The finite element method in electromagnetics

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