A comprehensive, step-by-step reference to the Nyström Method for solving Electromagnetic problems using integral equations
Computational electromagnetics studies the numerical methods or techniques that solve electromagnetic problems by computer programming. Currently, there are mainly three numerical methods for electromagnetic problems: the finite-difference time-domain (FDTD), finite element method (FEM), and integral equation methods (IEMs). In the IEMs, the method of moments (MoM) is the most widely used method, but much attention is being paid to the Nyström method as another IEM, because it possesses some unique merits which the MoM lacks. This book focuses on that method--providing information on everything that students and professionals working in the field need to know.
Written by the top researchers in electromagnetics, this complete reference book is a consolidation of advances made in the use of the Nyström method for solving electromagnetic integral equations. It begins by introducing the fundamentals of the electromagnetic theory and computational electromagnetics, before proceeding to illustrate the advantages unique to the Nyström method through rigorous worked out examples and equations. Key topics include quadrature rules, singularity treatment techniques, applications to conducting and penetrable media, multiphysics electromagnetic problems, time-domain integral equations, inverse scattering problems and incorporation with multilevel fast multiple algorithm.
* Systematically introduces the fundamental principles, equations, and advantages of the Nyström method for solving electromagnetic problems
* Features the unique benefits of using the Nyström method through numerical comparisons with other numerical and analytical methods
* Covers a broad range of application examples that will point the way for future research
The Nystrom Method in Electromagnetics is ideal for graduate students, senior undergraduates, and researchers studying engineering electromagnetics, computational methods, and applied mathematics. Practicing engineers and other industry professionals working in engineering electromagnetics and engineering mathematics will also find it to be incredibly helpful.
Autorentext
Mei Song Tong, PhD, is currently a Distinguished Professor, Chair of the Department of Electronic Science and Technology, and Vice-Dean of the College of Microelectronics, Tongji University, Shanghai, China.
Weng Cho Chew, PhD, is a Distinguished Professor at the School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana, USA, and a Fellow of IEEE, OSA, IOP, and HKIE.
Klappentext
A comprehensive, step-by-step reference to the Nyström method for solving electromagnetic problems using integral equations
Computational electromagnetics studies the numerical methods or techniques that solve electromagnetic problems by computer programming. Currently, there are mainly three numerical methods for electromagnetic problems: the finite-difference time-domain (FDTD), finite element method (FEM), and integral equation methods (IEMs). In the IEMs, the method of moments (MoM) is the most widely used method, but much attention is being paid to the Nyström method as another IEM, because it possesses some unique merits which the MoM lacks. This book focuses on that methodproviding information on everything that students and professionals working in the field need to know.
Written by the top researchers in electromagnetics, this complete reference book is a consolidation of advances made in the use of the Nyström method for solving electromagnetic integral equations. It begins by introducing the fundamentals of the electromagnetic theory and computational electromagnetics, before proceeding to illustrate the advantages unique to the Nyström method through rigorous worked out examples and equations. Key topics include quadrature rules, singularity treatment techniques, applications to conducting and penetrable media, multiphysics electromagnetic problems, time-domain integral equations, inverse scattering problems and incorporation with multilevel fast multipole algorithm.
- Systematically introduces the fundamental principles, equations, and advantages of the Nyström method for solving electromagnetic problems
- Features the unique benefits of using the Nyström method through numerical comparisons with other numerical and analytical methods
- Covers a broad range of application examples that will point the way for future research
The Nyström Method in Electromagnetics is ideal for graduate students, senior undergraduates, and researchers studying engineering electromagnetics, computational methods, and applied mathematics. Practicing engineers and other industry professionals working in engineering electromagnetics and engineering mathematics will also find it to be incredibly helpful.
Inhalt
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 TheoryWhy? 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