Title Page
Contents
Preface
1. Introduction
1.1
Scientific Computation, Numerical Analysis,and Engineering
1.2
Computational Electromagnetics
1.3
Accuracy and Efficiency
1.4 Programming Languages
1.5
Writing and Debugging Numerical Codes
1.6
Overview of Electromagnetic Field Theory
1.7 References
1.8 Problems
2. Basic Numerical Tasks
2.1 Introduction to MATLAB Programming
2.2 Numerical Differentiation
2.3 Numerical Integration
2.4 Interpolation
2.5 Curve Fitting
2.6 Newton's Method
2.7 References
2.8 Problems
3. Finite Difference Methods
3.1 Basic Components of Finite Difference Solvers
3.2
Wave Equation: 1-D FDTD Method
3.3
Laplace’s Equation: 2-D Finite Difference
Method
3.4
2-D FDTD Method
3.5
3-D FDTD Method
3.6
Perfectly Matched Layer
3.7 References
3.8 Problems
4. Numerical Integration
4.1 Types of Integration Rules
4.2 Classic Polynomial Rules
4.3 Gaussian Quadrature
4.4 Nonclassical Gaussian Quadrature Rules
4.5 Implementation
4.6 Other Methods for Singular Integrands
4.7 Multidimensional Integrals
4.8 MATLAB's Built-in Numerical Integration Functions
4.9 References
4.10 Problems
5. Integral Equations and the Method of Moments
5.1 Integral Operators
5.2
Integral Equations in Electromagnetics
5.3
Method of Weighted Residuals
5.4
Method of Moments for the TM-EFIE
5.5 Accuracy and Efficiency of the Method of Moments
5.6
Dielectric Structures
5.7
2.5-Dimensional Methods
5.8
3-D Electric Field Integral Equation
5.9 References
5.10 Problems
6. Solving Linear Systems
6.1 Linear Operators
6.2
Direct and Iterative Solution Methods
6.3
LU Decomposition
6.4 Iterative Methods
6.5
Krylov Subspace Iterations
6.6
Multiscale Problems
6.7 References
6.8 Problems
7. Variational Methods and the Rayleigh-Ritz Procedure
7.1
Operators and Functionals
7.2
Variational Principles
7.3 Rayleigh-Ritz Method
7.4 References
7.5 Problems
8. Finite Element Method
8.1 Overview of the Finite Element Method
8.2
Laplace’s Equation: 1-D FEM
8.3
Boundary Conditions for FEM
8.4
Helmholtz Equation: 2-D FEM
8.5
Finite Element Method--Boundary ElementMethod (FEM--BEM)
8.6
Numerical Results
8.7 References
8.8 Problems
9. Optimization Methods
9.1 Introduction
9.2 Classes of Optimization Methods
9.3 One-Dimensional Optimization
9.4 Nelder-Mead Simplex Method
9.5 References
9.6 Problems
10. Inverse Problems
10.1 Introduction
10.2 Types of Inverse Problems
10.3
Ill-Posed Problems
10.4 Born Approximation Methods
10.5
Regularized Sampling
10.6 References
10.7 Problems
Index
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