Computational Electromagnetics with MATLAB® – electromagnetics.abdphysics.org

Fundamental Concepts
- Introduction
  - Analytical methods (exact solutions)
    - Separation of variables
    - Series expansion
    - Conformal mapping
    - Integral solutions, for example, Laplace and Fourier transforms
    - Perturbation methods
  - Numerical methods (approximate solutions)
    - Finite difference method
    - Method of weighted residuals
    - Moment method
    - Finite element method
    - Transmission-line modeling
    - Monte Carlo method
    - Method of lines
- Review of EM Theory
  - eqn(1.1)
  - eqn(1.2)
    - Electrostatic Fields
      - eqn(1.3)
      - eqn(1.4)
      - eqn(1.5) to eqn(1.11a-b)
    - Magnetostatic Fields
      - eqn(1.12) to eqn(1.21)
    - Time-Varying Fields
      - eqn(1.22a) to eqn(1.24d)
      - eqn(1.25) and eqn(1.26)
    - Boundary Conditions
      - eqn(1.27a) to eqn(1.27d)
    - Wave Equations**
      - eqn(1.28) to eqn(1.34)
      - Time-Varying Potentials**
        
        eqn(1.35) to eqn(1.45)
      - Time-Harmonic Fields
        
        eqn(1.46) to eqn(1.54)
        
        Example 1.1
        
        eqn(1.55) to eqn(1.57)
        
        Example 1.2**
        
        Example 1.3
      - Classification of EM Problems
        
        Classification of Solution Regions
        
        Classification of Differential Equations**
        
        eqn(1.58) to eqn(1.68)
        
        Classification of Boundary Conditions
        
        eqn(1.70) to eqn(1.76)
        
        Example 1.4**
        
        Some Important Theorems
        
        Superposition Principle
        
        Uniqueness Theorem
Analytical Methods
- Introduction
- Separation of Variables**
  - eqn(2.1) to eqn(2.6a-b)
- Separation of Variables in Rectangular Coordinates
  - Laplace’s Equation
    - eqn(2.7) to eqn(2.16); eqn(2.8a-d); eqn(2.13a-d)
    - Case 1
      - eqn(2.14) and eqn(2.15)
    - Case 2
      - eqn(2.16) to eqn(2.18)
    - Case 3
      - eqn(2.19) to eqn(2.30); eqn(2.20a-b); eqn(2.31a-b)
  - Wave Equation
    - eqn(2.5b)
    - eqn(2.32) to eqn(2.36)
    - eqn(2.37a-f)
    - eqn(2.38) to eqn(2.41)
    - Example 2.1
      - eqn(2.42) to eqn(2.56)
    - Example 2.2
      - eqn(2.57) to eqn(2.65)
- Separation of Variables in Cylindrical Coordinates
  - eqn(2.66) to eqn(2.70); eqn(2.71a-b)
    - Wave Equation
- Separation of Variables in Spherical Coordinates
  - Laplace’s Equation
  - Wave Equation
- Some Useful Orthogonal Functions
- Series Expansion
  - Poisson’s Equation in a Cube
  - Poisson’s Equation in a Cylinder
  - Strip Transmission Line
- Practical Applications
  - Scattering by Dielectric Sphere
  - Scattering Cross Sections
- Attenuation due to Raindrops
Finite Difference Methods
- Introduction
- Finite Difference Schemes
- Finite Differencing of Parabolic PDEs
- Finite Differencing of Hyperbolic PDEs
- Finite Differencing of Elliptic PDEs
  - Band Matrix Method
  - Iterative Methods
- Accuracy and Stability of FD Solutions
- Practical Applications I: Guided Structures
  - Transmission Lines
  - Waveguides
- Practical Applications II: Wave Scattering (FDTD)
  - Yee’s Finite Difference Algorithm
  - Accuracy and Stability
  - Lattice Truncation Conditions
  - Initial Fields
  - Programming Aspects
- Absorbing Boundary Conditions for FDTD
- Advanced Applications of FDTD
  - Periodic Structures
  - Antennas
  - PSTD Techniques
  - Photonics
  - Metamaterials
  - MEEP
- Finite Differencing for Nonrectangular Systems
  - Cylindrical Coordinates
  - Spherical Coordinates
- Numerical Integration
  - Euler’s Rule
  - Trapezoidal Rule
  - Simpson’s Rule
  - Newton–Cotes Rules
  - Gaussian Rules
    - Multiple Integration
Variational Methods
Moment Methods
Finite Element Method
Transmission-Line-Matrix Method
Monte Carlo Methods
Method of Lines
- Introduction
- Solution of Laplace’s Equation
  - Rectangular Coordinates
  - Cylindrical Coordinates
- Solution of Wave Equation
  - Planar Microstrip Structures
  - Cylindrical Microstrip Structures
- Time-Domain Solution
- Concluding Remarks
Appendix A: Vector Relations
Appendix B: Programming in MATLAB
Appendix C: Solution of Simultaneous Equations
Appendix D: Computational Electromagnetic Codes