Course Description

 This course presents the application of the finite-difference time-domain technique for the full-wave analysis of time-depe ndent electromagnetic waves in complex media. Initially, an introduction of the solution of the time-dependent scalar wave equation using finite-difference techniques is presented. Issues of numerical dispersion and stability are derived and discussed. The Yee-algorithm is presented for the analysis of three-dimensional vector fields, and the numerical stability and dispersion of the algorithm are derived. This algorithm is then used for the analysis of 1) the interaction of time-dependent electromagnetic waves on printed microstrip circuits, 2) elec tromagnetic scattering by complex objects, and 3) for bioelectromagnetic applica tions.


Specific Course Outcomes

The following competencies should be imparted t o the students:

  1. an understanding of the solution of time-dependent partial differential equa tions using approximate finite differences
  2. an understanding of the development of explicit and implicit time-dependent schemes
  3. an understanding of the errors associated with discrete difference approxima tions
  4. an understanding of stability of a time-marching scheme and how to derive stability relationships from the discrete difference equations
  5. an understanding of the finite-difference time-domain method in 1, 2, and 3- dimensions
  6. the ability to develop a high-level computer codes (such as FORTRAN or C++) to perform the finite-difference time-domain solution of Maxwell's equations in 1, 2, and 3-dimensions
  7. an understanding of pseudo-differential absorbing boundary conditions and th eir performance and implementation
  8. an understanding of the perfectly matched layer technique as an absorbing bo undary and its performance and implementation
  9. an understanding of source conditions and discrete load conditions
  10. an understanding of network analysis and waveguide analysis using the FDTD m ethod
  11. an introduction to advanced FDTD methods, such as non-uniform gridding, subc ell modeling, and pseudo-spectral time-domain methods.