Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics

Book description


Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided.

Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing

Table of contents

  1. Introduction
    1. A Brief History of the FDTD Method
    2. Limitations of the FDTD Method
    3. Alternate Solution Methods
    4. FDTD Software
    5. Outline to the Remainder of the Text
    6. References (1/2)
    7. References (2/2)
  2. 1D FDTD Modeling of the Transmission Line Equations
    1. The Transmission Line Equations
    2. Finite Difference Approximations
    3. Explicit Time Update Solution
    4. Numerical Dispersion
    5. Stability
    6. Sources and Loads
    7. Problems
    8. References
  3. Yee Algorithm for Maxwell's Equations
    1. Maxwell's Equations
    2. The Yee-Algorithm
    3. Gauss's Laws
    4. Finite Integration Technique CH3.BIB5
    5. Stability
    6. Numerical Dispersion and Group Delay (1/2)
    7. Numerical Dispersion and Group Delay (2/2)
    8. Material and Boundaries (1/2)
    9. Material and Boundaries (2/2)
    10. Lossy Media
    11. Dispersive Media
    12. Non-Uniform Gridding
    13. Problems
    14. References
  4. Source Excitations
    1. Introduction
    2. Source Signatures
      1. The Gaussian Pulse
      2. The Blackman-Harris Window
      3. The Differentiated Pulse
      4. The Modulated Pulse
      5. Sinusoidal Steady-State
    3. Current Source Excitations
      1. Volume Current Density
      2. Surface Current Density
    4. Lumped Circuit Source Excitations
      1. Discrete Voltage Source
      2. Discrete Thévenin Source
      3. Lumped Loads
    5. Plane Wave Excitation
      1. The Total-Field Scattered Field Formulation
      2. General Description of a Uniform Plane Wave
      3. Computing the Discrete Incident Field Vector
      4. Numerical Dispersion
      5. Inhomogeneous Media
    6. Problems
    7. References
  5. Absorbing Boundary Conditions
    1. Introduction
    2. The First-Order Sommerfeld ABC
    3. The Higdon ABC
    4. The Betz-Mittra ABC
    5. Problems
    6. References
  6. The Perfectly Matched Layer (PML) Absorbing Medium
    1. Introduction
    2. The Anisotropic PML
    3. Stretched Coordinate Form of the PML
    4. PML Reflection Error
      1. The Ideal PML
      2. PML Parameter Scaling
      3. Reflection Error
      4. The Complex Frequency Shifted (CFS) PML
    5. Implementing the CFS-PML in the FDTD Method
      1. An ADE form of the CFS-PML
      2. Yee-Algorithm for the CFS-PML
      3. Example of the CFS-PML
    6. Problems
    7. References
  7. Subcell Modeling
    1. Introduction
    2. Thin Wires
      1. The Basic Thin-Wire Subcell Model
      2. Curvature Correction
      3. Modeling the End-Cap
      4. Delta-Gap Source
      5. A Transmission Line Feed
    3. Conformal FDTD Methods for Conducting boundaries
      1. Dey-Mittra (DM) Conformal FDTD Method for Conducting Boundaries
      2. Yu-Mittra (YM) Conformal FDTD Method for Conducting Boundaries
      3. BCK Conformal FDTD Method for Conducting Boundaries
    4. Narrow Slots
    5. Conformal FDTD Methods for Material Boundaries
    6. Thin Material Sheets
    7. Problems
    8. References
  8. Post Processing
    1. Introduction
    2. Network Analysis
      1. Discrete Network Port Parameterization
      2. Admittance-Parameters
      3. Scattering Parameters (1/2)
      4. Scattering Parameters (2/2)
    3. Near-Field to Far-Field (NF-FF) Transformations
      1. Huygen Surface
      2. Frequency Domain NF-FF Transform
      3. Antenna Gain
      4. Scattering Cross Section
    4. Problems
    5. References
  9. MATLAB Implementation of the 1D FDTD Model of a Uniform Transmission Line
    1. Translating the Discrete FDTD Equations to a High-Level Programming Language
  10. Efficient Implementation of the 3D FDTD Algorithm
    1. Top-Level Design
    2. Array Indexing the 3D-FDTD
    3. Lossy and Inhomogeneous Media
    4. Implementing the CFS-CPML (1/3)
    5. Implementing the CFS-CPML (2/3)
    6. Implementing the CFS-CPML (3/3)
    7. Edge Length Normalization
    8. General FDTD Update Equations
  11. Author's Biography
  12. Index

Product information

  • Title: Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics
  • Author(s): Stephen Gedney
  • Release date: January 2011
  • Publisher(s): Morgan & Claypool Publishers
  • ISBN: 9781608455232