JIAN-MING JIN, Ph.D., is the 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 The Finite Element Method in Electromagnetics, Third Edition (Wiley 2014) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and co-authored Computation of Special Functions (Wiley 1996), Finite Element Analysis of Antennas and Arrays (Wiley 2008), and Fast and Efficient Algorithms in Computational Electromagnetics. A Fellow of the IEEE, he is listed by ISI among the world's most cited authors.

Preface xv

Acknowledgments xxi

Part I Electromagnetic Field Theory 1

1 Basic Electromagnetic Theory 3

1.2 Maxwell’s Equations in Terms of Total Charges and Currents 11

1.3 Constitutive Relations 18

1.4 Maxwell’s Equations in Terms of Free Charges and Currents 25

1.5 Boundary Conditions 27

1.6 Energy Power and Poynting’s Theorem 31

1.7 Time-Harmonic Fields 33

References 46

Problems 46

2 Electromagnetic Radiation in Free Space 53

2.1 Scalar and Vector Potentials 53

2.2 Solution of Vector Potentials in Free Space 61

2.3 Electromagnetic Radiation in Free Space 69

2.4 Radiation by Surface Currents and Phased Arrays 78

References 84

Problems 85

3 Electromagnetic Theorems and Principles 89

3.1 Uniqueness Theorem 90

3.2 Image Theory 94

3.3 Reciprocity Theorems 101

3.4 Equivalence Principles 107

3.5 Duality Principle 120

3.6 Aperture Radiation and Scattering 121

References 128

Problems 129

4 Transmission Lines and Plane Waves 135

4.1 Transmission Line Theory 135

4.2 Wave Equations and General Solutions 144

4.3 Plane Waves Generated by a Current Sheet 156

4.4 Reflection and Transmission 159

4.5 Plane Waves in Anisotropic and Bi-Isotropic Media 174

References 190

Problems 191

5 Fields and Waves in Rectangular Coordinates 199

5.1 Uniform Waveguides 199

5.2 Uniform Cavities 220

5.3 Partially Filled Waveguides and Dielectric Slab Waveguides 229

5.4 Field Excitation in Waveguides 241

5.5 Fields in Planar Layered Media 245

References 257

Problems 257

6 Fields and Waves in Cylindrical Coordinates 261

6.1 Solution of Wave Equation 261

6.2 Circular and Coaxial Waveguides and Cavities 266

6.3 Circular Dielectric Waveguide 279

6.4 Wave Transformation and Scattering Analysis 287

6.5 Radiation by Infinitely Long Currents 300

References 319

Problems 320

7 Fields and Waves in Spherical Coordinates 325

7.1 Solution of Wave Equation 325

7.2 Spherical Cavity 331

7.3 Biconical Antenna 335

7.4 Wave Transformation and Scattering Analysis 341

7.5 Addition Theorem and Radiation Analysis 360

References 377

Problems 377

Part II Electromagnetic Field Computation 383

8 The Finite Difference Method 385

8.1 Finite Differencing Formulas 385

8.2 One-Dimensional Analysis 387

8.3 Two-Dimensional Analysis 393

8.4 Yee’s FDTD Scheme 397

8.5 Absorbing Boundary Conditions 402

8.6 Modeling of Dispersive Media 417

8.7 Wave Excitation and Far-Field Calculation 422

8.8 Summary 427

References 428

Problems 429

9 The Finite Element Method 433

9.1 Introduction to the Finite Element Method 434

9.2 Finite Element Analysis of Scalar Fields 439

9.3 Finite Element Analysis of Vector Fields 450

9.4 Finite Element Analysis in the Time Domain 465

9.5 Discontinuous Galerkin Time-Domain Method 472

9.6 Absorbing Boundary Conditions 483

9.7 Some Numerical Aspects 494

9.8 Summary 497

References 497

Problems 499

10 The Method of Moments 505

10.1 Introduction to the Method of Moments 506

10.2 Two-Dimensional Analysis 510

10.3 Three-Dimensional Analysis 523

10.4 Analysis of Periodic Structures 544

10.5 Analysis of Microstrip Antennas and Circuits 551

10.6 The Moment Method in the Time Domain 561

10.7 Summary 568

References 568

Problems 571

11 Fast Algorithms and Hybrid Techniques 575

11.1 Introduction to Fast Algorithms 576

11.2 Conjugate Gradient–FFT Method 578

11.3 Adaptive Integral Method 591

11.4 Fast Multipole Method 602

11.5 Adaptive Cross-Approximation Algorithm 614

11.6 Introduction to Hybrid Techniques 623

11.7 Hybrid Finite Difference–Finite Element Method 624

11.8 Hybrid Finite Element–Boundary Integral Method 630

11.9 Summary 642

References 643

Problems 649

12 Concluding Remarks on Computational Electromagnetics 651

12.1 Overview of Computational Electromagnetics 651

12.2 Applications of Computational Electromagnetics 659

12.3 Challenges in Computational Electromagnetics 670

References 671

Appendix A Vector Identities Integral Theorems and Coordinate Transformation 681

A.1 Vector Identities 681

A.2 Integral Theorems 682

A.3 Coordinate Transformation 682

Appendix B Bessel Functions 683

B.1 Definition 683

B.2 Series Expressions 683

B.3 Integral Representation 685

B.4 Asymptotic Expressions 685

B.5 Recurrence and Derivative Relations 685

B.6 Symmetry Relations 686

B.7 Wronskian Relation 686

B.8 Useful Integrals 686

Appendix C Modified Bessel Functions 687

C.1 Definition 687

C.2 Series Expressions 687

C.3 Integral Representations 688

C.4 Asymptotic Expressions 688

C.5 Recurrence and Derivative Relations 689

C.6 Symmetry Relations 690

C.7 Wronskian Relation 690

C.8 Useful Integrals 690

Appendix D Spherical Bessel Functions 691

D.1 Definition 691

D.2 Series Expressions 692

D.3 Asymptotic Expressions 693

D.4 Recurrence and Derivative Relations 693

D.5 Symmetry Relations 694

D.6 Wronskian Relation 695

D.7 Riccati–Bessel Functions 695

D.8 Modified Spherical Bessel Functions 695

Appendix E Associated Legendre Polynomials 697

E.1 Definition 697

E.2 Series Expression 698

E.3 Special Values 700

E.4 Symmetry Relations 701

E.5 Recurrence and Derivative Relations 701

E.6 Orthogonal Relations 702

E.7 Fourier–Legendre Series 702

Index 703

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