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 boundary-value 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, high-speed/high-frequency 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, high-frequency circuits, and crystal photonics
- The finite element analysis of wave propagation, scattering, and radiation in periodic structures
- The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena
- Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array 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.
Table of Contents:
Preface 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
