Theory and Computation of Electromagnetic Fields

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 xvAcknowledgments xxiPart I Electromagnetic Field Theory 11 Basic Electromagnetic Theory 31.2 Maxwell’s Equations in Terms of Total Charges and Currents 111.3 Constitutive Relations 181.4 Maxwell’s Equations in Terms of Free Charges and Currents 251.5 Boundary Conditions 271.6 Energy Power and Poynting’s Theorem 311.7 Time-Harmonic Fields 33References 46Problems 462 Electromagnetic Radiation in Free Space 532.1 Scalar and Vector Potentials 532.2 Solution of Vector Potentials in Free Space 612.3 Electromagnetic Radiation in Free Space 692.4 Radiation by Surface Currents and Phased Arrays 78References 84Problems 853 Electromagnetic Theorems and Principles 893.1 Uniqueness Theorem 903.2 Image Theory 943.3 Reciprocity Theorems 1013.4 Equivalence Principles 1073.5 Duality Principle 1203.6 Aperture Radiation and Scattering 121References 128Problems 1294 Transmission Lines and Plane Waves 1354.1 Transmission Line Theory 1354.2 Wave Equations and General Solutions 1444.3 Plane Waves Generated by a Current Sheet 1564.4 Reflection and Transmission 1594.5 Plane Waves in Anisotropic and Bi-Isotropic Media 174References 190Problems 1915 Fields and Waves in Rectangular Coordinates 1995.1 Uniform Waveguides 1995.2 Uniform Cavities 2205.3 Partially Filled Waveguides and Dielectric Slab Waveguides 2295.4 Field Excitation in Waveguides 2415.5 Fields in Planar Layered Media 245References 257Problems 2576 Fields and Waves in Cylindrical Coordinates 2616.1 Solution of Wave Equation 2616.2 Circular and Coaxial Waveguides and Cavities 2666.3 Circular Dielectric Waveguide 2796.4 Wave Transformation and Scattering Analysis 2876.5 Radiation by Infinitely Long Currents 300References 319Problems 3207 Fields and Waves in Spherical Coordinates 3257.1 Solution of Wave Equation 3257.2 Spherical Cavity 3317.3 Biconical Antenna 3357.4 Wave Transformation and Scattering Analysis 3417.5 Addition Theorem and Radiation Analysis 360References 377Problems 377Part II Electromagnetic Field Computation 3838 The Finite Difference Method 3858.1 Finite Differencing Formulas 3858.2 One-Dimensional Analysis 3878.3 Two-Dimensional Analysis 3938.4 Yee’s FDTD Scheme 3978.5 Absorbing Boundary Conditions 4028.6 Modeling of Dispersive Media 4178.7 Wave Excitation and Far-Field Calculation 4228.8 Summary 427References 428Problems 4299 The Finite Element Method 4339.1 Introduction to the Finite Element Method 4349.2 Finite Element Analysis of Scalar Fields 4399.3 Finite Element Analysis of Vector Fields 4509.4 Finite Element Analysis in the Time Domain 4659.5 Discontinuous Galerkin Time-Domain Method 4729.6 Absorbing Boundary Conditions 4839.7 Some Numerical Aspects 4949.8 Summary 497References 497Problems 49910 The Method of Moments 50510.1 Introduction to the Method of Moments 50610.2 Two-Dimensional Analysis 51010.3 Three-Dimensional Analysis 52310.4 Analysis of Periodic Structures 54410.5 Analysis of Microstrip Antennas and Circuits 55110.6 The Moment Method in the Time Domain 56110.7 Summary 568References 568Problems 57111 Fast Algorithms and Hybrid Techniques 57511.1 Introduction to Fast Algorithms 57611.2 Conjugate Gradient–FFT Method 57811.3 Adaptive Integral Method 59111.4 Fast Multipole Method 60211.5 Adaptive Cross-Approximation Algorithm 61411.6 Introduction to Hybrid Techniques 62311.7 Hybrid Finite Difference–Finite Element Method 62411.8 Hybrid Finite Element–Boundary Integral Method 63011.9 Summary 642References 643Problems 64912 Concluding Remarks on Computational Electromagnetics 65112.1 Overview of Computational Electromagnetics 65112.2 Applications of Computational Electromagnetics 65912.3 Challenges in Computational Electromagnetics 670References 671Appendix A Vector Identities Integral Theorems and Coordinate Transformation 681A.1 Vector Identities 681A.2 Integral Theorems 682A.3 Coordinate Transformation 682Appendix B Bessel Functions 683B.1 Definition 683B.2 Series Expressions 683B.3 Integral Representation 685B.4 Asymptotic Expressions 685B.5 Recurrence and Derivative Relations 685B.6 Symmetry Relations 686B.7 Wronskian Relation 686B.8 Useful Integrals 686Appendix C Modified Bessel Functions 687C.1 Definition 687C.2 Series Expressions 687C.3 Integral Representations 688C.4 Asymptotic Expressions 688C.5 Recurrence and Derivative Relations 689C.6 Symmetry Relations 690C.7 Wronskian Relation 690C.8 Useful Integrals 690Appendix D Spherical Bessel Functions 691D.1 Definition 691D.2 Series Expressions 692D.3 Asymptotic Expressions 693D.4 Recurrence and Derivative Relations 693D.5 Symmetry Relations 694D.6 Wronskian Relation 695D.7 Riccati–Bessel Functions 695D.8 Modified Spherical Bessel Functions 695Appendix E Associated Legendre Polynomials 697E.1 Definition 697E.2 Series Expression 698E.3 Special Values 700E.4 Symmetry Relations 701E.5 Recurrence and Derivative Relations 701E.6 Orthogonal Relations 702E.7 Fourier–Legendre Series 702Index 703