The finite element method in electromagnetics

1194 Pages·2014·51.6 MB·English

by  Jian-ming Jin

Contents
Cover
Half Title page
Title page
Copyright page
Dedication
Preface
Preface to the First Edition
Preface to the Second Edition
Chapter 1: Basic Electromagnetic Theory
1.1 Brief Review of Vector Analysis
1.2 Maxwell’s Equations
1.3 Scalar and Vector Potentials
1.4 Wave Equations
1.5 Boundary Conditions
1.6 Radiation Conditions
1.7 Fields in an Infinite Homogeneous Medium
1.8 Huygens’s Principle
1.9 Radar Cross Sections
1.10 Summary
References
Chapter 2: Introduction to the Finite Element Method
2.1 Classical Methods for Boundary-Value Problems
2.2 Simple Example
2.3 Basic Steps of the Finite Element Method
2.4 Alternative Presentation of the Finite Element Formulation
2.5 Summary
References
Chapter 3: One-Dimensional Finite Element Analysis
3.1 Boundary-Value Problem
3.2 Variational Formulation
3.3 Finite Element Analysis
3.4 Plane-Wave Reflection by a Metal-Backed Dielectric Slab
3.5 Scattering by a Smooth, Convex Impedance Cylinder
3.6 Higher-Order Elements
3.7 Summary
References
Chapter 4: Two-Dimensional Finite Element Analysis
4.1 Boundary-Value Problem
4.2 Variational Formulation
4.3 Finite Element Analysis
4.4 Application to Electrostatic Problems
4.5 Application to Magnetostatic Problems
4.6 Application to Quasistatic Problems: Analysis of
Multiconductor Transmission Lines
4.7 Application to Time-Harmonic Problems
4.8 Higher-Order Elements
4.9 Isoparametric Elements
4.10 Summary
References
Chapter 5: Three-Dimensional Finite Element
Analysis
5.1 Boundary-Value Problem
5.2 Variational Formulation
5.3 Finite Element Analysis
5.4 Higher-Order Elements
5.5 Isoparametric Elements
5.6 Application to Electrostatic Problems
5.7 Application to Magnetostatic Problems
5.8 Application to Time-Harmonic Field Problems
5.9 Summary
References
Chapter 6: Variational Principles for
Electromagnetics
6.1 Standard Variational Principle
6.2 Modified Variational Principle
6.3 Generalized Variational Principle
6.4 Variational Principle for Anisotropic Medium
6.5 Variational Principle for Resistive Sheets
6.6 Concluding Remarks
References
Chapter 7: Eigenvalue Problems: Waveguides and
Cavities
7.1 Scalar Formulations for Closed Waveguides
7.2 Vector Formulations for Closed Waveguides
7.3 Open Waveguides
7.4 Three-Dimensional Cavities
7.5 Summary
References
Chapter 8: Vector Finite Elements
8.1 Two-Dimensional Edge Elements
8.2 Waveguide Problem Revisited
8.3 Three-Dimensional Edge Elements
8.4 Cavity Problem Revisited
8.5 Waveguide Discontinuities
8.6 Higher-Order Interpolatory Vector Elements
8.7 Higher-Order Hierarchical Vector Elements
8.8 Computational Issues
8.9 Summary
References
Chapter 9: Absorbing Boundary Conditions
9.1 Two-Dimensional Absorbing Boundary Conditions
9.2 Three-Dimensional Absorbing Boundary Conditions
9.3 Scattering Analysis Using Absorbing Boundary Conditions
9.4 Adaptive Absorbing Boundary Conditions
9.5 Fictitious Absorbers
9.6 Perfectly Matched Layers
9.7 Application of PML to Body-of-Revolution Problems
9.8 Summary
References
Chapter 10: Finite Element–Boundary Integral
Methods
10.1 Scattering by Two-Dimensional Cavity-Backed Apertures
10.2 Scattering by Two-Dimensional Cylindrical Structures
10.3 Scattering by Three-Dimensional Cavity-Backed Apertures
10.4 Radiation by Microstrip Patch Antennas in a Cavity
10.5 Scattering by General Three-Dimensional Bodies
10.6 Solution of the Finite Element–Boundary Integral System
10.7 Symmetric Finite Element–Boundary Integral Formulations
10.8 Summary
References
Chapter 11: Finite Element–Eigenfunction Expansion
Methods
11.1 Waveguide Port Boundary Conditions
11.2 Open-Region Scattering
11.3 Coupled Basis Functions: The Unimoment Method
11.4 Finite Element–Extended Boundary Condition Method
11.5 Summary
References
Chapter 12: Finite Element Analysis in the Time
Domain
12.1 Finite Element Formulation and Temporal Excitation
12.2 Time-Domain Discretization
12.3 Stability Analysis
12.4 Modeling of Dispersive Media
12.5 Truncation via Absorbing Boundary Conditions
12.6 Truncation via Perfectly Matched Layers
12.7 Truncation via Boundary Integral Equations
12.8 Time-Domain Waveguide Port Boundary Conditions
12.9 Hybrid Field–Circuit Analysis
12.10 Dual-Field Domain Decomposition and Element-Level
Methods
12.11 Discontinuous Galerkin Time-Domain Methods
12.12 Summary
References
Chapter 13: Finite Element Analysis of Periodic
Structures
13.1 Finite Element Formulation for a Unit Cell
13.2 Scattering by One-Dimensional Periodic Structures:
Frequency-Domain Analysis
13.3 Scattering by One-Dimensional Periodic Structures: Time-
Domain Analysis
13.4 Scattering by Two-Dimensional Periodic Structures:
Frequency-Domain Analysis
13.5 Scattering by Two-Dimensional Periodic Structures: Time-
Domain Analysis
13.6 Analysis of Angular Periodic Structures
13.7 Summary
References
Chapter 14: Domain Decomposition for Large-Scale
Analysis
14.1 Schwarz Methods
14.2 Schur Complement Methods
14.3 FETI–DP Method for Low-Frequency Problems
14.4 FETI–DP Method for High-Frequency Problems
14.5 Nonconformal FETI–DP Method Based on Cement
Elements
14.6 Application of Second-Order Transmission Conditions
14.7 Summary
References
Chapter 15: Solution of Finite Element Equations
15.1 Decomposition Methods
15.2 Conjugate Gradient Methods
15.3 Solution of Eigenvalue Problems
15.4 Fast Frequency-Sweep Computation
15.5 Summary
References
Appendix A: Basic Vector Identities and Integral
Theorems
A.1 Vector Identities
A.2 Integral Theorems
A.3 Integral Theorems on a Surface
A.4 Dyadic Integral Theorems
References
Appendix B: The Ritz Procedure for Complex-Valued
Problems
Appendix C: Green’s Functions
C.1 Scalar Green’s Functions
C.2 Dyadic Green’s Functions
References
Appendix D: Singular Integral Evaluation
References
Appendix E: Some Special Functions
E.1 Bessel Functions
E.2 Spherical Bessel Functions
E.3 Associated Legendre Polynomials
E.4 Mathieu Functions
References
Index
THE FINITE ELEMENT METHOD IN
ELECTROMAGNETICS