JIAN-MING JIN, PhD, is Y. T. Lo Chair Professor in Electrical and Computer Engineering and Director of the Electromagnetics Laboratory and Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign. He authored Theory and Computation of Electromagnetic Fields (Wiley) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and coauthored Computation of Special Functions (Wiley) and Finite Element Analysis of Antennas and Arrays (Wiley). A Fellow of the IEEE, he is listed by ISI among the world’s most cited authors.

• Preface xix Preface to the First Edition xxiiiPreface to the Second Edition xxvii1 Basic Electromagnetic Theory 11.1 Brief Review of Vector Analysis 21.2 Maxwell's Equations 41.3 Scalar and Vector Potentials 61.4 Wave Equations 71.5 Boundary Conditions 81.6 Radiation Conditions 111.7 Fields in an Infinite Homogeneous Medium 111.8 Huygen's Principle 131.9 Radar Cross Sections 141.10 Summary 152 Introduction to the Finite Element Method 172.1 Classical Methods for Boundary-Value Problems 172.2 Simple Example 212.3 Basic Steps of the Finite Element Method 272.4 Alternative Presentation of the Finite Element Formulation 342.5 Summary 363 One-Dimensional Finite Element Analysis 393.1 Boundary-Value Problem 393.2 Variational Formulation 403.3 Finite Element Analysis 423.4 Plane-Wave Reflection by a Metal-Backed Dielectric Slab 533.5 Scattering by a Smooth, Convex Impedance Cylinder 593.6 Higher-Order Elements 623.7 Summary 744 Two-Dimensional Finite Element Analysis 774.1 Boundary-Value Problem 774.2 Variational Formulation 794.3 Finite Element Analysis 814.4 Application to Electrostatic Problems 984.5 Application to Magnetostatic Problems 1034.6 Application to Quasistatic Problems: Analysis of Multiconductor Transmission Lines 1054.7 Application to Time-Harmonic Problems 1094.8 Higher-Order Elements 1284.9 Isoparametric Elements 1444.10 Summary 1495 Three-Dimensional Finite Element Analysis 1515.1 Boundary-Value Problem 1515.2 Variational Formulation 1525.3 Finite Element Analysis 1535.4 Higher-Order Elements 1605.5 Isoparametric Elements 1625.6 Application to Electrostatic Problems 1685.7 Application to Magnetostatic Problems 1695.8 Application to Time-Harmonic Field Problems 1765.9 Summary 1886 Variational Principles for Electromagnetics 1916.1 Standard Variational Principle 1926.2 Modified Variational Principle 1976.3 Generalized Variational Principle 2016.4 Variational Principle for Anisotrpic Medium 2036.5 Variational Principle for Resistive Sheets 2076.6 Concluding Remarks 2097 Eigenvalue Problems: Waveguides and Cavities 2117.1 Scalar Formulations for Closed Waveguides 2127.2 Vector Formulations for Closed Waveguides 2257.3 Open Waveguides 2357.4 Three-Dimensional Cavities 2387.5 Summary 2398 Vector Finite Elements 2438.1 Two-Dimensional Edge Elements 2448.2 Waveguide Problem Revisited 2568.3 Three-Dimensional Edge Elements 2598.4 Cavity Problem Revisited 2708.5 Waveguide Discontinuities 2748.6 Higher-Order Interpolatory Vector Elements 2788.7 Higher-Order Hierarchical Vector Elements 2938.8 Computational Issues 3058.9 Summary 3099 Absorbing Boundary Conditions 3159.1 Two-Dimensional Absorbing Boundary Conditions 3169.2 Three-Dimensional Absorbing Boundary Conditions 3239.3 Scattering Analysis Using Absorbing Boundary Conditons 3289.4 Adaptive Absorbing Boundary Conditons 3399.5 Fictitious Absorbers 3489.6 Perfectly Matched Layers 3509.7 Application of PML to Body-of-Revolutions Problems 3689.8 Summary 37110 Finite Element-Boundary Integral Methods 37910.1 Scattering by Two-Dimensional Cavity-Backed Apertures 38110.2 Scattering by Two-Dimensional Cylindrical Structures 39910.3 Scattering by Three-Dimensional Cavity-Backed Apertures 41110.4 Radiation by Microstrip Patch Antennas in a Cavity 42510.5 Scattering by General Three-Dimensional Bodies 43010.6 Solution of the Finite Element-Boundary Integral System 43610.7 Symmetric Finite Element-Boundary Integral Formulations 44710.8 Summary 46211 Finite Element-Eigenfunction Expansion Methods 46911.1 Waveguide Port Boundary Conditions 47011.2 Open-Region Scattering 48711.3 Coupled Basis Functions: The Unimoment Method 49411.4 Finite Element-Extended Boundary Condition Method 50211.5 Summary 50912 Finite Element Analysis in the Time Domain 51312.1 Finite Element Formulation and Temporal Excitation 51412.2 Time-Domain Discretization 51812.3 Stability Analysis 52312.4 Modeling of Dispersive Media 52912.5 Truncation via Absorbing Boundary Conditions 53812.6 Truncation via Perfectly Matched Layers 54112.7 Truncation via Boundary Integral Equations 55112.8 Time-Domain Wqaveguide Port Boundary Conditions 56212.9 Hybrid Field-Circuit Analysis 56912.10 Dual-Field Domain Decomposition and Element-Level Methods 58712.11 Discontinuous Galerkin Time-Domain Methods 60512.12 Summary 62513 Finite Element Analysis of Periodic Structures 63713.1 Finite Element Formulation for a Unit Cell 63813.2 Scattering by One-Dimensional Periodic Structures: Frequency-Domain Analysis 65113.3 Scattering by One-Dimensional Periodic Structures: Time-Domain Analysis 65613.4 Scattering by Two-Dimensional Periodic Structures: Frequency-Domain Analysis 66313.5 Scattering by Two-Dimensonal Periodic Structures: Time-Domain Analysis 67013.6 Analysis of Angular Periodic Strctures 67813.7 Summary 68214 Domain Decompsition for Large-Scale Analysis 68714.1 Schwarz Methods 68814.2 Schur Complement Methods 69314.3 FETI-DP Method for Low-Frequency Problems 70514.4 FETI-DP Method for High-Frequency Problems 72814.5 Noncomformal FETI-DP Method Based on Cement Elements 74314.6 Application of Second-Order Transmission Conditions 75314.7 Summary 76015 Solution of Finite Element Equations 76715.1 Decomposition Methods 76915.2 Conjugate Gradient Methods 77815.3 Solution of Eigenvalue Problems 79115.4 Fast Frequency-Sweep Computation 79715.5 Summary 803Appendix A: Basic Vector Identities and Integral Theorems 809Appendix B: The Ritz Procedure for Complex-Valued Problems 813Appendix C: Green's Functions 817Appendix D: Singular Integral Evaluation 825Appendix E: Some Special Functions 829Index 837

JIAN-MING JIN, PhD, is Y. T. Lo Chair Professor in Electrical and Computer Engineering and Director of the Electromagnetics Laboratory and Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign. He authored Theory and Computation of Electromagnetic Fields (Wiley) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and coauthored Computation of Special Functions (Wiley) and Finite Element Analysis of Antennas and Arrays (Wiley). A Fellow of the IEEE, he is listed by ISI among the world’s most cited authors.

• Preface xix Preface to the First Edition xxiiiPreface to the Second Edition xxvii1 Basic Electromagnetic Theory 11.1 Brief Review of Vector Analysis 21.2 Maxwell's Equations 41.3 Scalar and Vector Potentials 61.4 Wave Equations 71.5 Boundary Conditions 81.6 Radiation Conditions 111.7 Fields in an Infinite Homogeneous Medium 111.8 Huygen's Principle 131.9 Radar Cross Sections 141.10 Summary 152 Introduction to the Finite Element Method 172.1 Classical Methods for Boundary-Value Problems 172.2 Simple Example 212.3 Basic Steps of the Finite Element Method 272.4 Alternative Presentation of the Finite Element Formulation 342.5 Summary 363 One-Dimensional Finite Element Analysis 393.1 Boundary-Value Problem 393.2 Variational Formulation 403.3 Finite Element Analysis 423.4 Plane-Wave Reflection by a Metal-Backed Dielectric Slab 533.5 Scattering by a Smooth, Convex Impedance Cylinder 593.6 Higher-Order Elements 623.7 Summary 744 Two-Dimensional Finite Element Analysis 774.1 Boundary-Value Problem 774.2 Variational Formulation 794.3 Finite Element Analysis 814.4 Application to Electrostatic Problems 984.5 Application to Magnetostatic Problems 1034.6 Application to Quasistatic Problems: Analysis of Multiconductor Transmission Lines 1054.7 Application to Time-Harmonic Problems 1094.8 Higher-Order Elements 1284.9 Isoparametric Elements 1444.10 Summary 1495 Three-Dimensional Finite Element Analysis 1515.1 Boundary-Value Problem 1515.2 Variational Formulation 1525.3 Finite Element Analysis 1535.4 Higher-Order Elements 1605.5 Isoparametric Elements 1625.6 Application to Electrostatic Problems 1685.7 Application to Magnetostatic Problems 1695.8 Application to Time-Harmonic Field Problems 1765.9 Summary 1886 Variational Principles for Electromagnetics 1916.1 Standard Variational Principle 1926.2 Modified Variational Principle 1976.3 Generalized Variational Principle 2016.4 Variational Principle for Anisotrpic Medium 2036.5 Variational Principle for Resistive Sheets 2076.6 Concluding Remarks 2097 Eigenvalue Problems: Waveguides and Cavities 2117.1 Scalar Formulations for Closed Waveguides 2127.2 Vector Formulations for Closed Waveguides 2257.3 Open Waveguides 2357.4 Three-Dimensional Cavities 2387.5 Summary 2398 Vector Finite Elements 2438.1 Two-Dimensional Edge Elements 2448.2 Waveguide Problem Revisited 2568.3 Three-Dimensional Edge Elements 2598.4 Cavity Problem Revisited 2708.5 Waveguide Discontinuities 2748.6 Higher-Order Interpolatory Vector Elements 2788.7 Higher-Order Hierarchical Vector Elements 2938.8 Computational Issues 3058.9 Summary 3099 Absorbing Boundary Conditions 3159.1 Two-Dimensional Absorbing Boundary Conditions 3169.2 Three-Dimensional Absorbing Boundary Conditions 3239.3 Scattering Analysis Using Absorbing Boundary Conditons 3289.4 Adaptive Absorbing Boundary Conditons 3399.5 Fictitious Absorbers 3489.6 Perfectly Matched Layers 3509.7 Application of PML to Body-of-Revolutions Problems 3689.8 Summary 37110 Finite Element-Boundary Integral Methods 37910.1 Scattering by Two-Dimensional Cavity-Backed Apertures 38110.2 Scattering by Two-Dimensional Cylindrical Structures 39910.3 Scattering by Three-Dimensional Cavity-Backed Apertures 41110.4 Radiation by Microstrip Patch Antennas in a Cavity 42510.5 Scattering by General Three-Dimensional Bodies 43010.6 Solution of the Finite Element-Boundary Integral System 43610.7 Symmetric Finite Element-Boundary Integral Formulations 44710.8 Summary 46211 Finite Element-Eigenfunction Expansion Methods 46911.1 Waveguide Port Boundary Conditions 47011.2 Open-Region Scattering 48711.3 Coupled Basis Functions: The Unimoment Method 49411.4 Finite Element-Extended Boundary Condition Method 50211.5 Summary 50912 Finite Element Analysis in the Time Domain 51312.1 Finite Element Formulation and Temporal Excitation 51412.2 Time-Domain Discretization 51812.3 Stability Analysis 52312.4 Modeling of Dispersive Media 52912.5 Truncation via Absorbing Boundary Conditions 53812.6 Truncation via Perfectly Matched Layers 54112.7 Truncation via Boundary Integral Equations 55112.8 Time-Domain Wqaveguide Port Boundary Conditions 56212.9 Hybrid Field-Circuit Analysis 56912.10 Dual-Field Domain Decomposition and Element-Level Methods 58712.11 Discontinuous Galerkin Time-Domain Methods 60512.12 Summary 62513 Finite Element Analysis of Periodic Structures 63713.1 Finite Element Formulation for a Unit Cell 63813.2 Scattering by One-Dimensional Periodic Structures: Frequency-Domain Analysis 65113.3 Scattering by One-Dimensional Periodic Structures: Time-Domain Analysis 65613.4 Scattering by Two-Dimensional Periodic Structures: Frequency-Domain Analysis 66313.5 Scattering by Two-Dimensonal Periodic Structures: Time-Domain Analysis 67013.6 Analysis of Angular Periodic Strctures 67813.7 Summary 68214 Domain Decompsition for Large-Scale Analysis 68714.1 Schwarz Methods 68814.2 Schur Complement Methods 69314.3 FETI-DP Method for Low-Frequency Problems 70514.4 FETI-DP Method for High-Frequency Problems 72814.5 Noncomformal FETI-DP Method Based on Cement Elements 74314.6 Application of Second-Order Transmission Conditions 75314.7 Summary 76015 Solution of Finite Element Equations 76715.1 Decomposition Methods 76915.2 Conjugate Gradient Methods 77815.3 Solution of Eigenvalue Problems 79115.4 Fast Frequency-Sweep Computation 79715.5 Summary 803Appendix A: Basic Vector Identities and Integral Theorems 809Appendix B: The Ritz Procedure for Complex-Valued Problems 813Appendix C: Green's Functions 817Appendix D: Singular Integral Evaluation 825Appendix E: Some Special Functions 829Index 837

JIAN-MING JIN, PhD, is Y. T. Lo Chair Professor in Electrical and Computer Engineering and Director of the Electromagnetics Laboratory and Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign. He authored Theory and Computation of Electromagnetic Fields (Wiley) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and coauthored Computation of Special Functions (Wiley) and Finite Element Analysis of Antennas and Arrays (Wiley). A Fellow of the IEEE, he is listed by ISI among the world’s most cited authors.

• Preface xix Preface to the First Edition xxiiiPreface to the Second Edition xxvii1 Basic Electromagnetic Theory 11.1 Brief Review of Vector Analysis 21.2 Maxwell's Equations 41.3 Scalar and Vector Potentials 61.4 Wave Equations 71.5 Boundary Conditions 81.6 Radiation Conditions 111.7 Fields in an Infinite Homogeneous Medium 111.8 Huygen's Principle 131.9 Radar Cross Sections 141.10 Summary 152 Introduction to the Finite Element Method 172.1 Classical Methods for Boundary-Value Problems 172.2 Simple Example 212.3 Basic Steps of the Finite Element Method 272.4 Alternative Presentation of the Finite Element Formulation 342.5 Summary 363 One-Dimensional Finite Element Analysis 393.1 Boundary-Value Problem 393.2 Variational Formulation 403.3 Finite Element Analysis 423.4 Plane-Wave Reflection by a Metal-Backed Dielectric Slab 533.5 Scattering by a Smooth, Convex Impedance Cylinder 593.6 Higher-Order Elements 623.7 Summary 744 Two-Dimensional Finite Element Analysis 774.1 Boundary-Value Problem 774.2 Variational Formulation 794.3 Finite Element Analysis 814.4 Application to Electrostatic Problems 984.5 Application to Magnetostatic Problems 1034.6 Application to Quasistatic Problems: Analysis of Multiconductor Transmission Lines 1054.7 Application to Time-Harmonic Problems 1094.8 Higher-Order Elements 1284.9 Isoparametric Elements 1444.10 Summary 1495 Three-Dimensional Finite Element Analysis 1515.1 Boundary-Value Problem 1515.2 Variational Formulation 1525.3 Finite Element Analysis 1535.4 Higher-Order Elements 1605.5 Isoparametric Elements 1625.6 Application to Electrostatic Problems 1685.7 Application to Magnetostatic Problems 1695.8 Application to Time-Harmonic Field Problems 1765.9 Summary 1886 Variational Principles for Electromagnetics 1916.1 Standard Variational Principle 1926.2 Modified Variational Principle 1976.3 Generalized Variational Principle 2016.4 Variational Principle for Anisotrpic Medium 2036.5 Variational Principle for Resistive Sheets 2076.6 Concluding Remarks 2097 Eigenvalue Problems: Waveguides and Cavities 2117.1 Scalar Formulations for Closed Waveguides 2127.2 Vector Formulations for Closed Waveguides 2257.3 Open Waveguides 2357.4 Three-Dimensional Cavities 2387.5 Summary 2398 Vector Finite Elements 2438.1 Two-Dimensional Edge Elements 2448.2 Waveguide Problem Revisited 2568.3 Three-Dimensional Edge Elements 2598.4 Cavity Problem Revisited 2708.5 Waveguide Discontinuities 2748.6 Higher-Order Interpolatory Vector Elements 2788.7 Higher-Order Hierarchical Vector Elements 2938.8 Computational Issues 3058.9 Summary 3099 Absorbing Boundary Conditions 3159.1 Two-Dimensional Absorbing Boundary Conditions 3169.2 Three-Dimensional Absorbing Boundary Conditions 3239.3 Scattering Analysis Using Absorbing Boundary Conditons 3289.4 Adaptive Absorbing Boundary Conditons 3399.5 Fictitious Absorbers 3489.6 Perfectly Matched Layers 3509.7 Application of PML to Body-of-Revolutions Problems 3689.8 Summary 37110 Finite Element-Boundary Integral Methods 37910.1 Scattering by Two-Dimensional Cavity-Backed Apertures 38110.2 Scattering by Two-Dimensional Cylindrical Structures 39910.3 Scattering by Three-Dimensional Cavity-Backed Apertures 41110.4 Radiation by Microstrip Patch Antennas in a Cavity 42510.5 Scattering by General Three-Dimensional Bodies 43010.6 Solution of the Finite Element-Boundary Integral System 43610.7 Symmetric Finite Element-Boundary Integral Formulations 44710.8 Summary 46211 Finite Element-Eigenfunction Expansion Methods 46911.1 Waveguide Port Boundary Conditions 47011.2 Open-Region Scattering 48711.3 Coupled Basis Functions: The Unimoment Method 49411.4 Finite Element-Extended Boundary Condition Method 50211.5 Summary 50912 Finite Element Analysis in the Time Domain 51312.1 Finite Element Formulation and Temporal Excitation 51412.2 Time-Domain Discretization 51812.3 Stability Analysis 52312.4 Modeling of Dispersive Media 52912.5 Truncation via Absorbing Boundary Conditions 53812.6 Truncation via Perfectly Matched Layers 54112.7 Truncation via Boundary Integral Equations 55112.8 Time-Domain Wqaveguide Port Boundary Conditions 56212.9 Hybrid Field-Circuit Analysis 56912.10 Dual-Field Domain Decomposition and Element-Level Methods 58712.11 Discontinuous Galerkin Time-Domain Methods 60512.12 Summary 62513 Finite Element Analysis of Periodic Structures 63713.1 Finite Element Formulation for a Unit Cell 63813.2 Scattering by One-Dimensional Periodic Structures: Frequency-Domain Analysis 65113.3 Scattering by One-Dimensional Periodic Structures: Time-Domain Analysis 65613.4 Scattering by Two-Dimensional Periodic Structures: Frequency-Domain Analysis 66313.5 Scattering by Two-Dimensonal Periodic Structures: Time-Domain Analysis 67013.6 Analysis of Angular Periodic Strctures 67813.7 Summary 68214 Domain Decompsition for Large-Scale Analysis 68714.1 Schwarz Methods 68814.2 Schur Complement Methods 69314.3 FETI-DP Method for Low-Frequency Problems 70514.4 FETI-DP Method for High-Frequency Problems 72814.5 Noncomformal FETI-DP Method Based on Cement Elements 74314.6 Application of Second-Order Transmission Conditions 75314.7 Summary 76015 Solution of Finite Element Equations 76715.1 Decomposition Methods 76915.2 Conjugate Gradient Methods 77815.3 Solution of Eigenvalue Problems 79115.4 Fast Frequency-Sweep Computation 79715.5 Summary 803Appendix A: Basic Vector Identities and Integral Theorems 809Appendix B: The Ritz Procedure for Complex-Valued Problems 813Appendix C: Green's Functions 817Appendix D: Singular Integral Evaluation 825Appendix E: Some Special Functions 829Index 837