The Finite Element Method in Electromagnetics, 3rd EditionISBN: 9781118571361
876 pages
March 2014, WileyIEEE Press

A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics
The finite element method (FEM) is a powerful simulation technique used to solve boundaryvalue problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, highspeed/highfrequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration.
The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems.
Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes:
 A wider range of applications, including antennas, phased arrays, electric machines, highfrequency circuits, and crystal photonics
 The finite element analysis of wave propagation, scattering, and radiation in periodic structures
 The timedomain finite element method for analysis of wideband antennas and transient electromagnetic phenomena
 Novel domain decomposition techniques for parallel computation and efficient simulation of largescale problems, such as phasedarray antennas and photonic crystals
Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.
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 BoundaryValue 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 OneDimensional Finite Element Analysis 39
3.1 BoundaryValue Problem 39
3.2 Variational Formulation 40
3.3 Finite Element Analysis 42
3.4 PlaneWave Reflection by a MetalBacked Dielectric Slab 53
3.5 Scattering by a Smooth, Convex Impedance Cylinder 59
3.6 HigherOrder Elements 62
3.7 Summary 74
4 TwoDimensional Finite Element Analysis 77
4.1 BoundaryValue 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 TimeHarmonic Problems 109
4.8 HigherOrder Elements 128
4.9 Isoparametric Elements 144
4.10 Summary 149
5 ThreeDimensional Finite Element Analysis 151
5.1 BoundaryValue Problem 151
5.2 Variational Formulation 152
5.3 Finite Element Analysis 153
5.4 HigherOrder 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 TimeHarmonic 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 ThreeDimensional Cavities 238
7.5 Summary 239
8 Vector Finite Elements 243
8.1 TwoDimensional Edge Elements 244
8.2 Waveguide Problem Revisited 256
8.3 ThreeDimensional Edge Elements 259
8.4 Cavity Problem Revisited 270
8.5 Waveguide Discontinuities 274
8.6 HigherOrder Interpolatory Vector Elements 278
8.7 HigherOrder Hierarchical Vector Elements 293
8.8 Computational Issues 305
8.9 Summary 309
9 Absorbing Boundary Conditions 315
9.1 TwoDimensional Absorbing Boundary Conditions 316
9.2 ThreeDimensional 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 BodyofRevolutions Problems 368
9.8 Summary 371
10 Finite ElementBoundary Integral Methods 379
10.1 Scattering by TwoDimensional CavityBacked Apertures 381
10.2 Scattering by TwoDimensional Cylindrical Structures 399
10.3 Scattering by ThreeDimensional CavityBacked Apertures 411
10.4 Radiation by Microstrip Patch Antennas in a Cavity 425
10.5 Scattering by General ThreeDimensional Bodies 430
10.6 Solution of the Finite ElementBoundary Integral System 436
10.7 Symmetric Finite ElementBoundary Integral Formulations 447
10.8 Summary 462
11 Finite ElementEigenfunction Expansion Methods 469
11.1 Waveguide Port Boundary Conditions 470
11.2 OpenRegion Scattering 487
11.3 Coupled Basis Functions: The Unimoment Method 494
11.4 Finite ElementExtended 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 TimeDomain 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 TimeDomain Wqaveguide Port Boundary Conditions 562
12.9 Hybrid FieldCircuit Analysis 569
12.10 DualField Domain Decomposition and ElementLevel Methods 587
12.11 Discontinuous Galerkin TimeDomain 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 OneDimensional Periodic Structures: FrequencyDomain Analysis 651
13.3 Scattering by OneDimensional Periodic Structures: TimeDomain Analysis 656
13.4 Scattering by TwoDimensional Periodic Structures: FrequencyDomain Analysis 663
13.5 Scattering by TwoDimensonal Periodic Structures: TimeDomain Analysis 670
13.6 Analysis of Angular Periodic Strctures 678
13.7 Summary 682
14 Domain Decompsition for LargeScale Analysis 687
14.1 Schwarz Methods 688
14.2 Schur Complement Methods 693
14.3 FETIDP Method for LowFrequency Problems 705
14.4 FETIDP Method for HighFrequency Problems 728
14.5 Noncomformal FETIDP Method Based on Cement Elements 743
14.6 Application of SecondOrder 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 FrequencySweep Computation 797
15.5 Summary 803
Appendix A: Basic Vector Identities and Integral Theorems 809
Appendix B: The Ritz Procedure for ComplexValued Problems 813
Appendix C: Green's Functions 817
Appendix D: Singular Integral Evaluation 825
Appendix E: Some Special Functions 829
Index 837
JIANMING 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 UrbanaChampaign. 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.