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Book SynopsisUseful in analyzing electromagnetic problems in a variety of engineering circumstances, the finite element method is a powerful simulation technique. This book explains the method's processes and techniques in careful, meticulous prose. It covers not only essential finite element method theory, but also its latest developments and applications.Table of ContentsPreface xix Preface to the First Edition xxiii Preface to the Second Edition xxvii 1 Basic Electromagnetic Theory 1 1.1 Brief Review of Vector Analysis 2 1.2 Maxwell's Equations 4 1.3 Scalar and Vector Potentials 6 1.4 Wave Equations 7 1.5 Boundary Conditions 8 1.6 Radiation Conditions 11 1.7 Fields in an Infinite Homogeneous Medium 11 1.8 Huygen's Principle 13 1.9 Radar Cross Sections 14 1.10 Summary 15 2 Introduction to the Finite Element Method 17 2.1 Classical Methods for Boundary-Value Problems 17 2.2 Simple Example 21 2.3 Basic Steps of the Finite Element Method 27 2.4 Alternative Presentation of the Finite Element Formulation 34 2.5 Summary 36 3 One-Dimensional Finite Element Analysis 39 3.1 Boundary-Value Problem 39 3.2 Variational Formulation 40 3.3 Finite Element Analysis 42 3.4 Plane-Wave Reflection by a Metal-Backed Dielectric Slab 53 3.5 Scattering by a Smooth, Convex Impedance Cylinder 59 3.6 Higher-Order Elements 62 3.7 Summary 74 4 Two-Dimensional Finite Element Analysis 77 4.1 Boundary-Value Problem 77 4.2 Variational Formulation 79 4.3 Finite Element Analysis 81 4.4 Application to Electrostatic Problems 98 4.5 Application to Magnetostatic Problems 103 4.6 Application to Quasistatic Problems: Analysis of Multiconductor Transmission Lines 105 4.7 Application to Time-Harmonic Problems 109 4.8 Higher-Order Elements 128 4.9 Isoparametric Elements 144 4.10 Summary 149 5 Three-Dimensional Finite Element Analysis 151 5.1 Boundary-Value Problem 151 5.2 Variational Formulation 152 5.3 Finite Element Analysis 153 5.4 Higher-Order Elements 160 5.5 Isoparametric Elements 162 5.6 Application to Electrostatic Problems 168 5.7 Application to Magnetostatic Problems 169 5.8 Application to Time-Harmonic Field Problems 176 5.9 Summary 188 6 Variational Principles for Electromagnetics 191 6.1 Standard Variational Principle 192 6.2 Modified Variational Principle 197 6.3 Generalized Variational Principle 201 6.4 Variational Principle for Anisotrpic Medium 203 6.5 Variational Principle for Resistive Sheets 207 6.6 Concluding Remarks 209 7 Eigenvalue Problems: Waveguides and Cavities 211 7.1 Scalar Formulations for Closed Waveguides 212 7.2 Vector Formulations for Closed Waveguides 225 7.3 Open Waveguides 235 7.4 Three-Dimensional Cavities 238 7.5 Summary 239 8 Vector Finite Elements 243 8.1 Two-Dimensional Edge Elements 244 8.2 Waveguide Problem Revisited 256 8.3 Three-Dimensional Edge Elements 259 8.4 Cavity Problem Revisited 270 8.5 Waveguide Discontinuities 274 8.6 Higher-Order Interpolatory Vector Elements 278 8.7 Higher-Order Hierarchical Vector Elements 293 8.8 Computational Issues 305 8.9 Summary 309 9 Absorbing Boundary Conditions 315 9.1 Two-Dimensional Absorbing Boundary Conditions 316 9.2 Three-Dimensional Absorbing Boundary Conditions 323 9.3 Scattering Analysis Using Absorbing Boundary Conditons 328 9.4 Adaptive Absorbing Boundary Conditons 339 9.5 Fictitious Absorbers 348 9.6 Perfectly Matched Layers 350 9.7 Application of PML to Body-of-Revolutions Problems 368 9.8 Summary 371 10 Finite Element-Boundary Integral Methods 379 10.1 Scattering by Two-Dimensional Cavity-Backed Apertures 381 10.2 Scattering by Two-Dimensional Cylindrical Structures 399 10.3 Scattering by Three-Dimensional Cavity-Backed Apertures 411 10.4 Radiation by Microstrip Patch Antennas in a Cavity 425 10.5 Scattering by General Three-Dimensional Bodies 430 10.6 Solution of the Finite Element-Boundary Integral System 436 10.7 Symmetric Finite Element-Boundary Integral Formulations 447 10.8 Summary 462 11 Finite Element-Eigenfunction Expansion Methods 469 11.1 Waveguide Port Boundary Conditions 470 11.2 Open-Region Scattering 487 11.3 Coupled Basis Functions: The Unimoment Method 494 11.4 Finite Element-Extended Boundary Condition Method 502 11.5 Summary 509 12 Finite Element Analysis in the Time Domain 513 12.1 Finite Element Formulation and Temporal Excitation 514 12.2 Time-Domain Discretization 518 12.3 Stability Analysis 523 12.4 Modeling of Dispersive Media 529 12.5 Truncation via Absorbing Boundary Conditions 538 12.6 Truncation via Perfectly Matched Layers 541 12.7 Truncation via Boundary Integral Equations 551 12.8 Time-Domain Wqaveguide Port Boundary Conditions 562 12.9 Hybrid Field-Circuit Analysis 569 12.10 Dual-Field Domain Decomposition and Element-Level Methods 587 12.11 Discontinuous Galerkin Time-Domain Methods 605 12.12 Summary 625 13 Finite Element Analysis of Periodic Structures 637 13.1 Finite Element Formulation for a Unit Cell 638 13.2 Scattering by One-Dimensional Periodic Structures: Frequency-Domain Analysis 651 13.3 Scattering by One-Dimensional Periodic Structures: Time-Domain Analysis 656 13.4 Scattering by Two-Dimensional Periodic Structures: Frequency-Domain Analysis 663 13.5 Scattering by Two-Dimensonal Periodic Structures: Time-Domain Analysis 670 13.6 Analysis of Angular Periodic Strctures 678 13.7 Summary 682 14 Domain Decompsition for Large-Scale Analysis 687 14.1 Schwarz Methods 688 14.2 Schur Complement Methods 693 14.3 FETI-DP Method for Low-Frequency Problems 705 14.4 FETI-DP Method for High-Frequency Problems 728 14.5 Noncomformal FETI-DP Method Based on Cement Elements 743 14.6 Application of Second-Order Transmission Conditions 753 14.7 Summary 760 15 Solution of Finite Element Equations 767 15.1 Decomposition Methods 769 15.2 Conjugate Gradient Methods 778 15.3 Solution of Eigenvalue Problems 791 15.4 Fast Frequency-Sweep Computation 797 15.5 Summary 803 Appendix A: Basic Vector Identities and Integral Theorems 809 Appendix B: The Ritz Procedure for Complex-Valued Problems 813 Appendix C: Green's Functions 817 Appendix D: Singular Integral Evaluation 825 Appendix E: Some Special Functions 829 Index 837

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Book SynopsisReviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell's equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more effiTable of ContentsPreface 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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