# The Finite Element Method in Electromagnetics, 3ed

ISBN: 9788126574308

876 pages

Exclusively distributed by I.K. International

## Description

As one of the most powerful simulation techniques for solving engineering boundary-value problems, the finite element method has been widely used for analysis of electromagnetic problems in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electrromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space explorations. The Third Edition of this essential and popular text teaches the finite element method for electromagnetic analysis in a systematic, comprehensive manner. It offers engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems.

Preface

Preface to the First Edition

Preface to the Second Edition

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 Huygen's Principle

1.9 Radar Cross Sections

1.10 Summary

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

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

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

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

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 Anisotrpic Medium

6.5 Variational Principle for Resistive Sheets

6.6 Concluding Remarks

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

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

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 Conditons

9.4 Adaptive Absorbing Boundary Conditons

9.5 Fictitious Absorbers

9.6 Perfectly Matched Layers

9.7 Application of PML to Body-of-Revolutions Problems

9.8 Summary

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

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

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 Wqaveguide 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

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-Dimensonal Periodic Structures: Time-Domain Analysis

13.6 Analysis of Angular Periodic Strctures

13.7 Summary

14 Domain Decompsition 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 Noncomformal FETI-DP Method Based on Cement Elements

14.6 Application of Second-Order Transmission Conditions

14.7 Summary

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

Appendix A: Basic Vector Identities and Integral Theorems

Appendix B: The Ritz Procedure for Complex-Valued Problems

Appendix C: Green's Functions

Appendix D: Singular Integral Evaluation

Appendix E: Some Special Functions

Index