184
Writing Computer Program	p. 187
Numerical Results	p. 190
Node-Edge Element	p. 192
Construction of Node-Edge Element	p. 192
Implementation of Node-Edge Element	p. 193
Numerical Examples	p. 195
Higher-Order Element	p. 196
Finite-Element Time-Domain Method	p. 200
More Comments on FEM	p. 203
References	p. 205
Finite-Difference Time-Domain Method	p. 207
Scattering from a Three-Dimensional Objects	p. 207
FDTD Solution Scheme	p. 208
Perfectly Matched Layers	p. 209
Yee Discretizing Scheme	p. 215
Discretization of the Scatterer Model	p. 220
Treatment on the Curved Boundary	p. 220
Determination of the Unit Size and the Time Step	p. 222
Plane Waves in Time Domain	p. 223
Calculation of Incident Plane Waves in Time Domain	p. 225
Calculation of the Radar Cross Section	p. 227
Computer Programing and Numerical Examples	p. 229
Treatment for Special Problems	p. 233
Treatments for Thin Metallic Wires	p. 233
Treatments for Dispersive Media	p. 235
Treatments for Lumped Elements	p. 237
Comparison of the MoM, FEM and FDTD Methods	p. 239
References	p. 240
Hybrid Methods	p. 243
Hybrid High-Frequency Asymptotic Methods and Full-Wave Numerical Methods	p. 244
Hybird Physical Optics Method and FEM	p. 244
Hybrid Physical Optics Method and Moment Method	p. 248
Hybrid Full-Wave Numerical Methods	p. 251
Hybrid FE-BI-MLFMA	p. 252
Hybrid Method Combining EFIE and MFBE	p. 266
Hybrid Method Combining FEM and Mode-Matching Method	p. 271
References	p. 276
Index	p. 277
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Essentials of Computational Electromagnetics

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